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The probability of the duration of human life, on which the whole doctrine of Life-annuities depends, has employed the talents of some of the most able Mathematiciansi Dr. Halley calculated tables for finding the value of Annuities on Lives, from the Bills of Mortality of Breslau, the capital of Silesia; and on these principles several others have been fince constructed, from Bills of Mortality kept in other places. The Doctor was persuaded that the degrees of mortality in Breslau were the most proper for a standard, because in that inland city the confluence of strangers is but small, and the births do not much exceed the funerals. Dr. Brakenridge, to whom this paper is addressed, had distinguished himself in calculations of this kind, which induced the Author to present his observations to him as the most able Master of the subject.

This Gentleman has shewn, that the generality of Writers have mistaken Dr. Halley's meaning, when they affert, that of two thousand children born at Breslau, two hundred and two only die under two years of age: whereas the truth is, that 34.2 die under that age; which the Writer says, is fomewhat more than he has observed in his parish ; and hence he justly infers, that there is nothing either remarkably healthy, or long-lived, in the inhabitants of Breslau, as has been imagined, by mistaking the Doctor's meaning.

But the greatest objection lies against the smallness of the numbers, a fault common to all the tables extant. The Author very justly observes, that whoever begins with a thousand only, muft necessarily cut off twenty or thirty years of the term of life, and undervalue it in Annuities, as nothing worth. Because it cannot be expected, that oụt of a thousand births, so much as one should arrive at the age of a hundred years. And hence the generality of tables terminate at ninety years, Consequently, all persons exceeding that age ought to have Annuities for nothing, or rather receive a premium for accepting them. And yet it is known from the London accounts during the interval of thirty years, viz. from 1728 $0 1757 inclusive, that 2979 persons were living at 90, 242 at 100, 10 at 110, and one reached the great age of 138.

In order to remove this objection, the Author proposes, that the radix of the tables should be 100,000, or a million; by ishich means they would extend to the utmost period of tuman 17., and exhibit the true value of Annuities at any ciod; and that the swift or flow increase of mortality

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should be noted in a subsequent column, and in consequence the term or expectation properly decreasing from the best life till the whole be exhausted,

There is no doubt but tables constructed in this manner from Bills of Mortality kept in some inland towns, where the resort of strangers is not very considerable, would be kindly received by the public, and, perhaps, answer the most fanguinary expectations of the Author. We mention inland towns, because in others, as London for instance, the prodigious and unequal afflux of persons of different ages, will render the Bills of Mortality very improper for this purpose. For tho' the continual resort of strangers to London, would not inAuence the value of Annuities deduced from observations on the Bills of Mortality, provided those who arrived and settled there, at the several different ages of life, were in the same proportion as the whole number of the living of the same ages; since this does not depend on the greatness of the numbers that die at each particular age, but on their ratio. But if there be any part of life wherein the number of those that remove to town falls short of the proportion above specified, the Bills of Mortality for that interval, will not truly exhibit the probability of mortality. Now experience has demonstrated, that very few persons come to live in town under the age of fifteen, in comparison of the numbers that arrive there between the ages of fifteen and thirty; tho’ the number of all the living comprehended in the former period is much greater than that of the latter.

Add to this, that the Bills of Mortality, with respect to small ages, are also lower than they would otherwise be, on account of a great number of youth, of the better fort, who are sent into the country, for the benefits of air and education. These, at their return, together with the arrival of a multitude of working people who having served an apprenticeship in the country, are willing to learn experience, and try their fortune in town) very much incrcafe the number of the inhabitants : and it is chiefly to this consideration, that the great increase observable in the London Bills of Mortality after the age of twenty, like a rivulet swoln by a fudden rain, is to be ascribed.

From what has been observed it is evident, that the London Bills are lefs proper to thew the probability of the dura:ion of human life, than others carefully kept in somne inland town, where the confluence of strangers is very small; and

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therefore we wish that this ingenious Writer may perfect his tables on the plan proposed by himself, as they cannot fail of being very acceptable to the public.

Art. 20. Elcments of new Tables of the Motions of Jupiter's Sa

tellites. By Mr. Richard Dunthorne. The abilities of Mr. Dunthorne in calculations of this kind, are well known to Astronomers, who have long expected the above tables from him ; and we are sorry to find, that these hopes will never te accomplished. However he has in this paper given the elements from which the tables may be calculated, if a person equal to the task, will undertake so laborious a work.

Art. 52. Of the Irregularities of the planetary Motions, caused

by the mutual Attratlions of the Planets. By Charles Walmesley, F. R.S.

