scholarly journals XXV. A new method of investigating the sums of infinite series. By the Rev. S. Vince, A.M. of Cambridge, in a letter to Henry Maty, A.M. Secretary

1782 ◽  
Vol 72 ◽  
pp. 389-416

Sir, Having lately discovered some very easy methods of investigating the sums of certain infinite series, I have taken the liberty of requesting the favour of you to present them to the Royal Society. I have divided the subject into three parts: the first contains a new and general method of finding the sum of those series which De Moivre has found in one or two particular cases; but whose method, although it be in appearance general, will, upon trial, be found to be absolutely impracticable. The second contains the summation of certain series, the last differences of whose numerators become equal to nothing. The third contains observations on a correction which is necessary in investigating the sums of certain series by collecting two terms into one, with its application to a variety of cases.

Among the losses which the Royal Society has recently sustained none has evoked deeper regret than the death of Sir Alfred Bray Kempe, who for twenty-one years, as its Treasurer and one of its Vice-Presidents, took a leading share in the management of its affairs and in the promotion of its prosperity. Some grateful record of his career could not find a more appropriate place than in the pages of the ‘Proceedings’ of the Society with which he was so long and so closely associated. The third son of Prebendary John Edward Kempe, Rector of St. James’s, Piccadilly, he was born on July 6, 1849. From St. Paul’s School, as Camden Exhibitioner, he passed to Trinity College, Cambridge, where, in 1872, he took his degree with special distinction in Mathematics. In the same year he published his first mathematical paper, the title of which—“A general method of solving equations of the n th degree by mechanical means”—showed the bent of his mind in scientific enquiry. For some years he continued to publish mathematical essays, but having chosen the Law as his profession, and become a Barrister of the Inner Temple and Western Circuit, he was soon immersed in legal business. To the last, however, he never wholly relinquished his mathematical studies. He used to say of himself that his favourite recreations were Mathematics and Music. He was hardly ever without some problem at which, in such leisure as he could find, he steadily worked. But he refused, as he said, to “empty his note-books into the ‘Proceedings’ of the Royal Society.” He would not be induced to publish his studies until he had really got to the bottom of his enquiry.


The Fellows of the Royal Society have a tradition of writing expositions of their work which rapidly attain the status of classics. Newton’s Principia, Darwin’s Origin of Species , Maxwell’s Theory of Electricity and Magnetism, Rutherford’s Radioactive Transformations , and Dirac’s Quantum Mechanics all served to define a field which their authors had played a major role in establishing, and as a source of knowledge and inspiration for succeeding generations. Rutherford’s book went through two metamorphoses before reaching its final form as Radiations from Radioactive Substances by Rutherford, Chadwick and Ellis (hereafter referred to as RCE). During the early 1930s, it was the principal source for all aspiring nuclear physicists, including Fermi's group in Rome and a whole generation in America. It thus, inadvertently, contributed to the erosion of the overwhelming dominance of the Cavendish Laboratory in the subject. It was often referred to as the ‘Bible’ of nuclear physics, but at least from 1932, ‘Old Testament’ might have been more appropriate. It is firmly based on the proton-electron model of the nucleus and the ‘new mechanics’ makes only a tentative appearance. Nevertheless it is a true masterpiece, clearly and elegantly written, full of incisive summaries and insights, and giving a remarkably faithful and complete picture, from an experimental viewpoint, of nuclear physics as it was around 1930.


1755 ◽  
Vol 49 ◽  
pp. 639-642 ◽  
Keyword(s):  

Three of these crocodile were ago to the late Dr. Mead, physician in ordinary to the Kings; two of which he preserved in his own collection, and presented the third to the late curious Mrs. Kennon; and since the decease of these eminently worthy persons, they are all become the property of Mr. James Leman, of London, who has obliged me with the use of one of them to produce, together with this account, to the inspection of the Royal Society; which is the subject here laid before you; and of which I present the Society with a figure, just of the size and form it appeared in, when taken out of the spirits (Tab. xxix).


