 A Reflection by Kate Chopin. Some people are born with a vital and responsive energy. It not only enables them to keep abreast of the times, it qualifies them to furnish in their own personality a good bit of the motive power to the mad pace. They are fortunate beings. They do not need to apprehend the significance of things. They do not grow weary nor misstep, nor do they fall out of rank, and sink by the wayside to be left contemplating the moving procession. Ah, the moving procession that has left me by the roadside! Its fantastic colors are more brilliant and beautiful than the sun on the undulating waters. What matters if souls and bodies are failing, beneath the feet of the ever-pressing multitude? It moves with the majestic rhythm of the spheres. Its discordant clashes sweep upward in one harmonious tone that blends with the music of other worlds, to complete God's orchestra. It is greater than the stars, that moving procession of human energy, greater than the palpitating earth, and the things growing thereon. Oh, I could weep at being left by the wayside, left with the grass and the clouds, and a few dumb animals. True, I feel at home in the society of these symbols of life's immutability. In the procession I should feel the crushing feet, the clashing discords, the ruthless hands, and stifling breath. I could not hear the rhythm of the march. Salve ye dumb hearts, let us be still, and wait by the roadside. End of a Reflection by Kate Chopin Recorded by April 6,090, California, United States of America Remarks of the President in presenting to Madame Curie a gift of radium from the American people by President Warren G. Harding. Madame Curie, it is within a special satisfaction that I perform the pleasant duty which has been assigned to me today. On behalf of the American nation, I greet and welcome you to our country in which you will everywhere find the most cordial possible reception. We welcome you as an adopted daughter of France, our earliest supporter among the great nations. We greet you as a native-born daughter of Poland, newest as it is also among the oldest of the great nations, and always bound by ties of closest sympathy to our own republic. In you we see the representative of Poland restored and reinstated to its rightful place, of France valiantly maintained in the highest state which has ever been its right. As a nation whose womanhood has been exalted to fullest participation in citizenship, we are proud to honor in you a woman whose work has earned universal acclaim and attested woman's equality in every intellectual and spiritual activity. We greet you as foremost among scientists in the age of science as leader among women in the generation which sees woman come tardily into her own. We greet you as an exemplar of liberty's victories in the generation wherein liberty has won her crown of glory. In doing honor to you we testify anew our pride in the ancient friendships which have bound us to both the country of your adoption and that of your nativity. We exalt anew our pride that we have stood with them in the struggle for civilization and have touched elbows with them in the march of progress. It has been your fortune, Madame Curie, to accomplish an immortal work for humanity. We are not without understanding of the trials and sacrifices which have been the price of your achievement. We know something of the fervid purpose and deep devotion which inspired you. We bring to you the meat of honor which is due to preeminence in science, scholarship, research, and humanitarianism. But with it all we bring something more. We lay at your feet the testimony of that love of which all the generations of men have been wanted to bestow upon the noble woman, the unselfish wife, the devoted mother. If indeed these simpler and commoner relations of life could not keep you from great attainments in the realms of science and intellect, it is also true that the zeal, ambition, and unswerving purpose of a lofty career could not borrow you from splendidly doing all the plain but worthy tasks which fall to every woman's lot. A number of years ago a reader of one of your earlier works on radioactive substances noted the observation that there was much divergence of opinion as to whether the energy of radioactive substances is created within those substances themselves or is gathered to them from outside sources and then diffused from them. The question suggested an answer which is doubtless hopelessly unscientific. I have liked to believe in an analogy between the spiritual and the physical world. I have been very sure that that which I may call the radioactive soul, or spirit, or intellect, call it what you choose, must first gather to itself from its surroundings the power that it afterwards radiates in beneficence to those near it. I believe it is the sum of many inspirations born in on great souls which enables them to