Smallpox and the double decrement table: a piece of actuarial prehistory

1979 ◽  
Vol 106 (3) ◽  
pp. 299-318 ◽  
Author(s):  
R. H. Daw
Keyword(s):  
Mathematical Model ◽  
Infectious Diseases ◽  
Life Table ◽  
Mathematical Theory ◽  
Royal Academy ◽  
Half Century ◽  
Original Memoir ◽  
Starting Point ◽  
The Subject ◽  
Academy Of Sciences

More than 200 years ago, on 30 April 1760, Daniel Bernoulli (1766) read a memoir to the Royal Academy of Sciences in Paris entitled Essai d'une nouvelle analyse de la mortalité causée par la petite vérole, et des avantages de l'inoculation pour la prévenir (see Bradley, 1971, for a translation). In this remarkable memoir Bernoulli produced the first double decrement life table and one of the related single decrement tables, as well as deriving a mathematical model of the behaviour of smallpox in a community. This model was the forerunner of considerable developments in the mathematical theory of infectious diseases, a description of which is given in N. T. J. Bailey (1975). During the half century following Bernoulli's memoir there were a number of papers by other authors on the subject of that memoir; these, and the original memoir, seem to be little known to actuaries and are the subject of the present paper. They could have been the starting point of the actuarial development of exposed-to-risk formulae, but in fact were not.

scholarly journals IV.On a supposed alteration in the amount of astronomical aberration of light, produced by the passage of the light through a considerable thickness of refracting medium

1872 ◽  
Vol 20 (130-138) ◽  
pp. 35-39 ◽  
Keyword(s):  
Royal Academy ◽  
Angular Displacement ◽  
Focal Length ◽  
The Sun ◽  
Change Of Direction ◽  
The Subject ◽  
The Difference ◽  
North Polar ◽  
Academy Of Sciences ◽  
Right Ascension

A discussion has taken place on the Continent, conducted partly in the 'Astronomische Nachrichten,’ partly in independent pamphlets, on the change of direction which a ray of light will receive (as inferred from the Undulatory Theory of Light) when it traverses a refracting medium which has a motion of translation. The subject to which attention is particularly called is the effect that will be produced on the apparent amount of that angular displacement of a star or planet which is caused by the Earth’s motion of translation, and is known as the Aberration of Light. It has been conceived that there may be a difference in the amounts of this displacement, as seen with different telescopes, depending on the difference in the thicknesses of their object-glasses. The most important of the papers containing this discussion are:—that of Professor Klinkerfues, contained in a pamphlet published at Leipzig in 1867, August; and those of M. Hoek, one published 1867, October, in No. 1669 of the 'Astronomische Nachrichten,’ and the other published in 1869 in a communication to the Netherlands Royal Academy of Sciences. Professor Klinkerfues maintained that, as a necessary result of the Undulatory Theory, the amount of Aberration would be increased, in accordance with a formula which he has given; and he supported it by the following experiment:— In the telescope of a transit-instrument, whose focal length was about 18 inches, was inserted a column of water 8 inches in length, carried in a tube whose ends were closed with glass plates; and with this instrument he observed the transit of the Sun, and the transits of certain stars whose north-polar distances were nearly the same as that of the Sun, and which passed the meridian nearly at midnight. In these relative positions, the difference between the Apparent Right Ascension of the Sun and those of the stars is affected by double the coefficient of Aberration; and the merely astronomical circumstances are extremely favourable for the accurate testing of the theory. Professor Klinkerfues had computed that the effect of the 8-inch column of water and of a prism in the interior of the telescope would be to increase the coefficient of Aberration by eight seconds of arc. The observation appeared to show that the Aberration was really increased by 7'' 1. It does not appear that this observation was repeated.

scholarly journals XXVI. On the sources and nature of the powers on which the circulation of the blood depends

1831 ◽  
Vol 121 ◽  
pp. 489-496
Keyword(s):  
Blood Vessels ◽  
Royal Academy ◽  
External Surface ◽  
Internal Surface ◽  
Constant Attention ◽  
Animal Economy ◽  
The Subject ◽  
Academy Of Sciences ◽  
Circulation Of The Blood

