bluuebunny/crossref_metadata_2025 huggingface dataset:
Art. XVIII.—The Northern Kshatrapas
Authors: Indrajī Paṇḍit Bhagvānlāl , Rapson E. J.
Published: June 2019

[Since the publication in this Journal of Paṇḍit Bhagvānlāl's article on the Western Kshatrapas, a period of no less than four years has elapsed. The delay in issuing this, the final portion of his notes, is due to the fact that a study of these notes convinced me of the impossibility of publishing them in anything like their original form; and my task was postponed, until Dr. Bühler most generously undertook to revise the most important part of the Paṇḍit's work, viz. that which deals with the inscriptions engraved on the Lion Capital. Dr. Bühler's results, which are published in another article in the present number, have enabled me to deal with the rest of the work. While I have been obliged to omit some portions and to correct others, I have endeavoured, as far as possible, to give a concise and connected exposition of the Paṇḍit's own views.
ENERGY PACKET NETWORKS WITH MULTIPLE ENERGY PACKET REQUIREMENTS
Authors: Doncel Josu , Fourneau Jean-Michel
Published: June 2019

We analyze Energy Packet Networks (EPNs) in which the service centers consist of multiclass queues and the Data Packets (DPs) initiate the transfer (i.e., the arrival of a DP at the battery triggers the movement) with multiple energy packet requirements. In other words, a class-k DP in cell i is sent successfully to the next cell if there are $c_i^{(k)}$ energy packets and it is dropped otherwise. Besides, we consider that the queues handling DPs operate under one of the following disciplines: First-Input-First-Output (FIFO), Processor Sharing (PS), or Preemptive Last-Input-First-Output (LIFO-PR). This model is an extension of previously studied EPNs [6,16] where the steady-state distribution of the number of jobs in the queues has a product form. In our model, we show the existence of a product form of the steady-state stationary distribution, where the load of the servers is given by a fixed point expression. We study the existence of a solution to the derived fixed point problem and we provide sufficient conditions for the stability of our model. Finally, we show that, for feed forward EPNs, the load of all the queues can be fully characterized.
A RANDOM ACCESS G-NETWORK: STABILITY, STABLE THROUGHPUT, AND QUEUEING ANALYSIS
Authors: Dimitriou Ioannis , Pappas Nikolaos
Published: June 2019

The effect of signals on stability, stable throughput region, and delay in a two-user slotted ALOHA-based random-access system with collisions is considered. This work gives rise to the development of random access G-networks, which can model security attacks, expiration of deadlines, or other malfunctions, and introduce load balancing among highly interacting queues. The users are equipped with infinite capacity buffers accepting external bursty arrivals. We consider both negative and triggering signals. Negative signals delete a packet from a user queue, while triggering signals cause the instantaneous transfer of packets among user queues. We obtain the exact stability region, and show that the stable throughput region is a subset of it. Moreover, we perform a compact mathematical analysis to obtain exact expressions for the queueing delay by solving a non-homogeneous Riemann boundary value problem. A computationally efficient way to obtain explicit bounds for the expected number of buffered packets at user queues is also presented. The theoretical findings are numerically evaluated and insights regarding the system performance are derived.
TACTICS, TROPHIES, AND TITLES: A COMPARATIVE PERSPECTIVE ON ANCIENT MAYA RAIDING
Authors: Helmke Christophe
Published: June 2019

Archaeological and epigraphic data have greatly increased our understanding of ancient Maya warfare in recent decades. Nevertheless, one of the aspects that has received relatively little attention is the disambiguation between the different types of wars waged. The procurement of human trophies as attested in the archaeological record and imagery, as well as the counts-of-captives and captive statements recorded textually, all provide tantalizing clues that raids formed an integral part of Classic Maya military tactics. This rings particularly true when we consider that the Classic Maya terms for “captive” and “bone” are one and the same, thereby betraying emic conceptions wherein captives were deemed to be an ideal source of bone; human trophiespar excellence. The features identified for the Classic Maya have to be set within a larger perspective since these are also found among other Mesoamerican cultures, as well as indigenous societies in both North and South America. In so doing, it becomes clear that raiding and the acquisition of captives and human trophies served to foster and heighten prestige, especially among societies that cultivated the warrior ethos. Therefore, raiding emerges as a shared Amerindian trait, rather than being the product of diffusion or independent innovation.
Bargain Shopping: How Candidate Sex Lowers the Cost of Voting
Authors: Ondercin Heather L. , Fulton Sarah A.
Published: June 2019