warm, to scintillate, to radiate, to illumine and serve those about them. I am so sure of this explanation for the radioactive personality that I feel somehow a conviction that science will one day establish a like explanation for radioactivity among inanimate substances. Perhaps in my innocence of science I am eerily rushing in where scientists fear to tread, but I am trying to express to you my conviction that the great things achieved by great minds would never have been wrought without the inspiration of an appealing need for them. That appeal comes as inspiration to successful effort, and success in turn enables the outgiving of benefits to millions whose only contribution has been the power of their united appeal. Let me press the analogy a little farther. The world today is appealing to its statesmen, its sociologists, its humanitarians, and its religious leaders for solution of appalling problems. I want to hope that the power and universality of that appeal will inspire strong, devout, consecrated men and women to seek out the solution and in the light of their wisdom to carry it to all mankind. I have faith to believe that precisely that will happen, and in your own career of fine achievement I find heartening justification for my faith. In testimony of the affection of the American people, of their confidence in your scientific work, and of their earnest wish that your genius and energy may receive all encouragement to carry forward your efforts for the advance of science and conquest of disease, I have been commissioned to present to you this little file of radium. To you we owe our knowledge and possession of it, and so to you we give it, confident that in your possession it will be the means further to unveil the fascinating secrets of nature to widen the field of useful knowledge to alleviate suffering among the children of man. Take it to use as your wisdom shall direct, and your purpose of service shall incline you. Be sure that we esteem it but a small earnest of the sentiments for which it stands. It betokens the affection of one great people for another. It will remind you of the love of a grateful people for yourself, and it will testify in the useful work to which you will devote it, the reverence of mankind for one of its foremost benefactors and most beloved of women. End of presenting to Madam Curie a gift of radium from the American people. By President Warren G. Harding, read by Anita Sloma Martinez. Chapter 3 of Lectures on 10 British Mathematicians of the 19th Century by Alexander McFarlane. This is a LibriVox recording. All LibriVox recordings are in the public domain. For more information or to volunteer, please visit LibriVox.org. Chapter 3 Sir William Rowan Hamilton, 1805 to 1865. This lecture was delivered April 16, 1901. William Rowan Hamilton was born in Dublin, Ireland on the 3rd of August, 1805. His father, Archibald Hamilton, was a solicitor in the city of Dublin. His mother, Sarah Hutton, belonged to an intellectual family. But she did not live to exercise much influence on the education of her son. There has been some dispute as to how far Ireland can claim Hamilton. Professor Tate of Edinburgh, in the Encyclopedia Britannica, claims him as a Scotsman. While his biographer, the Reverend Charles Graves, claims him as essentially Irish. The facts appear to be as follows. His father's mother was a Scotch woman. His father's father was a citizen of Dublin. But the name Hamilton points to Scottish origin. And Hamilton himself said that his family claimed to have come over from Scotland in the time of James I. Hamilton always considered himself an Irishman, and as Burns very early had an ambition to achieve something for the renown of Scotland. So Hamilton, in his early years, had a powerful ambition to do something for the renown of Ireland. In later life he used to say that at the beginning of the century people read French mathematics, but that at the end of it they would be reading Irish mathematics. Hamilton, when three years of age, was placed in the Church of Hisuncle, the Reverend James Hamilton, who was the Curate of Trim, a country town about 20 miles from Dublin, and who was also the master of the Church of England school. From Hisuncle he received all his primary and secondary education, and also instruction in the Oriental languages. As a child, Hamilton was a prodigy. At three years of age, he was a superior reader of English, and considerably advanced in arithmetic. At four, a good geographer. At five, able to read and translate Latin, Greek and Hebrew, and like to recite Dryden, Collins, Milton and Homer. At eight, a reader of Italian and French, and giving bent to his feelings in extemporized Latin. At ten, a student of Arabic and Sanskrit, when 12 years old he met Zeta Colburn, the American calculated boy, and engaged with him in trials of arithmetical skill, in which trials Hamilton