MacTutor
JAMES WHITBREAD LEE GLAISHER. By the death of our Vice-President, Dr. Glaisher, the Society loses one who served it most devotedly for more than half a century. He was elected a Fellow on 1871 April 14; became a member of the Council three years later, and was re-elected thereon continuously to the end of his life. It is beyond question that he loved his place at our Council table from first to last. He was chosen to succeed Mr. Dunkin as Secretary in 1877, and to fill the Presidential Chair in 1886-1888; and after being many times Vice-President was again elected President in 1901-1903. Others had been more than once President (for the full term) before him will he be the last of the series? Owing to serious illness he tendered his resignation from the Council at the end of 1927; but the Council refused to accept it, and nominated him Vice-President on the list then in preparation and the nomination was confirmed by the Society. He was deeply touched by this mark of esteem, and in response made a special effort to be present at a Council meeting at the earliest moment which his convalescence allowed. But this convalescence, which seemed to be progressing favourably, was interrupted by a sudden and serious relapse, and he died, with only a few days' warning, on 1928 December 7. James Whitbread Lee Glaisher was born at Lewisham, Kent, on 1848 November 5. He was the eldest son of James Glaisher, F.R.S. (1809-1904), a Fellow of this Society for sixty-three years, and well known from the balloon ascents which he made with meteorological instruments, in companionship with the aeronaut Mr. Henry Coxwell, who was a working astronomer in early life. The names of Whitbread and Lee given to the son were those of two friends of the father, closely associated with this Society. Moreover, Whitbread, Lee, and Glaisher were the three founders of the Meteorological Society in 1850 (Μ.Ν., 40, 207). S. C. Whitbread, F.R.S. (1796-1879) was Treasurer R.A.S. 1857-1878. Dr. John Lee (1783-1866) was Treasurer 1831-1840, and President 1861-1862. His Presidential address on the second occasion dealt with Argelander's Durchmusterung, but he refused to enter upon the main topic until he had paid a tribute of admiration to the recent "dauntless excursions in the firmament undertaken by our indefatigable colleague, Mr. Glaisher, and his fearless companion Mr. Coxwell."
The son was sent to St. Paul's School, and was always proud to remember that Samuel Pepys and Edmund Halley had been there too. The school lists show that, on 1858 September 17, nine scholars were admitted, the second in order being "James Whitbread Lee Glaisher, aged 9, son of James G., astronomer, Royal Observatory, Greenwich, VIII. 1867," and the eighth being "George Smyth Baden Powell, aged 10, son of Baden P., clergyman, 6 Stanhope Street, Hyde Park, VI. 1864." The latter boy in 1896 took a rather sensational expedition to Nova Zembla, in his yacht, to see the total eclipse. The yacht ran on a rock, but was got off without serious damage, and the eclipse was well observed by E. J. Stone and W. Shackleton, who got the earliest photograph of the "flash" spectrum. Later the yacht picked up Nansen on his way back from his great Polar expedition. On January 19 of the same year 1858 a single scholar was admitted, viz. "Edwin Ray Lankester, aged 10, son of P. Smith L., physician, 8 Savile Row, Regent Street, VIII. 1864." Sir Ray Lankester, who thus entered St. Paul's in the same year as, but left three years earlier than, Glaisher, kindly tells me that he remembers him at school as a very amiable and highly gifted mathematician, mainly directed in his studies by his father, who was well known to us all as an aeronaut. Glaisher was liked by everybody, but did nothing remarkable." His name occurs in later lists as having got the Campden Exhibition in 1867 and the Perry Exhibition in 1869. Three years later in each case we find another name honoured in our Society, that of Samuel Arthur Saunder. Lord Campden's exhibitions date back to 1634, and were only tenable at Trinity College, Cambridge. At Glaisher's date they were worth about £80 a year. (A new scheme came into force in 1875.) William Perry, a Fellow of Trinity, who died in 1696, also made his exhibitions attach to Trinity, but they were much smaller in value. Glaisher's name also appears as almost the last "apposer" of the school in 1881; and he was a Governor from 1885-1909. From St. Paul's Glaisher went, as above implied, to Trinity College, Cambridge, in 1867 October, was elected to a scholarship in 1868, and graduated as second wrangler (Hopkinson being senior) in 1871. In the same year he was elected to a Fellowship and to a Lectureship in Mathematics, an appointment which he held till 1901 by special resolution of the College Council. But in this long period of office no years were more remarkable than the early ones. By the end of 1873 he had published sixty-two papers, and he was made F.R.S. in 1875, before he was twenty-seven years of age. He was associated with the most eminent mathematicians not only on a Committee of the British Association on Mathematical Tables, but in the Editorship of two mathematical journals. And withal he gave excellent lectures in Trinity. "I went to his lectures" (wrote the present Master of Trinity in the Cambridge Review for January 25) "when I was an undergraduate, and they were far and away the best courses on Pure Mathematics I ever attended. He was remarkably clear, got over a great deal of ground, was interesting, and infused into his lectures a liveliness which was not characteristic of some of his contemporaries. For example, after talking about some theorem discovered by a mathematician X, he would say: 'It is quite a nice theorem, but X was a queer fish: he never met a girl without writing a sonnet to her the next day.' In addition to his work as a lecturer he was very active in encouraging and originating research, and the great development of pure mathematics in this University is due in no small degree to the pioneering work which Glaisher began more than fifty years ago."