It is remarkable that, notwithstanding the great importance of the circulation in the animal economy, the length of time which has elapsed since its discovery, and the constant attention it has obtained, there is hardly any department of physiology respecting which there appears to be greater uncertainty and contrariety of opinion than the sources and the nature of the powers on which this function depends. I propose in the following paper, by comparing the principal facts on the subject, and by such additional experiments as seem still to be required, to endeavour to determine these points. Much has lately been written and many experiments have been made with this view, and it has become customary to look for the causes which support the circulation to other sources beside the powers of the heart and blood-vessels. It has been supposed that what has been called the resilience of the lungs, that is, their tendency to collapse, by relieving the external surface of the heart from some part of the pressure of the atmosphere, is a principal means of causing it to be distended with blood, the whole weight of the atmosphere acting on its internal surface through the medium of the blood which is thus propelled from the veins into its cavities ; and in this way it has been supposed that the motion of the blood through the whole of the venous part of the circulation is maintained. A similar effect has been ascribed to the act of inspiration, which it is evident must operate on the same principle; and this opinion has even been sanctioned by the Report of a Committee of the Royal Academy of Sciences of Paris *, and in this country by men whose authority is deservedly high ; and the effect of these causes, it is asserted, is increased by the elastic power of the heart itself.

scholarly journals IV. Abstract from a letter sent by Monsieur Buffon, member of the Royal Academy of sciences at Paris, &c. To Martin Folkes Esq Pr. R. S. Concerning his re-invention of Archimedes’s burning specula

1748 ◽  
Vol 45 (489) ◽  
pp. 504-505
Keyword(s):  
Royal Academy ◽  
The Subject ◽  
Academy Of Sciences

As what I read some time since to our Royal Academy upon the Subject of my Re-invention of Archimedes's burning Specula , cannot appear in our memoirs before the year 1747, I think of publishing by themselves my observations upon these Mirrors, as soon as I shall satisfy myself upon certain Particulars, by some new Experiments I am preparing to make.

Archaeology in Ireland during the last 50 years: an outline

Antiquity ◽  
2002 ◽  
Vol 76 (292) ◽  
pp. 475-484
Author(s):  
George Eogan
Keyword(s):  
World War Ii ◽  
Historical Review ◽  
Considerable Change ◽  
Point Of View ◽  
World War ◽  
Half Century ◽  
Past Half Century ◽  
Starting Point ◽  
The Subject ◽  
Past Half

IntroductionThroughout the 20th century there were many notable developments in Irish archaeology, both academically and administratively. Already by the middle of the century considerable change had taken place, that was a time when new attitudes and initiatives were underway. It was also a time of economic development and social adjustments in the wake of World War II. The changes that took place in archaeology during the following half-century were extensive and varied and involved most aspects of the subject. The year 1950 is, therefore, a reasonable starting-point for commencing this review but this does not imply that a new and altered archaeology had emerged. On the contrary established personnel and institutions continued to play a major role, while some longstanding research projects continued. What is offered in this paper is a brief historical review largely considered from the academic point of view, it is selective and is not intended to provide detailed information about all aspects of research and other developments that have taken place over the past half-century. However, an attempt will be made to review the causes and influences that brought about such developments, but it is not a potted history, neither is it a review of intellectual developments.

scholarly journals XCII. A letter from Monsieur Clairaut, Member of the Royal Academy of Sciences at Paris, and F. R. S. to Thomas Birch, D. D. Secret. R. S. containing a comparison between the notions of M. de Courtivron and Mr. Melvil, concerning the difference of refrangibility of the rays of light

1753 ◽  
Vol 48 ◽  
pp. 776-780 ◽  
Keyword(s):  
Royal Society ◽  
Royal Academy ◽  
The Subject ◽  
The Difference ◽  
Academy Of Sciences

As I was perusing the last volume of the Philosophical Transactions, I fell upon a memoir of Mr. Melvil, the Subject of which having been handled in a book, that I presented some time ago to the Royal Society, from a friend of mine, and written upon a matter, which l had formerly studied myself, I first examined whether any notice had been taken of the things common to both of the works, and to what degree the two authors agreed together.

A Forum for Researchers: I Know What I Believe; Do I Believe What I Know?