came off with honor. Also Colburn was generally the victor. His encounters gave Hamilton a decided taste for arithmetical computation, and for many years afterwards he loved to perform long operations in arithmetic in his mind, extracting the square and cube root, and solving problems that related to that properties of numbers. When 13, he received his initiation into algebra from Clairold's algebra in the French, and he made an epitome, which he ambitiously entitled, A Compendious Treatise on Algebra, by William Hamilton. When Hamilton was 14 years old, his father died, and left his children as slenderly provided for. Henceforth, as the elder brother of three sisters, Hamilton had to act as a man. This year he addressed a letter of welcome, written in the Persian language, to the Persian ambassador, then on a visit to Dublin, and he met again Sarah Colburn. In the interval, Sarah had attended one of the great public schools of England. Hamilton had been in a country school in Ireland, and he was now able to make a successful investigation of the methods by which Sarah made his writing calculations. When 16, Hamilton studied the differential calculus by the help of a French textbook, and began the study of the Mechanique Celeste of Laplace, and he was able at the beginning of this study to detect a flaw in the reasoning by which Laplace demonstrates the theorem of the parallelogram forces. This criticism brought him to the notice of Dr Brinkley, who was then the professor of astronomy in the University of Dublin, and resided at Dunkirk, about five miles from the centre of the city. He also began an investigation for himself of equations which represent systems of straight lines in a plane, and in so doing hit upon ideas which he afterwards developed into his first mathematical memoir to the Royal Irish Academy. Dr Brinkley said to have remarked of him at this time, This young man, I do not say will be, but is, the first mathematician of his age. At the age of 18 Hamilton entered Trinity College, Dublin, the University of Dublin, founded by Queen Elizabeth, and deferring from the universities of Oxford and Cambridge in having only one college, and like Oxford, which has always given prominence to classics, and Cambridge, which has always given prominence to mathematics, Dublin at that time gave equal prominence to classics and to mathematics. In his first year, Hamilton won the very rare honour of Optime at his examination in Homer. In the old universities, Marx used to be, and in some cases still are, published, descending not in percentages, but by means of the scale of Latin adjectives, Optime, Waldevene, Bene, Satis, Mediocritor, Wix, Medi, Nun, Optime means past with the very highest distinction. Wix means past, but with great difficulty. This scale is still in use in the medical examinations of the University of Edinburgh. Before entering college, Hamilton had been accustomed to translate Homer into blank verse, comparing his result with the translations of Pope and Copper, and he had already produced some original poems. In this, his first year he wrote a poem on college ambition, which is a fair respecimen of his poetical attainments. Oh, ambition has its hour, of deep and a spirit-steering power, not in the tented field alone, nor pure and girded, coward and throne, nor the intrigues of busy life, but ardent boyhoods generous strive. While yet the enthusiast spirit turns, where the light of glory burns, things not how transient is the blaze, but longs to barter life for praise. Look round arena and just pie, pallid cheek and faded eye. Among the bands of rivals few, keep their native healthy hue. Night and thought have stolen away their once elastic spirits play. A few short hours and all is over. Some shall win, one dream of more, some from the place of contest go. Again defeated, sad and slow. What shall reward the conqueror then, for all his toil, for all his pain, for every midnight throb that stow, so often over his fevered soul? Is it the plodding's lout, or the wandering gazes of the crowd, disappointed envy's shame, or hollow boys of fickle fame? This may extort the sudden smile, may swell the heart a little while, but they leave no joy behind, where ethno-pure transport over the mind, nor will the thought of selfish gladness expand the brow of secret sadness. Yet if ambition has its hour, of deep and spirit-steering power, some bright rewards are all its own, and bless its votaries alone. The anxious friends approving eye, generous rivals sympathy, and at best and sweetest price, given by silent beauty's eyes. These are transports, true and strong, deeply felt, remembered long, time and sorrow passing over and their their memory but the more. The silent beauty was not an abstraction, but a young lady, whose brothers were fellow students of Trinity College. This led to much a fusion of poetry, but unfortunately, while