Another of his former pupils, Professor A. R. Forsyth, has very kindly sent me the following paragraphs specially written for this notice :-
"In the prime of his life, Glaisher was one of the outstanding English pure mathematicians among his contemporaries. He pursued mainly subjects that were well established in the Cambridge course, the principal exception being elliptic functions which, down to the time of his own Tripos, had been unrecognised. His methods of analysis were direct and simple, almost purely algebraical in character he did not use any of the more modern methods such as those developed from Cauchy, from Riemann, or from Weierstrass. Within the range of his selected subjects and in the use of his methods he was an acknowledged authority.
"The total of his papers is large, being nearly four hundred in number. Many of them are brief, dealing with detailed issues: some are long. A few remain classical: such are his memoir on the combination of observations (in the Memoirs of the R.A.S.), his memoir on Riccati's equation (in the Phil. Trans. of the R.S.), and a late historical paper on the introduction of the plus and minus signs. The subjects, on which his papers concentrated from time to time, were definite integrals, linear differential equations, elliptic functions, and special numerical functions such as arise in Jacobian -series. The definite integrals, which chiefly concerned him, were connected with the quarter-periods of elliptic functions. In differential equations he was unrivalled in his own day in the use of symbolical methods developed by Gaskin, Leslie Ellis, and Boole. In elliptic functions his interest centred in the Jacobian theory and, there, specially in -series: however far he might wander into apparently different regions, somehow many of his investigations would ultimately converge upon the use of those series. In the theory of numbers his principal concern was with particular properties of the resolution of integers into primes. And special mention must be made of the abundant care and time he devoted to the construction of numerical tables of various kinds.
"But it was not solely by his papers that Glaisher influenced mathematics. He was a member of the mathematical staff of Trinity College: as such, his lectures in courses on differential equations, or combination of observations, or elliptic functions, were a revelation to students. In those domains there were no recognised text-books in his earlier days: the examination schedule was not pedantically precise in its indicated range and these subjects did not fall within the field of applied mathematics, as favoured at Cambridge. So he was free to expound the subjects unfettered: this was done, systematically and continuously. The Tripos was not mentioned. His students were encouraged (then a rare practice) to consult original authorities; and, under his stimulus, they acquired a working knowledge of a subject without regard to the needs or the subtleties of examinations. The result was that successive bodies of Trinity students came under Glaisher's inspiring influence. In the course of the years, Cambridge pure mathematics went, in many directions, beyond the sphere of his own activities: such progress was due to men who, frequently, had been his students and had been encouraged by him in their research.
"Glaisher has left a name which, not in one department of human thought alone, stood high in his generation he has left, also, the memory of a personality of influence upon the men of his time."
A word or two may be added about the two mathematical journals of which he was for many years the sole editor.
The Quarterly Journal of Mathematics was started in 1857, and the first fifteen volumes were edited by Sylvester, Ferrers, Stokes, Cayley, and Hermite of Paris. In 1879 Sylvester, Stokes, and Hermite fell out and Glaisher came in. In 1885 Forsyth was added. Then Ferrers, Cayley, and Forsyth successively dropped out in 1893, 1895, 1896, leaving Glaisher alone. The Messenger of Mathematics was started in 1862 by the "junior mathematical students of the three universities, Oxford, Cambridge, and Dublin"; but in 1871 a new series was begun with five editors W. A. Whitworth, C. Taylor, W. J. Lewis, R. Pendlebury, and J. W. L. Glaisher. In 1880 to 1888 the others successively dropped out, again leaving Glaisher in sole charge. The fact that he so remained is partly to be explained by the necessity of a subsidy (since the war) for these unprofitable ventures, which he paid out of his own pocket.