1917 ◽  
Vol 63 (263) ◽  
pp. 488-494
Author(s):  
Charles A. Mercier

It is considerably more than a quarter of a century since I first promulgated the doctrine that madness and unsoundness of mind are not the same thing; that madness includes more than unsoundness of mind, and that unsoundness of mind very often occurs in the sane, and is, indeed, one of the most frequent disorders of the sane. This doctrine has always seemed to me as manifestly true as the doctrine of natural selection, and, like the doctrine of natural selection, needs, it appears to me, only to be stated to secure the adhesion of every reasonable mind. In fact, I have found by experience that to the immense majority of my acquaintance it does only need to be stated to secure their adherence. Nearly everyone—everyone outside the membership of this Association—to whom I have stated it, without a single exception, has, in fact, accepted as self-evident that what matters in influencing our judgment of madness or sanity is not what a man thinks or feels, but what he says or does; not his mind, but his conduct. Even within this Association the doctrine has many adherents among the younger members, for I often receive letters from them, telling me how great an assistance it has been to them; so that things are moving, and I trust that before long we shall reach the stage that I predicted in a correspondence in the British Medical Journal, when not only will the doctrine be universally admitted to be true, but also we shall all declare that we never held any other, and that any claim of mine to have originated it will be strenuously denied. However, litera scripta manet. The minute-book of the Educational Committee will show that when I urged that conduct, as being the most important factor in madness, should be systematically studied, I could not secure even a seconder. When I subsequently brought the subject forward in this Association I had not one supporter. Nor had I when I brought it before the Royal Society of Medicine three years ago. In the third edition of Dr. Craig's book on Psychological Medicine, which has just appeared, the doctrine is not so much as even mentioned, and Dr. Craig says that insanity cannot be defined. This he says in face of the fact that at the Royal Society of Medicine I showed that there are several different concepts confused under the name of insanity, and I carefully defined every one of them; nor has any one of my definitions ever been impugned. I venture to assert that if these definitions had emanated from a German source they would have been welcomed with enthusiasm and received with reverence.


1860 ◽  
Vol 150 ◽  
pp. 223-227

The difficulty of finding approximate values of elliptic functions of the third kind has led me to consider a general method of approximation, which I believe to be new, at least in its application to the evaluation of integrals of irrational functions. It depends on the known principle that the geometric mean between two quantities is also a geometric mean between their arithmetic and harmonic means. If we take any two positive quantities, we may approximate to their geometric means as follows:— Take the arithmetic and harmonic means of the two quantities, then again take the arithmetic and harmonic means of those means, and so on: the successive means will approximate with great rapidity to the geometric mean.


Author(s):  
Henry Clifton Sorby

Before treating of the subject before me, I must describe its history. At a soirée of the Royal Society on April 25, 1877, I showed a number of specimens illustrating a new class of optical properties, applicable to the identification of minerals. These greatly interested the late Sir G. G. Stokes, Bart., and led to a considerable amount of correspondence between us ; and he communicated a paper to the Royal Society on the mathematical part of the subject, and I sent a short one on my apparatus and observations. This was admitted to be very imperfect, since the crystals examined, though showing the general facts perfectly well, had not been cut so as to be suitable for such quantitative measurements as could be compared with Stokes's theoretical determinations.