Hamilton was writing poetry about her, another young man was talking prose to her, with the result that Hamilton experienced a disappointment. An account of his self-consciousness, inseparable probably from his genius, he felt a disappointment keenly. He was then known to the professor of astronomy, and walking from the college to the observatory along the Royal Canal, he was actually tempted to terminate his life in the water. In his second year, he formed a plan of reading as so as to compete for the highest honors both in classics and in mathematics. At graduation, two gold medals were awarded, two one for distinction in classics, the other for distinction in mathematics. Hamilton aimed at carrying off both. In his junior year, he received an Optime in Mathematical Physics, and, as the winner of two Optimus, the one in classics and the other in mathematics, he immediately became a celebrity in the intellectual circle of Dublin. In his senior year, he presented to the Royal Irish Academy a memoir embodying his research on systems of lines. He now called it a theory of systems of race, and it was printed in the transactions. About this time, Dr. Bringley was appointed to the bishopric of Cloe, and in consequence, resigned the professorship of astronomy. In the United Kingdom, it is customary, when a post becomes vacant, for aspirants to lodge a formal application with a pointing board, and to supplement their own application by testimonial letters from competent authorities. In the present case, quite a number of candidates appear, among them Airy, who afterwards became Astronomer Royal of England, and several fellows of Trinity College, Dublin. Hamilton did not become a formal candidate, but he was invited to apply, with the result that he received the appointment while still an undergraduate, and not 22 years of age. Thus, was his undergraduate career, signalized much more than by the carrying off of the two gold medals. Before assuming the duties of his chair, he made a tour through England and Scotland, and met for the first time the poet Wordsworth at his home at Ridal Mount, in Cumberland. They had a midnight walk, oscillating backwards and forwards between Ridal and Ambleside, absorbed in converse on high themes, and finding it almost impossible to part. Wordsworth afterwards said that Coleridge and Hamilton were the two most wonderful men, taking all their endowments together that he had ever met. In October, 1827, he came to reside at a place which was destined to be the scene of his scientific labours. I had the pleasure of visiting it last summer, as the guest of his successor. The observatory is situated on the top of a hill, dancing about five miles from Dublin. The house adjoins the observatory, to the east is an extensive lawn, to the west a garden with stone wall and shaded walks, to the south a terraced field. At the foot of the hill is the Royal Canal, to the south-east the city of Dublin, while the view is bounded by the sea and the Dublin and Wicklow mountains, a fine home for a poet or a philosopher or a mathematician, and in Hamilton all three were combined. Settled at the observatory, he started out diligently as an observer, but he found it difficult to stand the low temperatures incident to the work. He never attained the skill as an observer, and unfortunately he depended on a very poor assistant, himself a brilliant computer with a good observer for assistant, the work of the observatory ought to have flourished. One of the first distinguished visitors at the observatory was the poet Wordsworth, in commemoration of which one of the shaded walks in the garden was named Wordsworth Walk. Wordsworth advised him to concentrate his powers on science, and, not long after, wrote him as follows. You send me showers of verses, which I receive with much pleasure as do we all, yet we have fears that this employment misadduce you from the path of science, which you seem destined to tread, with so much honor to yourself and profit to others. Again and again I must repeat that a composition of verse is infinitely more of an art than men are prepared to believe. An absolute success in it depends upon innumerable munochai, which it grieves me you should stoop to acquire a knowledge of. Again, I do venture to submit to your consideration, whether the poetical parts of your nature would not find a field more favorable to their exercise in the regions of prose. Not because those regions are humbler, but because they may be gracefully and profitably trod, with footsteps less careful, and in measure less elaborate. Hamilton possessed the poetic imagination, what he was deficient in, was the technique of the poet. The imagination of the poet is akin to the imagination of the mathematician, both extract ideal from a mass of circumstances. In this connection, the Morgan wrote, The moving power of mathematical invention is not reasoning, but