The present generation of astronomers would find many things to interest them in the pages of the Monthly Notices in Glaisher's early years of office. Opposite the page recording his election to Council in 1874 (whereon Adams succeeds Cayley as President) are some draw-ings of Jupiter made with Lord Rosse's 6-foot and we learn that the drawings had been made possible by the "recent application of clock-work" to the giant telescope: but there is an apologetic mention of an error in labelling the drawings because Sir John Herschel had given in his "Outlines of Astronomy" the figures for mean time rotation, but called them sidereal. We realise that it was before the days not only of the Red Spot (which first appeared in 1878) but of regular ephemerides and clock-driving. Opposite the page on which Glaisher's name first appears as Secretary is a circular from Le Verrier asking for a special search for Vulcan in transit. We seem to be returning to a different world. But the page recording his last election as Secretary in 1883 faces Dr. Common's account of his photograph of the Orion nebula, which brings us nearer modern times. He became Vice-President, and in 1886 succeeded Dunkin as President. The first page of the Monthly Notices under his presidency records the success of the Henrys in photographing nebulæ in the Pleiades. His first presidential address, on the award to G. W. Hill, was a masterly summary of the new methods in the Lunar Theory, with an account of the way in which J. C. Adams had been led to work on similar lines. His second address dealt equally well with Auwers's reduction of Bradley's observations. On the third occasion in 1902 he presented the medal to Kapteyn for his Durchmusterung, though it was still a year or two before the great discovery of star-streaming with which we now chiefly associate the medallist's name, and of which Glaisher would surely have made a brilliant summary. On the fourth occasion Glaisher was prevented from being present, owing to the death of his father a few days earlier; and the address on the work of Hermann Struve, which was read by Professor Turner, owes a great deal to the friendly co-operation of Professor Sampson. Struve's medal was handed to the German Ambassador, Count von Bernstorff, whose name became more widely known later in another connection.
An incident of a quite unusual nature occurred during Glaisher's term as Secretary. Dr. Lee, of whom mention has already been made, had presented the advowsons of the livings of Stone and Hartwell to the Society, but his heir, Mr. E. D. Lee, claimed the advowson of Stone. The Society was advised by Mr. Merriman, a solicitor who took great pains in the matter, that their own claim was valid, and accordingly they proceeded to present the Rev. Mr. Challis (son of Professor Challis of Cambridge) to the living of Stone. But the Bishop of Oxford, embarrassed by the dispute, delayed the "institution" which would have completed the transaction. In the end the Council was compelled to issue a Quare impedit writ on the Bishop, lest the presentation should be declared void. The state of affairs was only realised just in time, and owing to a chance meeting of Challis with Glaisher at the sea-side: indeed, to issue the writ a meeting of our Council had actually to be called on a Sunday, as the present writer has heard more than once from Glaisher's own lips. In the Council minutes there is no direct record of this Sunday meeting, but the minutes for 1878 November 8 contain the following: "Mr. Merriman was introduced to the Council and explained the circumstances connected with the refusal of the Bishop to institute Mr. Challis. He stated that the Quare impedit writ had been served on the Bishop on September 13, and that Mr. Lee had subsequently presented [another clergyman] to the living."
Apparently the decisive action of the Society in issuing the writ produced its effect on 1878 December 13, "Mr. Merriman reported that Mr. Lee is willing to give the Society £700 for the advowson of the living of Stone and for releasing all claims to the living of Hartwell," and Council accepted the offer on condition that all further opposition to the presentation of Mr. Challis ceased. Glaisher remembered the incident, especially his wholly fortuitous meeting with Mr. Challis, who was amiably letting things slide, and the extraordinary summons for a Sunday meeting of the Council, as a very unusual feature in his career as Secretary, not likely to have many parallels. One constitutional reform of some importance took place during his term of office, and was formally proposed by him. Up to the end of 1881 the Society's publications had been edited by a specially chosen Editor, the last being Professor Cayley. On 1881 December 9 it was proposed by Glaisher and Christie, and unanimously carried, "that the publications of the Society be in future edited by the Secretaries, with such assistance from Mr. Wesley as they may require, and that the sum of £50 per annum, in addition to his ordinary stipend, be paid to him for such services."
The first of Glaisher's contributions to our publications was a long memoir of 50 pages on the "Law of Facility of Errors of Observations and on the Method of Least Squares" (Mem. R.A.S., 39). It was read on 1872 April 12, just a year after his election as a Fellow, and is a somewhat remarkable early contribution for so young a man. It was inspired by a historical note (by Cleveland Abbe) on the apparently independent publication in 1808 of the Method of Least Squares, by Robert Adrain. He agrees with Abbe that we must " credit Dr. Adrain with the independent invention and application of the most valuable arithmetical process that has been invoked to aid the progress of the exact sciences": but he was disappointed in his expectation of finding new light on the theoretical justification of the principle underlying the use both of the arithmetic mean and least squares. As he put it:
Glaisher also wrote on logarithmic tables, of which he had special knowledge: he had contributed a paper on "Mathematical Tables " to the Phil. Trans. before taking his degree, and his report to the British Association in 1873 runs to 174 pages. In the Monthly Notices he made an elegant addition to a historic problem which had been revived in 1877 by Bertrand, " on the law of force to any point in the plane of motion in order that the orbit may be always a conic"; which paper was not printed until nearly a year after it had been sketched at the meeting of our Society on 1877 December 14, though an account of it, as given at the meeting, appeared in the first volume of The Observatory, and the main result had been set in a question in the Mathematical Tripos for 1878 January 2. Glaisher's keen desire to be complete and accurate sometimes led to these long delays. Perhaps his most valuable contribution to our Notices was his account of J. C. Adams, though all his work of that kind was quite first-rate. Adams died on 1892 January 21, and at first Glaisher thought that the notice might be included in the February report: but it soon became clear that more time was needed. The present writer, then Secretary, was, however, scarcely prepared for the difficulty in getting the finished memoir, which was ultimately delivered in MS. on the day when all the rest of the 1893 report had been passed for Press. But it was worth waiting for! Alongside it may be put the great address on Newton, which he delivered (as a substitute for Adams himself) on the occasion of the bicentenary of the Principia in the ante-chapel of Trinity College, Cambridge. This was printed in a Cambridge paper provisionally, but Glaisher had the intention of revising it for some scientific publication, adding a copy of the important letter of Newton's, which he and his father discovered about 1890. Unfortunately, that intention was never carried into effect. Of this address and that on Napier at the tercentenary of the discovery of Logarithms, Sir J. J. Thomson writes that they "have not been excelled as contributions to the early history of mathematics."