Previous research shows that candidate sex serves as a heuristic that lessens the informational burden of political decision making. Building upon this research, we investigate the heuristic effects of candidate sex on the decision to turnout to vote in an election. We posit that by providing ideological and nonideological information about the candidates, candidate sex serves as an informational shortcut that reduces the costs associated with voting and enhances the likelihood of voting in elections when a female candidate is present. Our expectations are supported, even after controlling for a variety of individual-, candidate- and district-level characteristics that are correlated with turnout. Individuals are more likely to turnout in elections featuring a woman candidate, and consistent with our expectations, these effects are especially strong for female Democrats, whose sex and party heuristics convey a consistent “liberal” cue. Our research offers theoretical and empirical contributions to the literature on gender, candidate heuristics, and voter turnout.
Reconstitution de la Société portugaise
Authors: Ador G. , Moynier G.
Published: June 2019

Par un avis inséré dans notre dernier Bulletin (p. 80), nous vous faisions pressentir la reconstitution de la Société portugaise de la Croix-Rouge, et nous avons aujourd'hui le plaisir de pouvoir vous confirmer officiellement celte bonne nouvelle. Elle nous a été notifiée par une lettre que nous nous faisons un devoir de vous communiquer textuellement:

« Monsieur le Président du Comité international de la Croix-Ronge, à, Genéve.
On the Origin and Nature of some of those Limited and Contingent Interests in Property which are commonly submitted to Actuaries for Valuation
Authors: Bunyon C. J.
Published: June 2019

The present paper is essentially elementary, and must therefore in a great measure be considered as addressed to the junior members of the Institute, although, perhaps, even to those more experienced persons to whom in the course of years these things have become familiar, a recapitulation, such as I now propose, may not be wholly uninstructive.
On the Apportionment, or Division by Mutual Consent, of a Fund between the Life Tenant and the Reversioner
Authors: Sprague T. B.
Published: June 2019

The subject of this paper has on two previous occasions been brought before the Institute; namely, by Mr. Jellicoe on 26 November 1855, and by Mr. Baden on 27 March 1871. The former of these gentlemen stated that, at the time his paper was written, a great diversity of opinion existed among actuaries, as to the proper method to be adopted in advising upon the proportions in which a settld fund should be divided by mutual consent between the life tenant and the reversioner; and so far as can be judged from the discussion that followd the reading of the latter paper, a similar diversity still existed then. One point, however, was clearly establisht by the discussion, namely, that Mr. Baden was quite mistaken in supposing that, because Mr. Jellicoe's conclusions had not been publicly calld in question, therefore they wer generally accepted by members of the profession.
On Some Legal Incidents Affecting the Duration of base fees in the Hands of Purchasers
Authors: Bunyon C. J.
Published: June 2019

As a wish has been expressed for some further information as to the manner in which a base fee created by the conveyance of a tenant in tail may be converted into a fee simple, it is proposed to consider the question in the following pages.

It is well understood, that an estate in tail is an estate in fee inheritable by heirs special, namely by lineal descendants generally as heirs, or such descendants of a particular class, and that a tenant in tail may convert such an estate into a fee qualified to last so long as there shall be issue inheritable under the entail. Such a conversion may be made by any conveyance sufficient to pass a fee, and will in any such case bind the heir until entry by him,(a) but if enrolled in Chancery in the manner required by the Act for the Abolition of Fines and Recoveries will, notwithstanding the want of the consent of the protector of the settlement, wholly bar the issue in tail, leaving the estate absolute during their existence, and liable only to be defeated by the failure of issue, and then by the entry of the remainderman. When the protector consents in the manner prescribed by the Act, there is no base fee, but the estate tail is converted into a fee simple and the remainders are absolutely barred.
On the Method used by Dr. Price in the construction of the Northampton Mortality Table
Authors: Sutton William
Published: June 2019

The Northampton Table has played such an important part in the life insurance transactions of this country, and is still used to such a considerable extent, that a short explanation of the method by which it was constructed, may not even at the present day be without interest to the actuarial profession. In many ways we are greatly indebted to Dr. Price, and in the writer's opinion anything emanating from him is well worthy of our consideration. It is to be hoped, therefore, that no further apology need be made for the following remarks on one of his most important works.
A comparison of Reserves brought out by the Use of different Data in the Valuation of the Liabilities of a Life Office
Authors: Valentine James
Published: June 2019

It is not intended in this paper to do more than go briefly again over part of the ground covered by Mr. Manly, in his admirable essay, printed in the 14th volume of the Journal of this Institute, on the Values of Policies as found by means of various Tables and Methods of Valuation.
On the Computation of Annuities on Mr. Makeham's hypothesis
Authors: McClintock Emory
Published: June 2019

It is now some seven years since Mr. Makeham pointed out that if our mortality tables were graduated by his formula, , “all summations connected with questions of population, the expectation of life, as well as the values of annuities, would be reduced” to the form . Since that time Mr. Makeham's formula, though not representing the law of mortality so closely as some others which have been or can be presented, has nevertheless, on account of its comparative simplicity and its great practical advantages, made manifest progress in the favor of the profession. Messrs. Woolhouse and Brown, among others, have constructed life tables in accordance with it, and it is understood that many actuaries favor its general adoption.
On the Value of a complete Annuity when payable by m equal Instalments in each Year
Authors: Carr Thomas
Published: June 2019