imagination. We no longer apply the homely term maker in literal translation of poet, but discoverers of all kinds, whatever may be their lines, are makers, or as we now say, have the creative genius. Hamilton spoke of the mechanical analytic of Lagrange as a scientific poem. Hamilton himself was styled the Irish Lagrange. Engineers venerate Rankine, electricians venerate Maxwell, both were scientific discoverers and likewise poets, that is Amateur poets. The proximate cause of the shower of verses was that Hamilton had fallen in love for the second time. The young lady was Miss the Beer, the other of an accomplished Irish baronet, and who like Tennyson's Lady Clara Beer the Beer could look back on a long and illustrious descent. Hamilton had a pupil in Lord Adard, the eldest son of the Earl of Dunraven, and it was while visiting Adard Minor that he was introduced to the Beer family, who lived nearby at the Kuroch Chase. His suit was encouraged by the countess of Dunraven, and it was favorably received by both father and mother. He had written many sonnets of which Elaine the Beer was the inspiration. He had discussed with her astronomy, poetry and philosophy, and was on the eve of proposing, when he gave up, because the young lady incidentally said to him that she could not live happily anywhere but at Cora. His action shows the working of a too self-conscious mind, proud of his own intellectual achievements, and too much odd by her long descent. So he failed for the second time, but both of these ladies were friends of his to the last. At the age of 27 he contributed to the Irish academy a supplementary paper on his theory of systems of race, in which he predicted the phenomenon of the conical refraction, namely that under certain conditions a single ray incident on a biaxial crystal would be broken up into a cone of rays, and likewise that under certain conditions a single emerging ray would appear as a cone of rays. The prediction was made by Hamilton on October 22nd, and it was experimentally verified by his colleague Professor Lloyd on December the 14th. It is not experiment alone or mathematical reasoning alone, which has built up the splendid temple of physical science, but the two working together, and of this we have notable exemplification in the discovery of conical refraction. Twice Hamilton chose well, but failed. Now he made another choice and succeeded. The lady was a Miss Bailey, who visited at the home of her sister near Dancing Hill. The lady had serious misgivings about the state of her health, but the marriage took place. The kind of wife which Hamilton needed was one who could govern him and efficiently supervise all domestic mothers, but the wife he chose was, from weakness of body and mind, incapable of doing it. As a consequence, Hamilton worked for the rest of his life under domestic difficulties of no ordinary kind. At the age of 28 he made a notable addition to the theory of dynamics by extending to it the idea of a characteristic function, which he had previously applied with success to the science of optics in his theory of systems of race. It was contributed to the Royal Society of London and printed in their philosophical transactions. The Royal Society of London is the great scientific society of England, founded in the reign of Charles II, and of which Newton was one of the early presidents. Hamilton was invited to become a fellow, but did not accept, as he could not afford expense. At the age of 29 he read a paper before the Royal Irish Academy, which set forth the result of a long meditation and investigation on the nature of algebra as a science. The paper is entitled Algebra as the Science of Pure Time. The main idea is that as geometry considered as a science is founded upon the pure intuition of a space, so algebra as a science is founded upon the pure intuition of time. He was never satisfied with Peacock's theory of algebra as systems of signs and their combinations, nor with the Morgan's improvement of it. He demanded a more real foundation. In reading Kant's critique of pure reason, he was struck by the following passage. Time and space are two sources of knowledge, from which various a priori synthetical cognitions can be derived. Of this, pure mathematics gives a splendid example in the case of our cognitions of a space and its various relations, as they are both pure forms of sensuous intuition. They render synthetical propositions a priori possible. Thus, according to Kant, space and time are forms of the intellect, and Hamilton reasoned that as geometry is the science of the former, so algebra must be the science of the latter. When algebra is based on any unidimensional subject, such as time or a straight line, a difficulty arises in explaining the roots of a quadratic equation when they are imaginary. To get over this difficulty, Hamilton invented a theory of algebraic couplets