Glaisher was a great collector of pottery, china, needlework, old books, valentines, and other things, but especially of pottery. His rooms in Trinity (over the gateway of the famous avenue to "the Backs"), numerous as they were, became crowded with his collection of pottery-tables, walls, cases, even the chairs. It is a remarkable testimony to the devotion of his special college servants that they took care of this bewildering accumulation with scarcely an accident. He took an extra room in Cambridge to house a great deal of it; and he presented in his lifetime a large contribution to the Fitzwilliam Museum, to which all was to go at his death but nothing seemed to make any impression on the congested state of his rooms. We may recur to the words of the Master of Trinity about these wonderful collections and their origin :-
"For the last thirty years of his life Glaisher's keenest interest was making his great collection of pottery. It was, I think, soon after 1895 that he turned his attention to this. He had not been elected to the Sadlerian Professorship on Cayley's death, and the term for which he could hold his College Lectureship had nearly expired, he was thus faced with the cessation of work on which he had been engaged for nearly thirty years, and felt the need of another interest. I believe it was on the advice of a great friend of his, Professor McKenny Hughes, himself a keen collector, that he began to collect. The subject he chose was pottery: at first his idea, as he told me later, was to form a collection which would illustrate the development of technique in the manufacture of pottery to get an early specimen of each new method or process. This, I understand from experts, he succeeded in doing, and his collection is of great value to all students of the craft. But as collections are apt to do it developed far beyond his original intention; he got interested in certain types of pottery especially slipware-and gradually acquired what I understand is the finest collection of it in the world. He spent large sums in acquiring choice pieces if you own the best collection then when a very rare piece turns up you have to buy it or it may go to a rival collector and you will be deprived of the lead. He told me once he had never regretted his extravagances but often his economies which had made him let a piece go which afterwards he was always wanting to possess. Collecting was his greatest pleasure; when he came back to Trinity last spring after his serious illness, and when he was still too unwell to go to hall, he would brace himself up to go to the sales in London. Besides pottery he collected old samplers and formed a collection which is one of the best, if not the best, in the world. In a lighter vein, he collected valentines and children's books. These collections are to go to the Fitzwilliam Museum, and will form a delightful and enduring record of this many-sided man."
The Master adds some words about Glaisher's rare humanity:
"to no one did warm friendship mean more." We who enjoyed his friendship during his long presidency of the R.A.S. Club would all subscribe to that statement. The Club could not bear to lose him from the Chair. Even when he became President of the Society itself, in 1901-03, which had in previous instances meant automatic vacation of the Club Chair, it was insisted that he remain our President; and he faced the double responsibility and strain with keen appreciation of the affection so manifested. After he had been twenty-five years President, a special hammer and sounding-board were presented to the Club by one of its members, in honour of the occasion; but Glaisher was still not allowed to resign. After thirty-two years he expressed a decided wish to do so, which, from what we know now, may have had its origin in failing health: but as this valid reason was concealed, the Club insisted on one more year, in honour of which the number of members, formerly thirty-two, was ultimately raised to thirty-three. On the sounding-board, on which the names of successive presidents are inscribed, there was added under Glaisher's name, by special resolution, the words