If the death take place in the (t+1)th interval in the year of death, then the present value of the t instalments of each paid in that year previously to the death, is .
On the Interpretation of the Statements required by the “Life Assurance Companies Act, 1870”, with special reference to the question of Expenses
Authors: Deuchar David
Published: June 2019

Since the passing of the Life Assurance Companies Act, 1870, the accounts and valuation statements lodged by the various companies with the Board of Trade, in accordance with the requirements of the Act, have been printed and published annually. The valuation returns afford, in the majority of cases, sufficient information to enable an actuary to form a tolerably correct opinion of the financial strength or weakness of the companies to which they refer. In some cases, however, owing to the special character of the facts brought out in the schedules, it is important that the actuary should have before him, when testing the sufficiency of the reserve, some facts, relating to the growth of the business, and the purposes to which the expenditure has been applied, which are not elicited by the Act. For instance, he should know the annual amount of new business which has been transacted, and the annual amount of assurances surrendered and dropped, as well as the claims by death, in order to enable him to form an opinion as to the average duration of the existing policies. He should also have a division of the expenses, showing those applicable to new business and those applicable to the management of business already acquired. An approximation to these particulars may generally be made by the actuary after a study of the reports and other voluntary publications of the companies; so that, on the whole, it may be said that the Act affords to the public the means of judging, through the medium of the actuarial profession, of the relative positions of the various offices as regards stability and profitableness.
Does a Large New Business benefit the Policyholders of a Life Company?
Authors: Macfadyen James R.
Published: June 2019

The question with which I have headed this paper is one that may seem startling enough. It has been so widely taken for granted that a large new business must be an unmixed good to all concerned in a life company, that to debate whether it be so or no, will seem in the eyes of many to be a very idle thing. And yet, though I have been considering the subject for a long time, I cannot answer the question unhesitatingly in the affirmative. In saying this, it ought to be pointed out, that the matter is regarded from a purely practical point of view. The problem is not ought a large new business to benefit policyholders? but, as a matter of fact, does it? Even if the question were answered in the negative, it would not follow that no new business, or an insufficient quantity of it, would better suit the interests of the policyholders. Waste must be supplied, and a certain degree of magnitude maintained in life companies.
On the Rate of Mortality among Adult Government Emigrants on the Voyage to Australia, during the Years 1847-1861 inclusive, as determined from the Reports of the Emigration Commissioners
Authors: McLauchlan J. J.
Published: June 2019

The object of the following paper is to describe an investigation recently made, to determine, from observed facts, the risk incurred by persons making voyages to the Australian Colonies. This investigation was carried out under the superintendence of Mr. Sprague, at whose suggestion the following account of it was prepared.
On the Usefulness of Mathematical Studies to the Actuary.— An Address to the Actuarial Society of Edinburgh
Authors: Sprague T. B.
Published: June 2019

It may perhaps be thought by some persons, that the subject upon which I am to address you tonight, is one that requires no urging on your attention. It is admitted on all hands, I may be told, that a good actuary must necessarily go through a course of mathematical training, and nothing further need be said upon the point. But if an apology for the choice of my subject is required, I would remind you that a mathematician takes nothing for granted. Whereas many people will say that it is self-evident that “two and two make four”, and that this neither requires nor admits of proof, the mathematician knows that it is a proposition, which is not in the true sense of the word self-evident, but can be strictly proved. While we deal with simple matters of this kind, little harm is likely to result from assuming as self-evident, propositions which admit of proof. But the case is very different when we come to more complicated and obscure questions; and not the least advantage to be derived from a mathematical training, is the gradual forming of the habit of mind which requires strict proof to be furnished of many important propositions which are usually taken for granted. I purpose, then, instead of taking for granted the use of mathematical studies, to examine exactly why and how they are of service to the actuary; and I hope that the conclusions I shall arrive at, may be of some assistance to those among you who wish to extend their mathematical reading beyond the point that is by common consent considered indispensable to the actuary.
How does an Increast Mortality affect Policy-Values?
Authors: Sprague T.B.
Published: June 2019

In the reports ov life insurance companies ther is offen found a statement to the efect that the value ov the liabilities has been calculated by a tabl which exhibits a hiher rate ov mortality than has been experienst. The inference sugested, and aparently intended to be drawn, must be that such a cours is more prudent than a valuation made by a tabl that woud represent with tolerabl accuracy the mortality experienst. In other words, it is implied that, the hiher the rate ov mortality exhibited by the tabl uzed in the valuation, the greater wil be the values of the policies obtaind by its use. This may at first siht seem to be a very reasonabl conclusion, but those who hav made numerical comparisons between the values ov policies as givn by different tabls, wil not need to be told that it is wholly eroneos. This is by no means a new observation. Remarks to this efect wil be found in a paper by Mr. Jellicoe in the Assurance Magazine, vol. 3, p. 186: see also a paper in the same volume, p. 143, by the late Mr. Hopf. More recently the point is wel bro't out in Mr. Manly's Messenger Prize Essay, vol. 14, p. 304.
On the Institute of Actuaries' Life Tables
Authors: Pell M.B.
Published: June 2019