which has proved a conundrum in the mathematical world. Some 20 years ago, there nourished in Edinburgh a mathematician named Sang who had computed the most elaborate tables of logarithms in existence, which still exists in manuscript. On reading the theory in question, he first judged that either Hamilton was crazy or else that he, Sang, was crazy, but eventually reached the more comforting alternative. On the other hand, Professor Tate believes in its soundness and endeavors to bring it down to the ordinary comprehension. We have seen that the British Association for the Advancement of Science was founded in 1831 and that its first meeting was in the ancient city of York. It was a policy of the founders, not to meet in London, but in the provincial cities, so that thereby greater interest in the advance of science might be produced over the whole land. The cities chosen for the place of meeting in the following years were the university towns, Oxford, Cambridge, Edinburgh, Dublin. Hamilton was the only representative of Ireland present at the Oxford meeting, and at the Oxford, Cambridge, and Edinburgh meetings, he not only contributed scientific papers, but he acquired renown as a scientific orator. In the case of the Dublin meeting, he was chief organizer beforehand and chief orator when it met. The week of science was closed by a grand dinner, given in the library of Trinity College, and an incident took place, which is thus described by an American scientist. We assembled in the imposing hall of Trinity Library, 280 feet long at 6 o'clock. When the company was principally assembled, I observed a little stir near the place where I stood, which nobody could explain, and which in fact was not comprehended by more than two or three persons present. In a moment, however, I perceived myself standing near the Lord Lieutenant and his suit, in front of whom a space had been cleared, and by whom was Professor Hamilton looking very much embarrassed. The Lord Lieutenant then called him by name, and he stepped into the vacant space. I am, said his Excellency, about to exercise a prerogative of royalty, and it gives me great pleasure to do it on this splendid public occasion, which has brought together so many distinguished men from all parts of the empire, and from all parts even of the world where science is held in honor. But in exercising it, Professor Hamilton, I do not confer a distinction. I but said the royal, and therefore the national mark on a distinction already acquired by Georgianus and Labels. He went on in this way for three or four minutes, his voice very fine, rich and full, his manners as grateful and dignified as possible, and his language and allusions appropriate and combined into very ample flowing sentences. Then, receiving the state sword from one of his attendants, he said, kneel down, Professor Hamilton, and laying the blade gracefully and gently first on one shoulder, and then on the other, he said, rise up, Sir William Rowan Hamilton. The night rose, and the Lord Lieutenant went up, and with an appearance of great tact in his manner, shook hands with him. No reply was made. The whole scene was imposing, rendered so, partly by the ceremony itself, but more by the place in which it passed, by the body of very distinguished men who were assembled there, and especially by the extraordinarily dignified and beautiful manner in which it was performed by the Lord Lieutenant. The effect at the time was great, and the general impression was that, as the honor was certainly merited by him who received it, so the words by which it was conferred were so graceful and appropriate that they constituted a distinction by themselves, greater than the distinction of knighthood. I was afterwards told that this was the first instance in which why a person had been knighted by a Lord Lieutenant, either for scientific or literary merit. Two years after, another great honor came to Hamilton, the presidency of the Royal Irish Academy. While holding this office in the year 1843, when 38 years old, he made the discovery which will ever be considered his highest title to fame. The story of the discovery is told by Hamilton himself in a letter to his son. On the 16th day of October, which happened to be a Monday, and council day of the Royal Irish Academy, I was walking in to attend and preside, and your mother was walking with me along the Royal Canal, to which she had perhaps driven. And although she talked with me now and then, yet an undercurrent of thought was going on in my mind, which gave at last a result, whereof it is not too much to say that I felt at once the importance. An electric circuit seemed to close, and a spark flashed forth, the herald, as I foresaw immediately, of many long years to come of definitely directed thought and work. By myself, if spared, I know tall events on the part of others, if I should even be allowed to live