N. N. T.
The son was sent to St. Paul's School, and was always proud to remember that Samuel Pepys and Edmund Halley had been there too. The school lists show that, on 1858 September 17, nine scholars were admitted, the second in order being "James Whitbread Lee Glaisher, aged 9, son of James G., astronomer, Royal Observatory, Greenwich, VIII. 1867," and the eighth being "George Smyth Baden Powell, aged 10, son of Baden P., clergyman, 6 Stanhope Street, Hyde Park, VI. 1864." The latter boy in 1896 took a rather sensational expedition to Nova Zembla, in his yacht, to see the total eclipse. The yacht ran on a rock, but was got off without serious damage, and the eclipse was well observed by E. J. Stone and W. Shackleton, who got the earliest photograph of the "flash" spectrum. Later the yacht picked up Nansen on his way back from his great Polar expedition. On January 19 of the same year 1858 a single scholar was admitted, viz. "Edwin Ray Lankester, aged 10, son of P. Smith L., physician, 8 Savile Row, Regent Street, VIII. 1864." Sir Ray Lankester, who thus entered St. Paul's in the same year as, but left three years earlier than, Glaisher, kindly tells me that he remembers him at school as a very amiable and highly gifted mathematician, mainly directed in his studies by his father, who was well known to us all as an aeronaut. Glaisher was liked by everybody, but did nothing remarkable." His name occurs in later lists as having got the Campden Exhibition in 1867 and the Perry Exhibition in 1869. Three years later in each case we find another name honoured in our Society, that of Samuel Arthur Saunder. Lord Campden's exhibitions date back to 1634, and were only tenable at Trinity College, Cambridge. At Glaisher's date they were worth about £80 a year. (A new scheme came into force in 1875.) William Perry, a Fellow of Trinity, who died in 1696, also made his exhibitions attach to Trinity, but they were much smaller in value. Glaisher's name also appears as almost the last "apposer" of the school in 1881; and he was a Governor from 1885-1909. From St. Paul's Glaisher went, as above implied, to Trinity College, Cambridge, in 1867 October, was elected to a scholarship in 1868, and graduated as second wrangler (Hopkinson being senior) in 1871. In the same year he was elected to a Fellowship and to a Lectureship in Mathematics, an appointment which he held till 1901 by special resolution of the College Council. But in this long period of office no years were more remarkable than the early ones. By the end of 1873 he had published sixty-two papers, and he was made F.R.S. in 1875, before he was twenty-seven years of age. He was associated with the most eminent mathematicians not only on a Committee of the British Association on Mathematical Tables, but in the Editorship of two mathematical journals. And withal he gave excellent lectures in Trinity. "I went to his lectures" (wrote the present Master of Trinity in the Cambridge Review for January 25) "when I was an undergraduate, and they were far and away the best courses on Pure Mathematics I ever attended. He was remarkably clear, got over a great deal of ground, was interesting, and infused into his lectures a liveliness which was not characteristic of some of his contemporaries. For example, after talking about some theorem discovered by a mathematician X, he would say: 'It is quite a nice theorem, but X was a queer fish: he never met a girl without writing a sonnet to her the next day.' In addition to his work as a lecturer he was very active in encouraging and originating research, and the great development of pure mathematics in this University is due in no small degree to the pioneering work which Glaisher began more than fifty years ago."
Another of his former pupils, Professor A. R. Forsyth, has very kindly sent me the following paragraphs specially written for this notice :-
"In the prime of his life, Glaisher was one of the outstanding English pure mathematicians among his contemporaries. He pursued mainly subjects that were well established in the Cambridge course, the principal exception being elliptic functions which, down to the time of his own Tripos, had been unrecognised. His methods of analysis were direct and simple, almost purely algebraical in character he did not use any of the more modern methods such as those developed from Cauchy, from Riemann, or from Weierstrass. Within the range of his selected subjects and in the use of his methods he was an acknowledged authority.
"The total of his papers is large, being nearly four hundred in number. Many of them are brief, dealing with detailed issues: some are long. A few remain classical: such are his memoir on the combination of observations (in the Memoirs of the R.A.S.), his memoir on Riccati's equation (in the Phil. Trans. of the R.S.), and a late historical paper on the introduction of the plus and minus signs. The subjects, on which his papers concentrated from time to time, were definite integrals, linear differential equations, elliptic functions, and special numerical functions such as arise in Jacobian -series. The definite integrals, which chiefly concerned him, were connected with the quarter-periods of elliptic functions. In differential equations he was unrivalled in his own day in the use of symbolical methods developed by Gaskin, Leslie Ellis, and Boole. In elliptic functions his interest centred in the Jacobian theory and, there, specially in -series: however far he might wander into apparently different regions, somehow many of his investigations would ultimately converge upon the use of those series. In the theory of numbers his principal concern was with particular properties of the resolution of integers into primes. And special mention must be made of the abundant care and time he devoted to the construction of numerical tables of various kinds.
"But it was not solely by his papers that Glaisher influenced mathematics. He was a member of the mathematical staff of Trinity College: as such, his lectures in courses on differential equations, or combination of observations, or elliptic functions, were a revelation to students. In those domains there were no recognised text-books in his earlier days: the examination schedule was not pedantically precise in its indicated range and these subjects did not fall within the field of applied mathematics, as favoured at Cambridge. So he was free to expound the subjects unfettered: this was done, systematically and continuously. The Tripos was not mentioned. His students were encouraged (then a rare practice) to consult original authorities; and, under his stimulus, they acquired a working knowledge of a subject without regard to the needs or the subtleties of examinations. The result was that successive bodies of Trinity students came under Glaisher's inspiring influence. In the course of the years, Cambridge pure mathematics went, in many directions, beyond the sphere of his own activities: such progress was due to men who, frequently, had been his students and had been encouraged by him in their research.