After I had written the first draft of an article on the above subject, my attention was drawn to two articles by Mr. King “On Mortality amongst Assured Lives.” I had felt much diffidence in saying anything having the appearance of adverse criticism of the valuable works issued by the Institute; but now that I observe that Mr. King's articles, which are in some measure founded on opinions similar to my own, have been received with marked approval, I feel more confidence in stating plainly what appear to me defects in the HM and HM(5) Tables. But whatever I may say respecting them, I trust that my assurance will be accepted that I entertain feelings of the highest respect for the eminent knowledge and ability of the distinguished persons concerned in their preparation, with the most hearty and grateful appreciation of the benefits which they have conferred on the profession. I need hardly say that nearly all that I know of the subject of mortality amongst assured lives, is due to them.
The Values that should be allowed by a Life Office for the Surrender of its Policies, considered under their various aspects, as affecting the Interests of the Office and of the Policyholder
Authors: Crisford G.S.
Published: June 2019

The importance of this subject may be indicated by the fact that more than half a million a year is paid by the British Life Offices to their assured, as surrender values on the discontinuance of their policies. Competition also, and the increasing interest which is being taken in the subject by the insuring public, have a tendency to induce companies to make these surrender values a prominent feature in their prospectuses; perhaps also it may be an inducement to some companies to offer large values in order to bid for larger patronage.
Note on Prof. Pell's Paper on the Institute of Actuaries Life Tables
Authors: Sprague T.B.
Published: June 2019

As the formulas obtained by Prof. Pell differ from those generally in use among actuaries, it seems desirable for the sake of future students of the subject to point out that he has inadvertently fallen into an error which will necessitate considerable alteration in the reasoning on pages 142 to 144 of his paper. He uses k to denote what he calls “the absolute rate of mortality at the exact age x”, and k′ for the same at age x + 1; evidently meaning the same quantity that British actuaries now by common consent call the force of mortality. This term is embodied in the Scheme of Notation appended to the “Institute of Actuaries Life Tables”, regarding which the Council of the Institute say in the preface to the volume, that they strongly recommend the notation for general adoption, in the expectation that its use will contribute materially to advance the study of life contingencies, by promoting exactness of thought and expression. It would always be convenient, and occasionally save much trouble and confusion to readers, if all the writers in this Journal would invariably adhere to the recognized notation, so far as they can make it answer their purpose for the time being.
On the Method used by Milne in the Construction of the Carlisle Table of Mortality
Authors: King George
Published: June 2019

At a recent meeting of the Institute, Mr. Sutton read an instructive paper on the method used by Milne in the construction of the Carlisle Table of Mortality, and the paper gave rise to an interesting discussion. I was surprised to find that it was the general opinion of members that Milne's description of his method is vague, and still more so to discover that more than one able investigator had expended much pains and ingenuity, unsuccessfully in my view, to unravel the mystery. Years ago I had studied Milne's explanations, and they seemed to me perfectly clear; and I had more or less tested his figures, and proved that they worked out correctly. So much was I satisfied, that it never occurred to me that the matter required further elucidation. But the remarks of Mr. Sutton in his paper, and of Mr. Manly in the-subsequent discussion, show that Milne has been very much misunderstood; or else that he has not only failed to explain his method, but that he has explained a method which he did not in the slightest degree adhere to, and that he thus has almost wilfully misled the student. Under these circumstances I may, perhaps, be pardoned if I give with some detail the results of my own researches,—which, since Mr. Sutton's paper was read, have been carried out to greater fulness—especially as I think that thereby may be vindicated the character of Milne for both lucidity and accuracy.
On the probable effect of Withdrawals on the Rate of Mortality among Assured Lives
Authors: Gray William Thomas , Sprague T.B.
Published: June 2019

Questions as to the rate of mortality amongst assured lives, and enquiries based on re-arrangements of the mortality experience of life assurance companies collected by the Institute of Actuaries, have so frequently been discussed that I entertain some doubts as to whether the subject has not already been worn threadbare. Knowing, however, the kindness and consideration with which the Council receive contributions from junior members of the Institute, I venture to submit the results of some calculations I have lately made with a view of testing the probable effect of lapses and surrenders on the rate of mortality—a branch of the general question of mortality of assured lives which has not hitherto been directly dealt with.