long enough distinctly to communicate the discovery. Nor could I resist the impulse, unphilosophical as it may have been, to cut with a knife on a stone of Brohan Bridge, as we pasted the fundamental formula with the symbols I, J, K, namely, I squared equals J squared equals K squared equals I, J, K equals negative 1, which contains the solution of the problem, but of course as an inscription has long since moldered away, a more durable notice remains, however, in the council book of the academy for that day, which records the fact that I then asked for and obtained leave to read a paper on quaternions at the first general meeting of the session, which reading took place accordingly on Monday, the 13th of November following. Last summer, Professor Jolie and I took the walk here described. We started from the observatory, walked down the terraced field, then along the path by the site of the Royal Canal towards Dublin, until we came to the second bridge, spanning the canal. The path of the course goes under the bridge, and the inner side of the bridge presents a very convenient surface for an inscription. I have seen this incident quoted as an example of how a genius strikes on a discovery, all of a sudden. Not doubt a problem was solved then and there, but the problem had engaged Hamilton's thoughts and researches for 15 years. It is rather an illustration of how genius is patience or a faculty for the infinite labour. What was Hamilton struggling to do all these years? To emerge from flatland into space, in other words, algebra had been extended so as to apply two lines in a plane, but no one had been able to extend it so as to apply two lines in a space. The greatness of the feat is made evident by the fact that most analysts are still crawling in flatland. The same year in which he discovered quaternions, the government granted him a pension of 200 pounds per annum for life on account of his scientific work. We have seen how Hamilton gained two optimists, one in classics, the other in physics, the highest possible distinction in his college course, how he was appointed professor of astronomy while getting undergraduate, how he was a scientific chief in the British Association at 27, how he was knighted for his scientific achievements at 30, how he was appointed president of the Royal Irish Academy at 32, how he discovered quaternions and received a government pension at 38. Can you imagine that this brilliant and successful genius would fall a victim to intemperance? About this time, at the dinner of a scientific society in Dublin, he lost control of himself and was so mortified that, on the advice of friends, he resolved to abstain totally, this resolution he kept for two years. When happening to be a member of a scientific party at the castle of Lord Rose and a material astronomer, then the professor of the largest telescope in existence, he was taunted for sticking to water, particularly by Harry, the Greenwich astronomer. He broke his good resolution and from that time forward, the craving for alcoholic stimulants clung to him. How could Hamilton, with all his noble aspirations, fall into such a vice? The explanation lay in the wonder of order which reigned in his home. He had no regular times for his meals. Frequently had no regular meals at all, but resorted to the sideboard when hunger compelled him. What more natural in such condition that he should refresh himself with a quaff of that beaver ash for which Dublin is famous, porter labeled ex-cubed. After Hamilton's death, the dining room was found covered with huge piles of manuscript with convenient walks between the piles. When these literary remains were wheeled out and examined, china plates with the relics of food upon them were found between the sheets of manuscript, plates sufficient in number to furnish a kitchen. He used to carry on, says his oldest son, long trains of algebraical and arithmetical calculations in his mind, during which he was unconscious of the earthly necessity of eating. We used to bring in a snack and leave it on his study, but a brief nod of recognition of the intrusion of the chop or cutlet was often the only result, and his thoughts went on soaring upwards. In 1845 Hamilton attended the 2nd Cambridge Missing of the British Association, and after the meeting he was lodged for a week in the rooms of Trinity College, which tradition points out as those in which Sir Isaac Newton composed the Principia. This incident was intended as a compliment, and it seems to have impressed Hamilton powerfully. He came back to the observatory with the fixed purpose of preparing a work on quaternions, which might not be unworthily compared with the Principia of Newton, and in order to obtain more leisure for this undertaking he resigned the office of president of the Royal Irish Academy. He first of all set himself to the preparation of a course of lectures on