XVI. Observations on the expectations of lives, the increase of mankind, the influence of great towns on population, and particularly the state of London with respect to healthfulness and number of inhabitants. In a letter from Mr. Richard Price, F. R. S. to Benjamin Franklin, Esq; LL.D. and F. R. S Received April 20* XVl. Obfervations on the Eipe<3&tiojns of Lives y the Increafe of Mankind^ the In­ fluence of great fowns on faHiculafly the State of London refpeB to Healthfulnefs Number Inhabitants* \ In a Le Mr. Richard* Price, F. R. S; to Benjamin F r a n k l i i f f ^ I M ' D e a r S i r , Read April27a n d T B E G leave to fubmit to your pe* May 4,1769. fu£aj t^ e f0ij0Wjng obfervations. I f you think them o f any importance, I ihall be obliged to you for communicating them to th e ! Royal Society. You will find that the chief fubjedt o f them is the prefent Rate o f the city of London, With refpedt to healthfulnefs and num ber o f inha­ bitants, as far as it can be colle&ed from the bills of mortality. T his is a fubjeft that has been con- fidered by others $ but the proper method of calcu­ lating from the bills has not* I think, been fuffici- ently explained. N o competent judgm ent can be formed of the following obfervations, without a clear notion o f w hat Y o l . L IX . N the D ow nl oa de d fr om h tt ps :/ /r oy al so ci et yp ub li sh in g. or g/ o n 05 A pr il 2 02 1 C 9 ° ] the writers on L ife Annuities and have called th e Expectation ofPerhaps this is not in com mon properly underftood;; and M r. De M oivre’s m anner o f exprefling him felf ab o u t-it is very liable to be m idaken. ; T h e moft obvious fenfe o f th o f a given life is, “ T h a t particular num ber o f years ie which a life o f a given age has an equal chance “ o f enjoying.” T his is properly the time that a perfon may reafonably expeCt to live ; for the chances againft his living longer are greater than thofe f o r it and, therefore, he cannot entertain an expectation o f living longer, confiftent|y w ith probability. T his period does not coincide with w hat the writers on Annuities call the expectation of Itfe^ except on the fuppofition o f an uniform decreafe in the probabilities o f life, as M r. Simpfon has obferved in his SdeCt Exercifis, p / 2 7 3 .— - I t is neceffary to add, that, even on this fuppofition, it does not coincide with w hat is, called the expectation o f life in any cafe of joint lives. T hus,, two joint lives o f 40 have an even chance, ac­ cording to M r. D e Moivre’s hypothefis*, o f conti- f hypothecs, here referred, to, petes (as is well known to thofe who BkVe ftudred the tub- ject of Life Annuities) an equal decrement of human life through all its ftages.. T h a t is, it fuppofes that out of any given number alive at a given age, the fame number will die every year till they are all dead. T h u s ; 86 M r. De Moivre- makes the utmoft probable extent of W T h e ' number o f years ’ which^ any given life wants' of g6 he- Bills the that life.------56, therefore, is the cotopfrmint o f *0} and fun, poling 56 perlbns alive at this age, W w i l l die every year till m 56 years, they will be all dead.. T h e like will happen to 46 at 40, to 36 at 50, and fo on, for all other ages. T h is is an nuingo D ow nl oa de d fr om h tt ps :/ /r oy al so ci et yp ub li sh in g. or g/ o n 05 A pr il 2 02 1 [ 9 i ] nuing together only 134. years. But the expectation o f two equal joint lives being (according to the fame hypothecs) always a third o f the common , it is in this cafe 154. years. It is neceffary, therefore, toobferve, that there is another fenfe o f this phrafe which ought to be carefully diftinguifhed from that now mentioned. It may fignify u T h e - “ nuance o{ any given Jingle, jo in t, or lives, “ according to any given table of o b f e r v a t i o n s t h a t is, the number o f years which, taking them one with another, they a&ually enjoy, and may be confidered as fu re o f enjoying, thofe who live or furvi that period, enjoying as much more time in proportion to their number, as thofe who fallJhort of it enjoy lefs. T h u s, Suppofing 46 perfons alive, all 40 years of age, and that, according to M r. De Moivre’s - pothefis, one will die every year till they are all dead in 46 years, h alf 46 or 23 will be their o f life: that