"Glaisher has left a name which, not in one department of human thought alone, stood high in his generation he has left, also, the memory of a personality of influence upon the men of his time."
A word or two may be added about the two mathematical journals of which he was for many years the sole editor.
The Quarterly Journal of Mathematics was started in 1857, and the first fifteen volumes were edited by Sylvester, Ferrers, Stokes, Cayley, and Hermite of Paris. In 1879 Sylvester, Stokes, and Hermite fell out and Glaisher came in. In 1885 Forsyth was added. Then Ferrers, Cayley, and Forsyth successively dropped out in 1893, 1895, 1896, leaving Glaisher alone. The Messenger of Mathematics was started in 1862 by the "junior mathematical students of the three universities, Oxford, Cambridge, and Dublin"; but in 1871 a new series was begun with five editors W. A. Whitworth, C. Taylor, W. J. Lewis, R. Pendlebury, and J. W. L. Glaisher. In 1880 to 1888 the others successively dropped out, again leaving Glaisher in sole charge. The fact that he so remained is partly to be explained by the necessity of a subsidy (since the war) for these unprofitable ventures, which he paid out of his own pocket.
The present generation of astronomers would find many things to interest them in the pages of the Monthly Notices in Glaisher's early years of office. Opposite the page recording his election to Council in 1874 (whereon Adams succeeds Cayley as President) are some draw-ings of Jupiter made with Lord Rosse's 6-foot and we learn that the drawings had been made possible by the "recent application of clock-work" to the giant telescope: but there is an apologetic mention of an error in labelling the drawings because Sir John Herschel had given in his "Outlines of Astronomy" the figures for mean time rotation, but called them sidereal. We realise that it was before the days not only of the Red Spot (which first appeared in 1878) but of regular ephemerides and clock-driving. Opposite the page on which Glaisher's name first appears as Secretary is a circular from Le Verrier asking for a special search for Vulcan in transit. We seem to be returning to a different world. But the page recording his last election as Secretary in 1883 faces Dr. Common's account of his photograph of the Orion nebula, which brings us nearer modern times. He became Vice-President, and in 1886 succeeded Dunkin as President. The first page of the Monthly Notices under his presidency records the success of the Henrys in photographing nebulæ in the Pleiades. His first presidential address, on the award to G. W. Hill, was a masterly summary of the new methods in the Lunar Theory, with an account of the way in which J. C. Adams had been led to work on similar lines. His second address dealt equally well with Auwers's reduction of Bradley's observations. On the third occasion in 1902 he presented the medal to Kapteyn for his Durchmusterung, though it was still a year or two before the great discovery of star-streaming with which we now chiefly associate the medallist's name, and of which Glaisher would surely have made a brilliant summary. On the fourth occasion Glaisher was prevented from being present, owing to the death of his father a few days earlier; and the address on the work of Hermann Struve, which was read by Professor Turner, owes a great deal to the friendly co-operation of Professor Sampson. Struve's medal was handed to the German Ambassador, Count von Bernstorff, whose name became more widely known later in another connection.
An incident of a quite unusual nature occurred during Glaisher's term as Secretary. Dr. Lee, of whom mention has already been made, had presented the advowsons of the livings of Stone and Hartwell to the Society, but his heir, Mr. E. D. Lee, claimed the advowson of Stone. The Society was advised by Mr. Merriman, a solicitor who took great pains in the matter, that their own claim was valid, and accordingly they proceeded to present the Rev. Mr. Challis (son of Professor Challis of Cambridge) to the living of Stone. But the Bishop of Oxford, embarrassed by the dispute, delayed the "institution" which would have completed the transaction. In the end the Council was compelled to issue a Quare impedit writ on the Bishop, lest the presentation should be declared void. The state of affairs was only realised just in time, and owing to a chance meeting of Challis with Glaisher at the sea-side: indeed, to issue the writ a meeting of our Council had actually to be called on a Sunday, as the present writer has heard more than once from Glaisher's own lips. In the Council minutes there is no direct record of this Sunday meeting, but the minutes for 1878 November 8 contain the following: "Mr. Merriman was introduced to the Council and explained the circumstances connected with the refusal of the Bishop to institute Mr. Challis. He stated that the Quare impedit writ had been served on the Bishop on September 13, and that Mr. Lee had subsequently presented [another clergyman] to the living."
Apparently the decisive action of the Society in issuing the writ produced its effect on 1878 December 13, "Mr. Merriman reported that Mr. Lee is willing to give the Society £700 for the advowson of the living of Stone and for releasing all claims to the living of Hartwell," and Council accepted the offer on condition that all further opposition to the presentation of Mr. Challis ceased. Glaisher remembered the incident, especially his wholly fortuitous meeting with Mr. Challis, who was amiably letting things slide, and the extraordinary summons for a Sunday meeting of the Council, as a very unusual feature in his career as Secretary, not likely to have many parallels. One constitutional reform of some importance took place during his term of office, and was formally proposed by him. Up to the end of 1881 the Society's publications had been edited by a specially chosen Editor, the last being Professor Cayley. On 1881 December 9 it was proposed by Glaisher and Christie, and unanimously carried, "that the publications of the Society be in future edited by the Secretaries, with such assistance from Mr. Wesley as they may require, and that the sum of £50 per annum, in addition to his ordinary stipend, be paid to him for such services."
