The probability of the duration of human life, on which the whole doctrine of Life-annuities depends, has employed the talents of fome of the moft able Mathematicians. Dr. Halley calculated tables for finding the value of Annuities on Lives, from the Bills of Mortality of Breslau, the capital of Silefia; and on thefe principles feveral others have been fince conftructed, from Bills of Mortality kept in other places. The Doctor was perfuaded that the degrees of mortality in Breslau were the most proper for a standard, because in that inland city the confluence of ftrangers is but small, and the births do not much exceed the funerals. Dr. Brakenridge, to whom this paper is addreffed, had diftinguished himself in calculations of this kind, which induced the Author to prefent his obfervations to him as the most able Mafter of the fubject.

This Gentleman has fhewn, 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 342 die under that age; which the Writer fays, 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 Breflau, as has been imagined, by mistaking the Doctor's meaning.

But the greatest objection lies against the fmallness of the numbers, a fault common to all the tables extant. The Author very justly obferves, that whoever begins with a thoufand only, muft neceffarily 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 out 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, Confequently, all perfons 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 to 1757 inclufive, that 2979 perfons 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 fhould be 100,000, or a million; by which means they would extend to the utmoft period of human I, and exhibit the true value of Annuities at any

led; and that the fwift or flow increase of mortality

fhould

fhould be noted in a fubfequent column, and in confequence the term or expectation properly decreasing from the best life till the whole be exhausted.

There is no doubt but tables conftructed in this manner from Bills of Mortality kept in fome inland towns, where the refort of strangers is not very confiderable, 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 inftance, the prodigious and unequal afflux of perfons of different ages, will render the Bills of Mortality very improper for this purpofe. For tho' the continual refort of ftrangers to London, would not influence 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 fame proportion as the whole number of the living of the fame ages; fince 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 fhort of the proportion above specified, the Bills of Mortality for that interval, will not truly exhibit the probability of mortality. Now experience has demonftrated, that very few perfons 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 fmall ages, are alfo lower than they would otherwise be, on account of a great number of youth, of the better fort, who are fent into the country, for the benefits of air and education. Thefe, at their return, together with the arrival of a multitude of working people (who having ferved an apprenticeship in the country, are willing to learn experience, and try their fortune in town) very much increase the number of the inhabitants: and it is chiefly to this confideration, that the great increase obfervable in the London Bills of Mortality after the age of twenty, like a rivulet fwoln by a fudden rain, is to be ascribed.

From what has been obferved it is evident, that the London - Bills are lefs proper to fhew the probability of the duration of human life, than others carefully kept in fome inland town, where the confluence of ftrangers is very fmall; and

Dd 4

there

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. Elements of new Tables of the Motions of Jupiter's Satellites. By Mr. Richard Dunthorne.

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

Art. 52. Of the Irregularities of the planetary Motions, caufed by the mutual Attractions of the Planets. By Charles Walmefley, 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 fimilar influence upon each other to difturb mutually their motions: the former has been fufficiently afcertained; but the latter very little confidered. Mr. Walmefley has therefore undertaken to examine the influence which the planets must have upon one another, and to calculate the quantity of the variations in their motions, that must refult from the general law of Gravitation. This paper contains the first part of this fubtile theory, in which the ingenious Author has chiefly confidered the effects produced by the Earth and Venus upon cach other. But, by proper fubftitutions, the fame propofitions will alfo give the effects of the other planets on thefe two, or of these two upon the others. Few fubjects are attended with more difficulty than that of the paper before us; which, however, having had the advantage of being difcuffed by fo able a Mathematician, will be therefore perufed with the greatest fatisfaction, by fuch as are well fkilled in the higher Geometry; and fuch only are capable of understanding it.

MEDICAL, ANATOMICAL, and CHIRURGICAL.

Art. 28. A farther Account of the Cafe of William Carey, whofe Mufcles began to be offified. In a Letter from the Reverend Dr. Henry.

It appears, by this account, that the progrefs of the Offifi

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

Art. 49. The Cafe of a Patient who voided a large Stone through the Perindum from the Urethra. By Dr. Frewen.

To this cafe Mr. Warner, to whom it was communicated, has added the relation of a fimilar one, that fell under his own care and infpection. To this paper is annexed a plate, with drawings of the voided calculi,,

Art. 50. An Account of the Cafe of a Boy who had the Malleus of each Ear, and one of the Incufes, dropt out. Communicated by the Rev. Mr. Morant, of Colchester.

This is the cafe of a young lad at Manningtree in Effex, who had been ill for fome weeks of a putrid, malignant, inflammatory fever; or, according to others, of an ulcerous fore-throat. The difcharge of these bones feems to be the confequence of an abfcefs, which affected the contents of the Tympanum.

Art. 51. Obfervations concerning the Body of his late Majefly, October 26, 1760. By Dr. Nicholls.

It appears, from this paper, that the circumftances attending the death of the late King, were very extraordinary, and not eafily to be accounted for.

According to the report of the Pages in waiting at the time of this melancholy accident, a noife was heard, as if a large billet had tumbled down; and upon enquiry, his Ma-jefty was found fallen on the floor, fpeechlefs and motionlefs, with a flight contufed wound on his right temple,

On diffection, the immediate caufe of his death was difcovered to be the bursting of the Ventricle of the Heart; a cafe, fays Dr. Nicholls, entirely unknown in phyfical Writers, and which muft depend on many circumftances that rarely coincide. Upon opening the cheft, we are told, the lungs were found in their natural ftate, free from every appearance of inflammation, or tubercle; but that, upon examining the heart, its pericardium was found diftended, with a quantity of coa-. gulated blood, nearly fufficient to fill a pint cup. On the re

moval of this blood, a round orifice appeared in the middle of the upper fide 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 extravafated blood, confined between the heart and pericardium, the whole heart was very foon neceffarily fo compreffed, as to prevent any blood contained in the veins from being forced into the auricles; which, therefore, with the ventricles, were found abfolutely void of blood, either in a fluid or coagulated ftate. As, therefore, no blood could be tranfmitted through the heart, from the time that the extravafation was completed, fo the heart could deliver none to the brain ; and, in confequence, all the animal and vital motions, as they depend on the circulation of the blood through the brain, muft neceffarily have been ftopped from the fame instant; and his Majefty muft, therefore, have dropped down and died inftantaneously: and, as the heart is infenfible of acute and circumfcribed pain, his death must have been attended with as little of that diftrefs, which usually accompanies the feparation of the foul and body, as was poffible, under any circumftances whatsoever.

Dr. Nicholls goes on to account for the circumftance of the blood's forcing its way through the ventricle, rather than through the auricle, which is thinner and weaker. He obferves, that upon the examination of the parts, they found all the appearances of an incipient aneurifm of the aorta, As his Majefty had for fome years alfo, complained of frequent diftreffes and finkings about the region of the heart; and as his pulfe was, of late years, obferved to fall very much upon bleeding, it is fuppofed, that this diftenfion of the aorta had been of long ftanding; and as the pulmonary artery must be thereby neceffarily compreffed, and a refiftance, greater than natural, thereby oppofed to the blood's difcharge out of the right ventricle, it is concluded that a diftenfion and confequent weakness of the pulmonary artery and right ventricle, were nearly coeval with that of the aorta. The parts being thus circumftanced, it is very reasonably prefumed, that the violent preffure they fuffered, by his Majefty's having just been at the neceffary-ftool, was the immediate caufe of that fatal incident.

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

drawings