is; T h e number o f years enjoyed by them all will be juft the fame as if every one of them had lived 23 years, and then died $ fo that, fuppofing no intereft o f money, there would be no difference in va­ lue between annuities payable for life to every fingle perfon in fuch a fet, and equal annuities payable to another equal fet of perfons o f the fame common age, fuppofed to be all fare o f living juft 23 years and no more. excellent bypothejis. It eafes exceedingly the labour of calcu­ lating the values of lives. It is remarkably agreeable to D r. Halley’s Table of Obfervations ; and, as far as it implies an equal decrernent of life, is, in a great meafure, confirmed by other Tables. N 2 l a D ow nl oa de d fr om h tt ps :/ /r oy al so ci et yp ub li sh in g. or g/ o n 05 A pr il 2 02 1 [ 9 2 0 In like m anner y t h e third o f 46 years, or 15 years and 4 m onths, is th e expectat o f two joint lives both 40 ; and this is alfo th e expectation, o f the fur- vivor* T h a t i s ; fuppofing a let o f marriages be­ tw een perfons all 4 0 , they will, one w ith another, laft ju ft this tim e, and the furvivors will laft th e fame tim e ; and annuities payable during the conti­ nuance o f fuch, marriages w ould, fuppofing no inter- eft o f money, tie o f exa&ly the fame value w ith an­ nuities to begin at the extinction o f fuch marriages, and to be paid, during life, to the furvivors. In adding together the years w hich any great num ber o f fuch marriages and their furvivorftiips have lafted, the fums would be found to be equal. O ne is naturally led to underftand the expectation o f life in the firft o f the feufes now explained, w hen, by M r. Simpfon and M r. De M oivfe, it is called, her f year 1 which, upon an-equality of chance, a perfon may expeCt taenjoyy or, the time a perfon of a given age may juftly expeCt to continue in being and, in the laft fenfe, w hen it is called, the Jhare of life due to a perfon*. But, as in reality it is always ufed in form er language ftiould not be applied to i t : and it is in this laft fenfe th a t it coincides w ith thefums o f the probabilities th at any given lingle or jo in t lives fhall attain to the end o f the ift, 2d, 3d, &c. moments from this tim e to th e end o f their poffible exiftence or, in the cafe o f furvivorfliips, w ith the fum of th e probabilities th at * See M r. D e Moivre on Annu, p. 65, &c. 4th edition, and M r. Simpfoa’s Seled Exercifes, p. 255, 273.' there 1 D ow nl oa de d fr om h tt ps :/ /r oy al so ci et yp ub li sh in g. or g/ o n 05 A pr il 2 02 1 [[ 93 0 there (hall be a furvivor at th e end of the ift, 2d, 3d, &c. momentŝ from this time to the end o f the poflible exigence of furvivorfhip. T his coincidence every one converfant in thefe fubje&s muft fee, upon refleding, that both thefe fenfes give the true prefent value of a liferannuity fecured by land, without intereft of money * T h e fumof the probabilities that any given lives will attain to the end of the Tft, 2d, 3d, See.years from the prefent time to the utmoft extremity of life (for inftance, 4 + +. + h e . to ±£ 2 2 | for lives of 40, by the may be called their ■ expectation^ or the numbep of payments due to them, as yearly annuitants* T h e fum of the probabilities that they will at­ tain to the end of the ift, 2d, 3d, (or, in the par­ ticular cafe fpecified, |_1. 4 ~~4 4 — V years, or 22% years) is their expedition as half yearly And the fums juft mentioned of the probabilities of their attain­ ing to the end of the iff, 2d, 3d, he.moments (equal in the fame particular cafe to ,23 years) is properly their expectation o f lifey or their expectation as,annuitants fecured by land. Mr. De Mbivre has concealed the demonftrations of the rules he has given for finding thefe expectations of life, and only intimated, in general, that he difeovered them by a calculation deduced from the method of fluxions, p. 66> pf his Treatifeon Annuities. It ’will, "perhaps, Be ’'agreeable to fdme to fee how eafily they are deduced iothfs method upon the by pot hefts of an equal decrement of life. Let x ftand for a moment of time and n the complement of any afligned life. T hen n~,he,mil be the prefent probabilities of its continuing to the end of the ift, 2d, 3d, h e . moments j and- the probability of Its continuing to the end of %x- w $ ther^fb^e be of the fum of 71 the probabilities, ot of i a ’-ana reprefenting this fum, whofe T im D ow nl oa de d fr om h tt ps :/ /r oy al so ci et yp ub li sh in g. or g/ o n 05 A pr il 2 02 1 [ 9 4 ] T his period in joint lives, I have obferved, is never • ’ $2 X ~ — !