The subject of this paper was some years ago suggested to me by a careful perusal of Mr. Sprague's paper (J.I.A. xv, 328), entitled “On the Rate of Mortality prevailing among “Assured Lives as influenced by the length of time for which they “have been assured”; but, although I had frequently turned the matter over in my mind, it was only recently I saw my way to give practical effect to my ideas.
On a Method for determining the Extra Premiums to be charged in respect of Two-Life Assurances
Authors: Ryan Gerald Hemmington
Published: June 2019

There are few matters in connection with actuarial science of which it can be said with truth that professional knowledge has gained little during the past two decades—a period which has witnessed a remarkable expansion in both the theoretical and practical branches of the subject of life contingencies. Questions relating to extra risks, and the premiums which should be charged for them, scarcely appear, however, to have occupied the attention of actuaries to a degree at all commensurate with their commercial importance. Within the space of time alluded to above the practical side of the subject has received consideration at the hands of Mr. A. H. Bailey (J.I.A. xv, 77), and Mr. J. Meikle (J.I.A. xix, 268) ; while lines of inquiry and investigation bearing upon points of theory have been pursued by Mr. W. M. Makeham (J.I.A. xiv, 159 and 242), and Mr. J. R. Macfadyen (J.I.A. xvii, 77). Mr. A. G. Mackenzie has also contributed to our available stock of information on the subject in his Note on War Mortality, read before the Actuarial Society of Edinburgh in 1872. I venture to submit, however that there still remains much to be done to bring this branch of the main subject to the same state of enlightenment and completeness that other parts of the science have now attained. The following paper is an attempt to throw light upon a point which has hitherto escaped scientific treatment; and I entertain the hope that, in some cases of official routine, the methods proposed will be found of service.
A Suggestion towards adding a New Feature of Usefulness to the Institute of Actuaries of Great Britain and Ireland
Authors: Walford Cornelius
Published: June 2019

That the Institute of Actuaries has, during the one-third of a century of its existence (1847-79), been of real utility to the Life Offices—directly by the training of experts, and by the compilation of the Actuaries Experience Tables; and indirectly by lending practical aid to the development of the science of life contingencies—is a fact which will readily be admitted by all who are conversant with its history. That another function may he added to its utility it is my purpose on the present occasion to show.

The business of life insurance has, during the present generation, undergone a very complete transformation. The change began in the year 1844 with the passing of the Joint Stock Companies' Registration Act, 7 & 8 Vict., c. 110. Under this Act facilities were given for the formation of Joint Stock Insurance Companies such as had never before existed. The life insurance associations existing at that date were institutions of good repute; were, in fact, regarded as money-making projects of the highest class, and it was certain, therefore, that promoters would turn their attention in this direction. The failures which had resulted from the Joint Stock Company Epidemic of 1824-5 had passed out of remembrance; the course was clear for a new spurt in the same direction. Hence, a large number of new life offices were, in fact, founded; and in their struggle for existence, an amount of competition was engendered, which (while productive of good in widening the area of the insuring class, by bringing the practice down to the middle, and, gradually, to the lower ranks of the population) has eventuated in the evils whereof I here propose to speak, and concerning which it is my design to attempt a remedy.
On the Rate ov Remarryge among Widoers
Authors: Sprague T. B.
Published: June 2019

The question ov the calculation ov premiums for the insurance agenst issue to a man at present marryd but without a family, has been on two ocasions bro't under the notis ov the Institute by Mr. Archibald Day. On 31 January 1859 he redd his paper On the determination ov the rates ov Premium for asuring agenst Issue (Journal viii, 127), in which he explaind his proces of calculating, by means ov statistics furnisht by the Registrar General's returns, the present value ov £1 payabl at the end ov the year in which a husband shal contract a second marryge. On 24 March 1862 he redd a stil more important paper, On the statistics ov first and subsequent Marryges among the Familys of the Peerage, considerd specially with reference to the calculation ov Premiums for Asurances agenst Issue, in which the same method was employd to obtain more accurat premiums from the more apropriat statistics furnisht by the peerage familys. The general problem is a very complex one involving several distinct contingencys. Mr. Day delt very succesfully with som ov these contingencys, but his treatment ov the subject was confessedly incomplete, and he himself speaks ov it as giving only a ruf aproximation. He omitted altogether from the calculations the circumstances that the insurance is not payabl until the deth ov the husband after contracting the second marryge, and that ther is a probability ov his second marryge being unfruitful. I hope on som future ocasion to take up the general question and carry the investigation ov it one or two steps beyond the point at which Mr. Day left it, but on the present ocasion I shal deal only with one element involvd in the calculation, namely, the probability ov the remarryge ov a widoer.
On the Reserve that should be made for Policies on Recently Assured Lives
Authors: Teece Richard
Published: June 2019

The question of the reserve which a life assurance society should hold, in order to meet the claims under the policies issued by it as they mature, is one of such vital importance that I am led to hope that, notwithstanding the many and valuable papers on the subject which have from time to time appeared in the Journal of the Institute of Actuaries, the following reflections may not be without interest, even though they may not throw much fresh light on the subject. I may premise by stating that the conclusions arrived at, and hereafter referred to, are the result of an investigation undertaken as a matter of curiosity, and carried on in the midst of laborious and urgent official duty; consequently the scheme propounded may appear somewhat crude and ill-defined, and doubtless lacks the completeness which a more mature consideration of the point taken up would possibly have developed. Further, the results given here were arrived at before Mr. Sprague's paper “On the Construction of Select Mortality Tables” (Journal of the Institute, vol. xxi, p. 229) appeared in print; otherwise I should probably not have undertaken the investigation.