The motions of the Moon are known to be greatly disturbed by the force of the Sun, from the general principle of gravitation; the primary planets have a similar influence upon cach other to disturb mutually their motions: the former has been fufficiently ascertained; but the latter very little considered. Mr. Walmesley has therefore undertaken to ex, amine the influence which the planets must have upon one another, and to calculate the quantity of the variations in their motions, that must result from the general law of Gravitation. This paper contains the first part of this subtile theory, in which the ingenious Author has chiefly considered the effects produced by the Earth and Venus upon each other. But, by proper substitutions, the fame propositions will also give the effects of the other planets on these two, or of these two upon the others. Few subjects are attended with more difficulty than that of the paper before us; which, however, having had the advantage of being discuffed by fo able a Mathematician, will be therefore peruled with the greatest satisfaction, by such as are well skilled in the higher Geometry; and such only are capable of underítanding it.

MEDICAL, ANATOMICAL, and CHIRURGICAL.
Art. 28. A farther Account of the Case of William Cares, while

Muscles began to be offified. In a Letter from the Reverend
Dr. Henry,
It appears, by this account, that the progress of the Olifi-

cation has been stopped by means of salivation, bathing in the sea, and other remedies. Dr. Henry, however, fays, the poor man seems to be mistaken in thinking it entirely stopped ; and yet he confesses, there is reason to hope it will not increaje. Surely either the man or the Doctor must be mistaken!

Art. 49. The Case of a Patient who voided a large Stone through

the Perinæum from the Urethra. By Dr. Frewen. To this case Mr. Warner, to whom it was communicated, has added the relation of a similar one, that fell under his own care and inspection. To this paper is annexed a plate, with drawings of the voided calculi.

Art. 50. An Account of the Case of a Boy who had the Malleus of

each Ear, and one of the Incujes, dropt out. Communicated by the Rev. Mr. Morant, of Colchester.

This is the case of a young lad at Manningtree in Eflex, who had been ill for some weeks of a putrid, malignant, infiammatory fever; or, according to others, of an ulcerous fore-throat. The discharge of these bones seems to be the consequence of an abscess, which affected the contents of the Tympanum.

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Art. 51. Observations concerning the Body of his late Majesty,

October 26, 1760. By Dr. Nicholls. It appears, from this paper, that the circumstances attending the death of the late King, were very extraordinary, and not easily to be accounted for.

According to the report of the Pages in waiting at the. time of this melancholy accident, a noise was heard, as if a large billet had tumbled down; and upon enquiry, his Ma-: jefty was found fallen on the floor, specchless and motionless, with a night contused wound on his right temple,

On diflection, the immediate cause of his death was discovered to be the bursting of the Ventricle of the Heart; a case, says Dr. Nicholls, entirely unknown in physical Writers, and which must depend on many circumstances that rarely coincide. Upon opening the chest, we are told, the lungs were found in their natural state, free from every appearance of inflammation, or tubercle; but that, upon examining the heart, its pericardium was found distended, with a quantity of coagulated blood, nearly sufficient to fill a pint cup. On the re

moval of this blood, a round orifice appeared in the middle of the upper side of the right ventricle of the heart, large enough to admit the extremity of the little finger. Through this orifice, all the blood brought to the right ventricle had been discharged into the cavity of the pericardium ; and by that extravasated blood, confined between the heart and pericardium, the whole heart was very soon necessarily so compressed, as to prevent any blood contained in the veins from being forced into the auricles; which, therefore, with the ventricles, were found absolutely void of blood, either in a Auid or coagulated state. As, therefore, no blood could be transmitted through the heart, from the time that the extravasation was completed, so the heart could deliver none to the brain ; and, in consequence, all the animal and vital motions, as they depend on the circulation of the blood through the brain, muft necessarily have been stopped from the fame instant; and his Majesty must, therefore, have dropped down and died instantaneously: and, as the heart is insensible of acute and circumscribed pain, his death must have been attended with as little of that distress, which usually accompanies the separation of the soul and body, as was possible, under any circumftances whatsoever.

Dr. Nicholls goes on to account for the circumstance of the blood's forcing its way through the ventricle, rather than through the auricle, which is thinner and weaker. He observes, that upon the examination of the parts, they found all the appearances of an incipient aneurism of the aorta, As his Majesty had for some years also, complained of frequent distresses and sinkings about the region of the heart; and as his pulse was, of late years, observed to fall very much upon bleeding, it is supposed, that this distension of the aorta had been of long standing; and as the pulmonary artery must be thereby necessarily compressed, and a resistance, greater than natural, thereby opposed to the blood's discharge out of the right ventricle, it is concluded that a distension and consequent weakness of the pulmonary artery and right ventricle, were nearly coeval with that of the aorta. The parts being thus circumstanced, it is very reasonably presumed, that the violent pressure they suffered, by his Majesty's having just been at the necessary-stool, was the immediate cause of that fatal incident.

The Doctor attempts farther to explain this matter, and has acquitted himself in a yery satisfactory manner: two

drawings

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