— T h e th i s e x p re ftio n , '[ : . J | ̂ 4 , ,! .. . |r| | or a— ~ is the fum itfelf for the time a- ; and this, when betomes | « , and gives t h e expectation of; .the.affigned life, cr the fum of all the probabilities juft mentioned'for its whole poiTibie duration.— In like manner: Since n- ~ is the probability that two equal joint lives will continue * time - — * x i will be the«* fluxion of the fum o f the probabilities. T h e fluent is X*“ M x — q. - —-a, which when « z ; ^ i s — th6 expectation of two fftfiltr * 3 equal joint lives.-—— -Again : Since — x —r is the proba- bility that there will be a furvivor of two equal joint lives at the end of x time, x — x * will be the of the fum of the probabilities; and the flmntyor is (when *t or the expectation of furvivorfhip between two equal lives, which therefore appears to be equal to the of their joint continuance. T h e expectation of two unequal joint lives found in the fame way is - — • g j , m being the o f the old eft life, and» the complement of the yonngeft; T h e whole expectation o f fu rvivorfhip is ^ -f — T h e expe&ation i ■ : *1 ] - 2 | j 5 Jjf| 2 , | J| i,i A of furvivorfhip on the part of the oldeift lsv and the ex- 6» i 11 ■' t" | j J peftatjon on the part of the youngeft i s , — -f I t is eafy to apply this inveftigation to any number of joint lives, and to all cafes of furvivorfhip. «j *y I 4 1 have above endeavoured to fhew d iftin % how the expecta­ tions oifingle lives may be found, agreeably to any Table of ‘ Ob- fervations, without having recourfe to any principles, except fuch as are plain and common. the D ow nl oa de d fr om h tt ps :/ /r oy al so ci et yp ub li sh in g. or g/ o n 05 A pr il 2 02 1 C 95 J the fame with the period which they have an equal haiice of enjoying y and in fingle lives, I have ob- ferved, they are the fame only on the fuppofition of an uniform decreafe in the probabilities of life. I f this decreafe, inftead o f being always uniform, is celerated in, the laft ftages o f life, the former period, in fingie lives, will be ^ than the latter; if it will be greater. It is necefiary to add, that the number expreffing the former period, multiplied by the number o f fingle or joint lives whofe expedition it is added annually to a fociety or town, gives the whole num ­ ber living together, to which fuch an annual addition would in time grow. T h u s ; fince 19, or the third of 57, is the expectation- of two joint lives whofe common age is 29, or common complement 57, twenty marriages every year between perfons o f this age. would, in 57,years^ grow to 20 times 19, or 380 marriages always ex itin g together. T h e number o f Jw vivors alfo arifing from thefe marriages, and always- living together, would, in twice 57 years, increafe to the fame number. And, fince the expectation o f a fingle: life is always half its complement ̂ in 57 years likewife 20. fingle perfons aged 29, added annually to a town, would increafe to 20 times 28,5 or 570 y and when arrived at this number, the deaths every* year will juft equal the acceftlons, and no further in­ creafe bepoflible. ■ , oy, > It appears from hence, that the particular propdr- ' t;on that becomes extinct evefy year, out of the whole number conftantly exifting together of fingle or joint lives, muft, wherever this number undergoes no variation, D ow nl oa de d fr om h tt ps :/ /r oy al so ci et yp ub li sh in g. or g/ o n 05 A pr il 2 02 1 t ¥> 1 variation, be exadtly the lam e w ith the o f thofe lives at the l i n e w hen their exigence com ­ menced. T h u s ; was it found that a 19th part o f all the marriages among any body of m en, whofe num bers do not vary, are diffolved every year by the deaths o f either th e hufbarid o r 4 wife; it would Ap­ pear that 19 was, at the tim e they were contracted, x\\texpeBation o f thefe marriages* In like m a n n e r; was it found in a fbciety, lim ited to a fixed num ber of members, that a 28th part dies annually out o f the whole num ber o f m em bers, it would appear that 2,8 was