What I have aimed at is the discovery of some method of arriving at the requisite reserves for new policies, which shall be somewhat further removed from the realm of pure theory than some others which have been suggested; a method which can be readily applied in practice; and, what is of more importance, one which can be made intelligible to the ordinary man of business.
Note on the Calculation of Logarithms to a large number of places by means of Factor Tables
Authors: Glaisher J. W. L.
Published: June 2019

There are several cases in which the factors of a number may be of use in ordinary mathematical processes; as for example, in the calculation of logarithms. This, although not the raison d’être of such a table, is so important an application as to deserve special notice, for by its means the number of numbers whose logarithms are known is greatly extended. For example, Abraham Sharp’s table contains 61-decimal Briggian logarithms of primes to 1,100, so that the logarithms of all numbers whose greatest prime factor does not exceed this number, may be obtained by simple addition. Similarly, Wolfram’s table gives 48-decimal hyperbolic logarithms of primes up to 10,009. Thus a factor table forms a very valuable complement to many-place logarithmic tables, the range of which must necessarily be comparatively limited ; and even in the case of large prime numbers, or numbers exceeding the limits of the factor table, it affords a very convenient method of calculating logarithms.
On the Rates of Marriage among Widows and Spinsters
Authors: Sprague T. B.
Published: June 2019

In my paper On the Construction ov a Combined Marryge and Mortality Tabl (J.I.A. xxi, 423), I shoed how the statistics suplyd by the Scottish Registrar-General may be employd to calculate the marryge rate among bachelors. I wil now use the same statistics to calculate the marryge rate among widos and spinsters. As I stated in the paper abov referd to, the Scottish marryge statistics apear to be furnisht with greater exactnes than the English, and the conclusions drawn from them as to the marryge rate, seem therefore much more trustworthy than the corresponding conclusions drawn from the English statistics.
Notes on the Mortality of the Danish Clergy, from 1650 to 1878
Authors: Westergaard Harald
Published: June 2019

A considerable number of investigations on mortality in times past has already been published, and without scarcely any exception they all go to show the same thing, that the mortality now-a-days is much smaller than it used to be. Some of these results are, however, only found by a sort of induction, in considering the conditions of life and the state of medical science in past centuries, and most of the statistical facts do not go farther back than to 1750; for more remote periods, the statistical information which has been gathered is scanty, untrustworthy, and dispersed.

I therefore undertook the task of investigating a distinct class of society during as long a period as possible, hoping thus to be able to confirm or correct our notions on the variations of mortality. The materials were taken from an elaborate biographical work by the Rev. S. V. Wiberg, published 1870—71, with a supplement from 1879.

I confess that the general impression of the results was that of a disappointment. In fact, the materials appeared so incorrect, that distinct numerical conclusions were not admissible. Still, I have thought it of interest to publish the chief results, hoping that, by-and-by, more correct materials may be at hand, and that the readers will consider the results here laid down as merely preliminary.
On a Certain Method of Distributing the Surplus among the Assured, and the Construction of an Equitable Scale of Office Premiums with reference thereto
Authors: Manly H. W.
Published: June 2019

It is not my intention in this paper to travel over the same ground as that followed by Mr. Sprague in his paper in the 7th vol. of the Journal, p. 61, “On Certain Methods of Dividing the Surplus among the Assured in a Life Assurance Company; and on the Rates of Premium that should be Charged to Render them Equitable”, and that by Mr. Tucker, in the 9th vol., p. 245, “On the Rates of Premiums Required to Provide certain Periodical Returns to the Assured”, although the changes which have been introduced into the methods described by both writers, and the increased knowledge we possess of life assurance mortality statistics, would fully justify a revision and extension of their labours. Such a work, if undertaken, would fully repay the time spent upon it, and would prove a valuable addition to the information we already possess upon a very important subject.

Both the above-mentioned gentlemen enlarged upon what “H. A. S.”, in the 8th vol. of the Journal, p. 167, describes as “The incongruity existing between the rates of premium charged at certain ages and the benefits accruing therefrom”; and they have shown that when the net cost of the assurances and bonuses is calculated upon a certain basis, the figures differ, often very materially, from those of the premiums charged.
On the Rate of Interest in Annuities-Certain
Authors: Hardy George F.
Published: June 2019

The problem of finding the rate of interest corresponding to a given annuity-value, has engaged considerable attention at various times; and many formulas have been proposed for obtaining approximate solutions by the aid of existing tables of annuities. Most of these will be found in Mr. Sutton's paper on the Rate of Interest yielded by Foreign Loans (J.I.A., xix, 77). Of the 5 formulas there given, (2) is probably the most generally useful, (3), (4), and especially (5) (Prof. De Morgan's formula), involving a good deal of calculation. The object of the present short paper is to suggest 2 new formulas, which give very accurate results, and at the same time require but little work in their practical application.