1983 ◽  
Vol 14 (2) ◽  
pp. 119-125
Author(s):  
Kathleen M. Hart
Keyword(s):  
The State ◽  
Teaching Mathematics ◽  
National Academy Of Sciences ◽  
Quarter Century ◽  
Half Century ◽  
Government Report ◽  
History Of ◽  
The Subject ◽  
Teaching Of Mathematics ◽  
Academy Of Sciences

“We believe that all these perceptions of the usefulness of mathematics arise from the fact that mathematics provides a means of communication which is powerful, concise and unambiguous” (Committee of Inquiry into the Teaching of Mathematics in Schools, 1982). Thus begins the latest report, the Cockcroft Report, on the state of mathematics in British schools. Needless to say, the picture is not one of pride and satisfaction but more of the “should do better” variety. The report quotes other such exercises from a century, a half-century, and a quarter-century ago, and each in turn has the Aavor of “should do better.” The American National Academy of Sciences' Report of a Convocation (1982) carries a similar message with the added note: “used to do better.” The history of teaching mathematics in Britain fails to support this contention. Prior to 1836 there was no reaching of mathematics at Eton, although some arithmetic appeared in the curriculum. At Harrow mathematics was compulsory by 1837, and by 1868 we already have a government report saying, “The teaching of mathematics in English schools is rarely satisfactory.” One wonders whether we have ever managed to match the subject to the child.

أسلوب التعليل القرآني وبعض آثاره التعليمية (The Principles of Qur’anic Argumentation and Its Educational Effects)

2017 ◽  
Vol 14 (1) ◽  
pp. 1-33
Author(s):  
رضوان جمال الأطرش ◽  
نجوى نايف شكوكاني
Keyword(s):  
Analytical Method ◽  
New Age ◽  
Traditional Education ◽  
Inductive Method ◽  
Education Effect ◽  
Starting Point ◽  
Innovative Thinking ◽  
The Subject ◽  
Practical Impact ◽  
Education Process

        الملخّص      هدف هذا البحث إبراز إمكانية التأثر العملي بأسلوب التعليل في القرآن الكريم، ومحاولة البحث في تطبيقاته في واقع العملية التعليمية من العالم والمتعلم، بحيث لم يقتصر على الدراسة اللغوية أو الأصولية النظرية؛ وخصوصاً بعد التعريف بهذا الأسلوب وأدواته وأهميته وبيان اللوازم الخاصة للعالم والمتعلم للتأثر به، وقد تم ذلك من خلال استخدام المنهج الاستقرائي بتتبع أعمال العلماء في ذلك وتم رصد أقوال المفسرين فيما يتعلق بالأساليب البيانية وآيات التعليل ووجوه الإعجاز القرآني، ومن ثم استُخدم المنهج التحليلي لإثبات ذلك الأثر وإثبات وجود إشارات وأدلة على مظاهر التأثر؛ واستنتاج حقيقة إمكانية استمرارية البحث في كل أدوات وآيات ومواضيع ذلك الأسلوب بنفس الطريقة التي تمّ طرحُها، مما يثري هذا المجال، ويفتح العقول ويدفعها للنظر والتدبر والبحث في آي القرآن، وفي كل المناحي، منطلقةً من فكر التجديد، والإفادة من مستجدات العصر وعلومه ضمن ضوابط العقيدة الغراء والشرع الحنيف. الكلمات المفتاحية: أسلوب التعليل، أدوات أسلوب التعليل، التدبر، التعليم التقليدي، أثر.  Abstract This study intends to highlight the possible practical impact of the principles of argumentation found in the Qur’an. The study attempts to apply the principles on the actual education process of the scholars and students without limiting it to linguistic studies or theoretical principles. This was done after introducing the principles of reasoning, its tools, its importance, and disclosing the special requirements for the scholars and students in order to be influenced by the latter principles.  The work used inductive method to track the works of the scholars on the subject and observe the opinions of the Qur’an-commentators in relation to principles of explanation, verses of argument, and aspects of Qur’anic Inimitability. Analytical method was used to establish the impacts of the Qur’anic arguments; to prove the presence of signs and evidences for the manifestation of the impacts; and to make the continuity of this research possible in all the tools, verses and topics related to the principles of Qur’anic argument. Among those things that enrich this work is that it opens the minds, and pushes it to ponder and study the verses of the Qur’an. For every direction it becomes the starting point for the innovative thinking, and benefit for the new age and its sciences while maintaining the harmony with the principles of creed and the true SharÊ‘ah. Keywords: Principles of Argumentation, Tools of Argumentation Principles, Thinking, Traditional Education, Effect.

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