their eoriirnon expectation o f life at the tim e they entered* So 1 ! likew ife; were it found it! any.tow n otdiftriCt, Where the dum ber o f births and burials are equal, that a 20th or 30 th part o f the in­ habitants die annually, it would appear that 20 or 30 was the expectationo f a tM ld jd ft born in that town or diftriCb T hefe expectationtherefore, for ^Jingle lives, are eafily found by a 'Table ofObjema* iions, foe wing thfe dum ber that die annually at all ages, out o f a given num ber alive at thofe ag es; and the general rule for this purpofe is “ to divide “ the fum o f all the living in th e T ab le at the age « whofe expectation is required, and at all greater <£i ages, by the fum o f ail that die annually at “ that age, and above i t ; or, w hich is the fame, by “ the num ber in the T able o f the living at that age 5 “ and h a lf fubtraCled from the quotient will be the c< required expectation ̂ T h u s, in D r. H alley s T able, the fum of all th e living at 2.0 and upwards is 2 0 ,7 2 4 ; T h e num ber living at th at age is 598 ; and the form er num ber divided by the latter, and h a lf D ow nl oa de d fr om h tt ps :/ /r oy al so ci et yp ub li sh in g. or g/ o n 05 A pr il 2 02 1 [ 97 1 . h alf unify * fubtra&ed from the quotient, gives 34- ̂ 5 fo r the e m B a tim -of H2o/v T t e expectation o f the lame life by M r MmffinsTable, formed from the bills of mortality of London, is 28.9* T hefe obfervations bring me to the principal point which I have had all along in view. T h ey L o e f t t o us an ealy method of finding the num ber of inhabitants in a place from a fable oj Observations, or the bills o f mortality for that place, fuppofmg the yearly births and burials equal. “ Find by the « Table, in the way juft defcribed, the « o f an infant juft born, and this, multiplied by the «< number o f : yearly births, will be the number of «< inhabitants.” A t Brejlaw, according to D r. H al­ ley’s Table f , though half die under 16, and there­ fore an infant juft born has an equal chance of living only 16 years, yet Imexpetiatmfo u n d by th6 rule I have given, is near 28 years > and this, multiphe by 1238 the number born annually, gives 34,664, * T his fubtraaion is neceffary, becaufe the divifor ought to be made as much greater than the number dying annual y given in the Table, as the expectation, with \ unity added, is greater than the expectation, on account of the number that will die, in the courfe of the year, out of thofe who are continually added, In order to preierve thb}nurnbef bf the living the tame. In other w ords: If we conceive the recruit neceflary to fupply the wade of every year to be made al ways at the end o f the year, the dividend ought to be the me between the numbers jiving at the beginning and the end of the y ear; that is, it bug t to be taken lefs than thb Tiim of the hving m th eT ab le at and abbvb the given age,* by Jjalfthelum ber thatchein the yearj, the of which dimwmon yMbe the fame with th have directed. . !(f . , • i - r , r„_ t Vid. Lowthorp’s Abridgment of the Philofbphieal 1 tanfac- tions, vol. III. p .6 6 9 . , Vo l. L 1X. 0 the D ow nl oa de d fr om h tt ps :/ /r oy al so ci et yp ub li sh in g. or g/ o n 05 A pr il 2 02 1 the num ber o f inhabitants. In like m a n n e r; it ap* pears from M r . Simpfon’s Table, th a t, though an in­ fant ju ft born in London has not an equal chance o f living 3 years, his expeBationis 20 years; and this num ber, multiplied by the yearly births, would give the num ber of inhabitants in London, were th e births and burials equal; T h e m edium o f the yearly births, for the laft 10 years, has been 15,710. T h is num ber, multiplied by 2 0 , /̂is 314,2005 w hich is th e num ber o f inhabitants that there would be in Lon* don, according to*the bills, were th e yearly burials no more than equal to the b irth s : th a t is, were it to fupport itfelf in its num ber o f inhabitants w ithout any fupply from the country.1 B ut for the laft 10 years, the burials have, at an average, been 2 2 ,9 5 6 , and exceeded the chriftenings 7 ,2 4 6 . T h is is, there­ fore, at prefent, the yearly addition o f people to L on­ don from other parts o f the kingdom , by w hom it i s kept up. Suppofe them to be all, one w ith another, perfons who have, when they remove to L