The first of Glaisher's contributions to our publications was a long memoir of 50 pages on the "Law of Facility of Errors of Observations and on the Method of Least Squares" (Mem. R.A.S., 39). It was read on 1872 April 12, just a year after his election as a Fellow, and is a somewhat remarkable early contribution for so young a man. It was inspired by a historical note (by Cleveland Abbe) on the apparently independent publication in 1808 of the Method of Least Squares, by Robert Adrain. He agrees with Abbe that we must " credit Dr. Adrain with the independent invention and application of the most valuable arithmetical process that has been invoked to aid the progress of the exact sciences": but he was disappointed in his expectation of finding new light on the theoretical justification of the principle underlying the use both of the arithmetic mean and least squares. As he put it:
Although some of the investigations of the law of facility are far from rigorous, still there is not one that is not of some importance as throwing additional light on the properties of this law; so that a fresh investigation, and one, moreover, by which the law, not previously known to the author, was discovered, might be expected to be a real addition to, or at all events confirmation of, the known processes.
But he found nothing new of any value, and concluded that Dr. Adrain had "first remarked the convenience of treating equations by the method of least squares, and subsequently endeavoured to justify it by the Theory of Probabilities." The incident is, however, important from having attracted Glaisher's attention to the search for a fundamental proof of the underlying principle, which he conducted with great thoroughness, incidentally rejecting the argument from mere simplicity by quoting an amusing analogy from Professor Tait.
We might suppose a calculator to insist on gravity varying as the direct distance instead of the inverse square on the ground that the problem of Three Bodies would then become as simple and its solution as exact as they are now complicated and at best only approximate.
But Glaisher did not find any of the proofs satisfactory, and was led to the conclusion that this was only to be expected, since the arith-metic mean does not represent a final solution but only a first approximation. As suggested by De Morgan, the next approximation should be to weight the observations according to their distance from this mean, and solve again: and, if necessary, to make further approximations on these lines. De Morgan's enunciation (Mem. R.A.S., 39, 103) is for the method of least squares, and is as follows:-
Assuming the weights as nearly as they can be found, ascertain the most probable result, from which find the weights of the equations. If these agree with the assumed weights the process is finished; if not, repeat the process with the new weights, and so on, until a result is obtained for which the assumed and deduced weights of the equations are sufficiently near to equality.
Glaisher quotes this principle with approval, but the full value of it was only slowly appreciated by him, as is apparent in a subsequent paper "On the Rejection of Discordant Observations" (M.N., 33, 391), in which he points out that the above method obviates the necessity for rejecting anything the improved weighting will automatically reduce a discordant observation to insignificance. This led to a brief controversy with E. J. Stone, who had proposed a criterion for rejection. The whole incident has been recalled in some detail, chiefly because it is characteristic of Glaisher's thoroughness in the examination of a scientific question, not only in its theoretical but in its historical aspects, and of his bearing in controversy; and because the principle he advocated seems sound though it has dropped again into the background. He disavows the intention to insist on the continued approximations in every instance: "I make no proposition that observations should always be treated in this manner in practice – the work is sufficiently long as at present but merely point out that the above is the proper mode of proceeding, if more accuracy be re-quired." The fact that the work is already long (some sets of observations have required many weeks of work to solve the least squares) may, however, be cited as an argument for lengthening it if a better ultimate result can be found. Those who do not know these papers will certainly find them enjoyable reading.
Glaisher also wrote on logarithmic tables, of which he had special knowledge: he had contributed a paper on "Mathematical Tables " to the Phil. Trans. before taking his degree, and his report to the British Association in 1873 runs to 174 pages. In the Monthly Notices he made an elegant addition to a historic problem which had been revived in 1877 by Bertrand, " on the law of force to any point in the plane of motion in order that the orbit may be always a conic"; which paper was not printed until nearly a year after it had been sketched at the meeting of our Society on 1877 December 14, though an account of it, as given at the meeting, appeared in the first volume of The Observatory, and the main result had been set in a question in the Mathematical Tripos for 1878 January 2. Glaisher's keen desire to be complete and accurate sometimes led to these long delays. Perhaps his most valuable contribution to our Notices was his account of J. C. Adams, though all his work of that kind was quite first-rate. Adams died on 1892 January 21, and at first Glaisher thought that the notice might be included in the February report: but it soon became clear that more time was needed. The present writer, then Secretary, was, however, scarcely prepared for the difficulty in getting the finished memoir, which was ultimately delivered in MS. on the day when all the rest of the 1893 report had been passed for Press. But it was worth waiting for! Alongside it may be put the great address on Newton, which he delivered (as a substitute for Adams himself) on the occasion of the bicentenary of the Principia in the ante-chapel of Trinity College, Cambridge. This was printed in a Cambridge paper provisionally, but Glaisher had the intention of revising it for some scientific publication, adding a copy of the important letter of Newton's, which he and his father discovered about 1890. Unfortunately, that intention was never carried into effect. Of this address and that on Napier at the tercentenary of the discovery of Logarithms, Sir J. J. Thomson writes that they "have not been excelled as contributions to the early history of mathematics."