2003 ◽  
Vol 49 ◽  
pp. 351-365 ◽  
Author(s):  
Mikuláš Teich

In July 1994 I was approached by The Royal Society asking whether I would be willing to help in putting together a biographical memoir for Dr Dorothy Moyle Needham, who died in December 1987. For a variety of reasons, the Fellow of The Royal Society who originally undertook to write the memoir had been unable to deliver it before his death. After responding that I would be happy to assist, I was informed that I would, no doubt, be contacted by the writer who undertook to complete the task. As it turned out, I heard nothing more and, while occasionally wondering at the unusual delay in the publication of the memoir, I left it at that. That is, until in the spring of 2000 when I noticed that there was still no memoir on ‘Dophi’, as she was known to friends and colleagues. I found this very strange in view of the fact that almost 111/2 years had elapsed since her death and that she was among the first 10 elected female Fellows of The Royal Society. After some hesitation, I wrote on 7 May 2000 to The Lord Lewis of Newnham FRS (then Warden of Robinson College, Cambridge), alerting him to the situation. He was more than surprised and, following his enquiries, in July 2000 I became the third author invited to prepare Dr D.M. Needhams biographical memoir. As in private duty bound, I accepted the invitation, although not without anxiety over predicaments perceived beforehand. For one thing, though I had been collaborating with Dorothy Needham since 1972, the subject was history of biochemistry. Usually a biographical memoir is prepared by a person acquainted at first hand with the experimental/theoretical features of the work of the deceased Fellow. For another thing, I realized that I would be able to work on the memoir only intermittently because of other commitments, including prolonged stays abroad. All this has something to do with the delay in preparing this memoir, including the format.


1873 ◽  
Vol 21 (139-147) ◽  
pp. 105-107 ◽  

The observations made by slitless spectroscopes during the eclipse of Dec. 11, 1871, led one of us early this year to the conclusion that the most convenient and labour-saving contrivance for the daily observation of the chromosphere w ould be to photograph daily the image of a ring-slit, which should be coincident with an image of the chromosphere itself. The same idea has since occurred to the other. We therefore beg leave to send in a joint communication to the Royal Society on the subject, showing the manner in which this kind of observation can be carried out, remarking that, although the method still requires some instrumental details, which will make its working more perfect, images of the chromosphere, almost in its entirety, have already been seen on several days during the present month and the latter part of last month.


Among the losses which the Royal Society has recently sustained none has evoked deeper regret than the death of Sir Alfred Bray Kempe, who for twenty-one years, as its Treasurer and one of its Vice-Presidents, took a leading share in the management of its affairs and in the promotion of its prosperity. Some grateful record of his career could not find a more appropriate place than in the pages of the ‘Proceedings’ of the Society with which he was so long and so closely associated. The third son of Prebendary John Edward Kempe, Rector of St. James’s, Piccadilly, he was born on July 6, 1849. From St. Paul’s School, as Camden Exhibitioner, he passed to Trinity College, Cambridge, where, in 1872, he took his degree with special distinction in Mathematics. In the same year he published his first mathematical paper, the title of which—“A general method of solving equations of the n th. degree by mechanical means”—showed the bent of his mind in scientific enquiry. For some years he continued to publish mathematical essays, but having chosen the Law as his profession, and become a Barrister of the Inner Temple and Western Circuit, he was soon immersed in legal business. To the last, however, he never wholly relinquished his mathematical studies. He used to say of himself that his favourite recreations were Mathematics and Music. He was hardly ever without some problem at which, in such leisure as he could find, he steadily worked. But he refused, as he said, to “empty his note-books into the ‘Proceedings’ of the Royal Society.” He would not be induced to publish his studies until he had really got to the bottom of his enquiry.


1864 ◽  
Vol 154 ◽  
pp. 445-500 ◽  

The principal part of the following communication was presented to the Royal Society of London, in November 1859, and formed the subject of the Croonian Lecture for 1860. An abstract of it was published in the ‘Proceedings’ of the Society for April of that year. It was subsequently withdrawn for extension and revision, and I have to express rny regret that the time occupied in this work has, from various unforeseen causes, been much longer than I anticipated. The paper, as now presented, consists of four parts or sections,—the first section being devoted to the anatomy of the ventricle of the fish; the second to the anatomy of the ventricle of the reptile; the third and fourth treating of the ventricles of the bird and mammal. I have adopted this arrangement, because the structure of the ventricle in the fish and reptile is to a certain extent rudimentary, and a knowledge of it forms an appropriate introduction to the more intricate structure met with in the ventricles of the bird and mammal.


Sign in / Sign up

Export Citation Format

Share Document