ondon, an expeffiation o f life equal to years. T h a t is 5 fup- pofe them to be all o f the age o f 18 or 20 , a fuppo- fition certainly far beyond the truth. F rom hence will arife, according to w hat has been before ob­ served, an addition o f 30 multiplied by 7 ,2 4 6 , that is 217,380 inhabitants. T h is num ber, added to the former, makes 5 3 1 ,5 8 0 ; and this, I thin k , at m oft, would be the num ber o f inhabitants in London w ere the bills perfect. But it is certain that they give the num ber o f births and burials top little. T h e re are many burying-places that are never brought into the bills. M any alfo emigrate to the navy and arm y and c o u n try ; and theie ought to be added to the num ber D ow nl oa de d fr om h tt ps :/ /r oy al so ci et yp ub li sh in g. or g/ o n 05 A pr il 2 02 1 f 9 » ] ' number o f deaths. W h a t the deficiencies arifing from hence are, cannot be determined. Suppofe them equivalent to 6000 every year in the births, and 60 0 0 in the burials. T his would make an addition of 20 times 6000 or 120,000 to the lad number, and the whole number o f inhabitants would be 651,580. I f the burials are deficient only two thirds of this number, or 4000, and the births the whole o f it ; 20 multiplied by 6000, m u d be added to 314,290 on account o f the defe&s in the b irth s : and, fince the excels of the burials above the births will then be only 5 ,2 4 6 ; 30 multiplied by 5,246 or 157,380, will be the num ber to be added on this account; and the fum, or num ber of inhabitants, will be 591.580. But if, on the contrary, the burials are deficient 6 0 0 0 , and the births only 4 0 0 0 ; 80,000 m uft be added to 314,290, on account of the defi­ ciencies in the births ; and 30 multiplied by-9,246, on account o f the excefs o f the burials above the births, and the whole number of inhabitants will be 6 71.580. Every fuppofition in thefe calculations feems to me too high. Emigrants from London are; in par­ ticular, allowed the fame expe ffiation of continuance in London with thofe who are born in it, or who come to it in the firmed part of life, and never afterwards leave i t ; whereas it is not credible that the former expectation fhouid be fo much as half the latter. But I have a further reafon for thinking that this calculation gives too high numbers, which has with me irrefidible weight. It has been, feen that the number o f inhabitants comes out lefs on the fuppo-’ fition, that the d e fe rs in the chridenings are greater O 2 t h a n ; D ow nl oa de d fr om h tt ps :/ /r oy al so ci et yp ub li sh in g. or g/ o n 05 A pr il 2 02 1 1 , . f w ] _ than thofe in. the burials. N o w it: feems evident tn& tftW is1reŶIy th d lcaj®' ; and, as it is a fadt not at- * tended t6, t will here endeavour to explain didin& ly the reafon which proves it. 1 T h e , proportion of the num ber o f births in L o n ­ don, to the num ber w hp live to be i o years o f age, is, by t|ie bills, 16 to 5; A n y o n e may find this to be true, by fubtrailing the annual medium o f thofe w h o have died under 10, for forne years p a d , from the annual medium o f births for the fame num ber o f y e a rs .------N o w , tho*, w ithout doubt, London is very fatal to children, yet it is incredible that it fhould be fo fa ta l as" this implies.} T h z bills]theftfore, very proba­ bly, give the num ber o f thofe w ho die under 10 too great in proportion to the num ber o f births 5 and there can be no other caufe of this, than a greater deficiency in the births than in the . W ere tn etijnciencies.m both equal, that is, were the fo - fj&lfc In proportion t o ftheir num ber, j u d as deficient a^tdie births are in proportion to their num ber, the proportion o f thofe who reach 10 years o f age to the num ber bornf would be right in 'th e bills, let the defi­ ciencies themfelves be ever fo confiderable. O n th e contrary, were the deficiencies in the greater tjjan in the births, this proportion would be given too great ; and it is only w hen the form er are lead that this proportion can be given too little.-------T h u s ; let thê num ber o f annual burials be 2 3 ,0 0 0 ; o f births 1,5,70,0; and the num ber dying annually under 10, 10*800*. T h e n 4 ,9 0 0 will reach 10 o f 15,700 born -an n u d ly j that is, 5 out o f 16.