Let a be the value of an annuity for n years certain, at a rate of interest i, (which it is required to find), and let a1, a2, a3, be the tabulated annuity-values for the same term at the rates i1, i1 + h, i1 + 2h, where a lies between a1 and a2, and consequently i between i1 and i1 + h.
On the Adjustment of Mortality Tables
Authors: Higham John Adams
Published: June 2019

Mr. John Finlaison's method of graduation (Journal, vol. xxi, page 50) deals with an irregularity, which, for convenience, may be assumed to be unity, in the following manner:—It diminishes the irregularity to a small fraction on its first appearance at one end of the formula; conducts it along the formula by easy stages, as over a double inclined plane; and dismisses it gently at the other end. The method has the advantage of simplicity in working and check, but it is correct to first differences only.

Mr. Woolhouse's method is correct to third differences, and the irregularity glides over a curve; but the application of the formula requires sustained attention.

The object of this paper is to combine the facility of the one method with the smoothness and correctness of the other.

Let S be the sum of nine numbers, u0 to u8, increasing by third differences,

the central term,

whence .
On the Graduation of Mortality Tables
Authors: Higham John Adams
Published: June 2019

Mr. Sprague, in his report on Mr. Finlaison's Tables of Mortality among Government Life Annuitants, states as the result of his study of the subject of graduation that the most satisfactory system of adjustment is the graphic method; and he supports this opinion by referring to the irregularities which he regards as a consequence of the use of Mr. Woolhouse's method of adjustment. I do not doubt that Mr. Sprague would conceive and correctly draw a curve to satisfy all the conditions of good graduation; but in my own hands the graphic method would be a failure, and there may be others who doubt if they have skill to draw the curve and patience to amend it by the successive trials which Mr. Sprague himself finds necessary.
On the Rate of Mortality in the Navy
Authors: Sprague T. B.
Published: June 2019

I have lately examined the Blue Book on the Health of the Navy for the year 1878, in order to ascertain whether the information contained in it could be utilized for life insurance purposes. I thought that it might perhaps assist the Actuary in fixing the rate of extra premium to be charged for sea risk; but the general conclusion at which I have arrived is, that while the information contained in the Blue Book is extremely valuable for the purpose of estimating the healthiness or unhealthiness of different naval stations, and the special risks that have to be guarded against in each, and for other kindred purposes, yet the information is of very little value (if any) to insurance companies. It may, nevertheless, be useful to lay before the readers of the Journal of the Institute of Actuaries a few of the figures contained in the book.
On Mortgages of Reversionary Interests
Authors: Godefroi Henry
Published: June 2019

Amongst the various descriptions of securities, whether requiring for their absolute safety the insurance of a life or lives or not, it is well known by those who are called upon to advise lenders with regard to them, that none require more anxious care and caution than dealings involving expectancies, reversions and postobits. A long course of judicial decisions makes it manifest that our Courts are averse from giving any facilities for enabling persons entitled to such interests to obtain money on them; and until the Legislature interfered to modify the doctrine so often enunciated by the judges, so far at least as sales of reversions are concerned, the purchase of expectant titles was rendered almost impossible. But even the Act to which we allude protects the purchaser only in a modified degree, for instead of relegating his position to that of ordinary purchasers of other kinds of property, it enacts merely that a sale, otherwise bona fide, and without fraud or unfair dealing, is not to be set aside on the ground of undervalue alone. We have intimated that this enactment applies only to sales of reversions. This is the received opinion in the legal profession, although it is quite arguable, from the scope of the interpretation clause in the Statute, that it might be held to apply equally to advances on reversionary interests.
Some Account of the Census, from 1801 to 1881
Authors: Burridge Arthur Francis
Published: June 2019

Prior to the commencement of the present century, no direct method had been adopted to ascertain the number of the population in England. Various estimates, founded upon Domesday Books, Subsidy Rolls, and payments of Hearth and Poll taxes furnish, with more or less exactness, the numbers at previous periods. Three such calculations relating to the population towards the close of the 17th century are mentioned by Macaulay as being entitled to peculiar attention. “Of these computations one was made in the year 1696 by Gregory King, Lancaster Herald, a political arithmetician of great acuteness and judgment. The basis of his calculations was the number of houses returned in 1690 by the officers who made the last collection of hearth money. The conclusion at which he arrived was that the population of England was nearly five millions and a half. About the same time, King William the Third was desirous to ascertain the comparative strength of the religious sects into which the community was divided. According to the reports laid before him from all the dioceses of the realm, the number of his English subjects must have been about 5,200,000. Lastly, in our own days, Mr. Finlaison, an actuary of eminent still, subjected the parochial registers to all the tests which the modern improvements in statistical science enabled him to apply. His opinion was, that, at the close of the seventeenth century, the population of England was a little under 5,200,000 souls. … We may, therefore, with confidence pronounce that, when James the Second reigned, England contained between five million and five million five hundred thousand inhabitants.”
On the Graduation of Mortality Tables
Authors: Higham John Adams
Published: June 2019

It has been suggested that a formula given at page 17 of the present volume should be demonstrated, and its use in graduation more clearly explained.