Glaisher was a great collector of pottery, china, needlework, old books, valentines, and other things, but especially of pottery. His rooms in Trinity (over the gateway of the famous avenue to "the Backs"), numerous as they were, became crowded with his collection of pottery-tables, walls, cases, even the chairs. It is a remarkable testimony to the devotion of his special college servants that they took care of this bewildering accumulation with scarcely an accident. He took an extra room in Cambridge to house a great deal of it; and he presented in his lifetime a large contribution to the Fitzwilliam Museum, to which all was to go at his death but nothing seemed to make any impression on the congested state of his rooms. We may recur to the words of the Master of Trinity about these wonderful collections and their origin :-
"For the last thirty years of his life Glaisher's keenest interest was making his great collection of pottery. It was, I think, soon after 1895 that he turned his attention to this. He had not been elected to the Sadlerian Professorship on Cayley's death, and the term for which he could hold his College Lectureship had nearly expired, he was thus faced with the cessation of work on which he had been engaged for nearly thirty years, and felt the need of another interest. I believe it was on the advice of a great friend of his, Professor McKenny Hughes, himself a keen collector, that he began to collect. The subject he chose was pottery: at first his idea, as he told me later, was to form a collection which would illustrate the development of technique in the manufacture of pottery to get an early specimen of each new method or process. This, I understand from experts, he succeeded in doing, and his collection is of great value to all students of the craft. But as collections are apt to do it developed far beyond his original intention; he got interested in certain types of pottery especially slipware-and gradually acquired what I understand is the finest collection of it in the world. He spent large sums in acquiring choice pieces if you own the best collection then when a very rare piece turns up you have to buy it or it may go to a rival collector and you will be deprived of the lead. He told me once he had never regretted his extravagances but often his economies which had made him let a piece go which afterwards he was always wanting to possess. Collecting was his greatest pleasure; when he came back to Trinity last spring after his serious illness, and when he was still too unwell to go to hall, he would brace himself up to go to the sales in London. Besides pottery he collected old samplers and formed a collection which is one of the best, if not the best, in the world. In a lighter vein, he collected valentines and children's books. These collections are to go to the Fitzwilliam Museum, and will form a delightful and enduring record of this many-sided man."
The Master adds some words about Glaisher's rare humanity:
"to no one did warm friendship mean more." We who enjoyed his friendship during his long presidency of the R.A.S. Club would all subscribe to that statement. The Club could not bear to lose him from the Chair. Even when he became President of the Society itself, in 1901-03, which had in previous instances meant automatic vacation of the Club Chair, it was insisted that he remain our President; and he faced the double responsibility and strain with keen appreciation of the affection so manifested. After he had been twenty-five years President, a special hammer and sounding-board were presented to the Club by one of its members, in honour of the occasion; but Glaisher was still not allowed to resign. After thirty-two years he expressed a decided wish to do so, which, from what we know now, may have had its origin in failing health: but as this valid reason was concealed, the Club insisted on one more year, in honour of which the number of members, formerly thirty-two, was ultimately raised to thirty-three. On the sounding-board, on which the names of successive presidents are inscribed, there was added under Glaisher's name, by special resolution, the words
per xxxiii annos Praeses Gratissimus.
But in spite of his warm affections he never married, so that the name of Glaisher disappears from our lists of Fellows after having had an honoured place therein since 1841, and in the lists of the Royal Society since 1849. From 1871-1903 our lists, and from 1875-1903 the Royal Society lists, contained the names of both father and son. Moreover, for one other year only our lists had the names of James Glaisher (senior) and his brother John, who lived with him at the Cam-bridge Observatory until he succeeded him in 1836 as the Assistant, when James removed to Greenwich with Airy. In 1845 John Glaisher left Cambridge to become observer to the Rev. J. B. Reade of Stone and Dr. Lee of Hartwell-another link between Dr. Lee and the Glaisher family. In the same year he joined our Society: but he lost his wife only three weeks after marriage, and from that great shock he never recovered. His own death followed within a year. A younger son of James Glaisher, Ernest Henry Glaisher, who followed his elder brother at St. Paul's School and Trinity, and then went out as Curator of the Museum in Georgetown, Demerara, died many years ago.
N. N. T.
James Whitbread Lee Glaisher's obituary appeared in Journal of the Royal Astronomical Society 89:4 (1929), 300-308.