quaternions, which were delivered in Trinity College, Dublin, in 1848, and were six in number. Among his hearers were George Solomon, now well known for his highly successful series of manuals on analytical geometry, and Arthur Cayley, then a fellow of Trinity College, Cambridge. These lectures were afterwards expanded and published in 1853 under the title of Lectors on Quaternions at the expense of Trinity College, Dublin. Hamilton had never had much experience as a teacher, the volume was criticized for diffuseness of style, and certainly Hamilton sometimes forgot the expository in the rager. The book was a paradox, a sound paradox, and of his experience as a paradoxer Hamilton wrote. It required a certain capital of scientific reputation a massed in former years to make it other than dangerously imprudent to hazard the publication of a work which has, although at bottom quite conservative, a highly revolutionary air. It was part of the ordeal through which I had to pass, an episode in the battle of life, to know that even candid and friendly people, secretly or as it might happen openly, censored or ridiculed me for what appeared to them my monstrous innovations. One of these monstrous innovations was the principle that ij is not equal to ji, but equal to negative ji, the truth of which is evident from the diagram. Critics said that he held that 3 times 4 is not equal to 4 times 3, which proceeds on the assumption that only numbers can be represented by letter symbols. Soon after the publication of the Lectors, he became aware of its imperfection as a manual of instruction, and he set himself to prepare a second book on the model of Euclid's elements. He estimated that it would fill 400 pages and take two years to prepare. It amounted to nearly 800 closely printed pages, and took seven years. At times he would work for 12 hours on a stretch, and he has also suffered from anxiety as to the means of publication. Trinity College advanced to 100 pounds. He paid 50 pounds out of his own pocket, but when illness came upon him at the expense of paper and printing, had mounted up to 400 pounds. He was seized by an acute attack of gout, from which, after several months of suffering, he died of September 2, 1865, in the 61st year of his age. It is pleasant to know that this great mathematician received during his last illness an honor from the United States, which made him feel that he had realized the aim of his great labors. While the war between north and south was in progress, the National Academy of Sciences was founded, and the news which came to Hamilton was that he had been elected one of the 10 foreign members, and that his name had been voted to occupy the specially honorable position of first on the list. Sir William Rowan Hamilton was thus the first foreign associate of the National Academy of Sciences of the United States. As regards religion, Hamilton was deeply reverential in nature. He was born and brought up in the Church of England, which was then the established Church in Ireland. He lived in the time of the Oxford movement, and for some time he sympathized with it, but when several of his friends, among them the brother of Miss De Beer, passed over into the Roman Catholic Church, he modified his opinion of the movement, and remained protestant to the end. The immense intellectual activity of Hamilton, especially during the years when he was engaged on the enormous labor of writing the elements of Coturnians, made him a recluse, and necessarily took away from his power of attending the practical affairs of life. Some said that however great a master of pure time he might be, he was not a master of subliminary time. His neighbors also took advantage of his goodness of heart. Surrounding the house, there is an extensive lawn affording good pastor, and on it Hamilton pastored a cow. A neighbor advised Hamilton that his cow would be much better contented by having another cow for company, embargoing with Hamilton to furnish the companion, provided Hamilton paid something like a dollar per month. Here is Hamilton's own estimate of himself. I have very long admired Potolam's description of his great astronomical master, Hipparchus, as, Hamilton family consisted of two sons and one daughter. At the time of his death, the elements of Coturnians was all finished, except in one chapter. His eldest son, William Edwin Hamilton, wrote a preface and the volume was published at the expense of Trinity College, doubling. Only 500 copies were printed, and many of those were presented. In consequence, it soon became a scarce book, and as much as 35 dollars had been paid for a copy. A new edition, in two volumes, is now being published by Professor Jolly, his successor in Dancing Observatory. End of Chapter 3, Sir William Rowan Hamilton, of Lectors on 10 British Mathematicians of the 19th Century, by Alexander McFarlane, read by Hernan Ibarra.