A series of numbers increasing by third differences is summed continuously p at a time, the results are summed q at a time, these results again r at a time, and so on, until all is collected into one term, S.
Opening Address by the President, 1885
Authors: Sprague Thomas Bond
Published: June 2019

Gentlemen, on the present occasion I propose to submit to you a few remarks upon the business aspects of our work, and some of the circumstances on which the prosperity of a life insurance office depends. In the first instance, it may be useful to examine what is the real importance of life insurance to the country; and for this purpose I will take some of the figures which are now available by means of the returns made in pursuance of the Act of 1870, and compare them with other figures relating to the position and progress of the country. It appears from the Board of Trade returns that the income and assets of the life offices are steadily, not to say rapidly, increasing; the total income of the British life offices having increast from nearly 14½ millions sterling in 1871 to over 22 millions in 1884. The total life funds of the same companies now amount to about 140 millions, the increase of the funds since 1871 having been over 52 millions. These are very large figures, and they prove that the business in which we are engaged is a very important one. If, however, we confine our attention to them, we shall perhaps conceive an exaggerated idea of the importance of our business; and I will therefore compare them with the figures relating to some other industries. Thus I find it stated in the Statesman's Year-Book that the value of the total imports into the United Kingdom in the year 1883, was nearly 427 millions sterling; and the value of the exports of British produce about 240 millions; the largest articles of import being corn and flour of the value of about 67½ millions, and the largest item of export being cotton manufactures of the value of about 76½ millions.
On the Assessment of Life Risks
Authors: Chisholm James
Published: June 2019

By the assessment of life-risks, I mean the gathering together all the scattered influences that bear on the duration of life of particular individuals; the connoting in the mind the weight to be attached to the several factors that make up such influences; and, finally, the fixing the price of assurance for each individual life which approximately puts all upon a level.
History of Life Assurance in the United Kingdom (Continued)
Authors: Walford Cornelius
Published: June 2019

We commence our third epoch with the year 1721, and with the fact that there was at that period but one Life Assurance Office in existence in Great Britain—the Amicable, founded 1706. That too, so far as we have the means of knowing, was the only Life Assurance Association in the world. It was very defective in its mode of working, at the best; but it stood alone. The Society had at this date an accumulated fund of about £50,000; it had distributed in death claims £118,000. Thus it had obtained a solid hold upon public confidence, but I suspect its business suffered considerably from the general shock to public credit. The days of Mutual Contribution Life Assurance Associations, as such, were gone for ever in England. This Society had to take steps to mitigate the element of uncertainty, or it would most probably have died out. Solidity was now the one thing sought for.
Temperature Evolution of the Indo‐Pacific Warm Pool Over the Holocene and the Last Deglaciation
Authors: Moffa‐Sanchez Paola , Rosenthal Yair , Babila Tali L. , Mohtadi Mahyar , Zhang Xu
Published: June 2019

The Indo‐Pacific Warm Pool (IPWP) contains the warmest surface ocean waters on our planet making it a major source of heat and moisture to the atmosphere. Changes in the extent and position of the IPWP likely impacted the tropical and global climate in the past and may also do in the future. With the aim to put recent ocean changes into a longer temporal context, we present new paleoceanographic sea surface temperature reconstructions from the heart of the Western Pacific Warm Pool, which is the warmest region within the IPWP, across the last 17,000 years. To provide an improved spatial and temporal regional context we use new and published sea surface temperature records from the IPWP and update previous compilation efforts (Linsley et al., 2010, https://doi.org/10.1038/ngeo1920). We similarly conclude that the IPWP was warmer in the early Holocene compared to the late Holocene. However, with the new data we are able to argue against a western displacement/expansion of the IPWP and suggest a warmer southern IPWP in the early Holocene. We explore the potential drivers of the Holocene IPWP cooling and propose a combination of processes including changes in the monsoonal winds associated with the position of the rain belt, the tropical Pacific mean climate, and upper water column mixing. The proposed climatic processes differentially impacted the IPWP subregions resulting in spatially diverse trends. Additionally, the late deglacial section of the records mostly show a gradual IPWP warming similar in structure to the atmospheric CO2 and/or Antarctica rising temperatures.