-—— W ere there no deficiencies in t h e burials, and w e r e it-fa& that only cue under 10, it would follow, that there was an annual D ow nl oa de d fr om h tt ps :/ /r oy al so ci et yp ub li sh in g. or g/ o n 05 A pr il 2 02 1 [ ] annual deficiency equal to 4 ,9 ° ° fubtraded from ] 0 ,8oo, or 5,900 in the birthsWere the births a third part too little, and the alfo a third part too little, the true number o f , and of children dying under 10, would be 2 0 ,933—— 30,666, and 14,400 5 and, therefore, the number that would live to 10 years of age would be 6,533 out of 20,933, or 5 o f 16 as before.-------W ere the biiths a third part, and the burials fo much as two-fifths wrong, the num ber of births, burials9 and children dying un­ der 10 would be 20,933*" and 1 5 ,1 2 0 ; and, therefore, the num ber that would live to 10 would be 5,813 out of 20,933, or 5 out of 1 8 - — W ere the births a 3d part wrong, and the burials but a 6th, the foregoing numbers would be 20,933— — 26,833____ 12,6005 and, therefore, the number that would live to 10 would be 8,333 out o f 2 0 ,9 3 3 , or 5 ollt of 1 2 .5 6 ; and this proportion feems as low as is confident with any degree of probability. It is fomewhat lefs than the propor­ tion in M r. Simpfon’s Table of Ohferva- tionsy and near one half lefs than the proportion in the T able of Obfervations for Breflaw, w h ereit appears that above 9 of 16 live to be 10, and that one h a lf live to be 16. T h e deficiencies, therefore, in the births cannot be much Ids than double thofe in the burials* y and the lead numbers I have given * One obvious reafon of this fa& is, that of the births among Jews,Quakers, Paptfis, and the denominations o f DiJJenters are included in the bills, whereas of their burials are. It is further to be attended to, that the abortive and itiU- born, amounting to about 600 annually, are included in the burials, but never in the births. If we add thefe to the chriften- m ud, D ow nl oa de d fr om h tt ps :/ /r oy al so ci et yp ub li sh in g. or g/ o n 05 A pr il 2 02 1 . 1 1 0 2 ] rrmft, probably, be neareft to the true num ber o f inha­ bitants. H ow ever; fhouId any one; after all, think that it is not improbable that only 5 o f 16 fhould live in London to be 10 years o f age, or that above two thirds die under this age, the confequence o f ad­ m itting this will ftill be, that the foregoing calcula­ tion has been carried too high. F or it will from hence follow, that the expectation o f a child j u f t born in London cannot be fo m uch as I have taken it. This expectation is 20, on the fuppofition that h a lf die under 3 years o f age, and that 5 o f 16 live to be 29 years o f age, agreeably to M r. Sirnp- fon’s T ab le, But if it is indeed true, that half die under 2 years o f age, and 5 o f 16 under 10, agreeably to the hills- this expectation m uft be lefs than 20, and all the numbers before given will be co n fid en tly reduced. Upon the w h o le : I am forced to conclude from thefe observations; that the fiecond num ber I have gi­ ven, or 6 5 1 ,5 8 0 , though fhort o f the num ber o f in­ habitants com m only fuppofed in London, is, very probably, greatery b u t cannot be m uch lefs, than th e true num ber. Indeed, it is in general evident, that in cafes o f this kind numbers are very m uch over­ rated, T h e ingenious D r. Brakenridge 14 years ago, w hen the bills were low er th a n they are now , from the num ber o f houfes, and allowing fix to a houfe, made the num ber o f inhabitants 7 5 1 ,8 0 0 . B ut his m ethod of determ ining the n u m - mgs," 3 " prefeiving the burials the fame, the proportion of the born, according to the bills, who have reached ten for the laft fix- teen years, will be very nearly one inftead of * Vid. PhifTranfaa. vol.XLVIII. her D ow nl oa de d fr om h tt ps :/ /r oy al so ci et yp ub li sh in g. or g/ o n 05 A pr il 2 02 1 C ±63 1 ber onioufes is tooprecarious j. and, befides, fix. to a houle is, probably too large an allowance. Many families now ,haye two houfes to live in. T h e ma* giftrates of Norwich, 101752, took an exadt account of both the number of houles and individuals in that city.. 'f T h e number o f houfes was 7,139, and o f * If this is true, D r. Brakenrldge has alfo over-ratyd the number of people iti England; T h e number of houfes rated to the window tax he had, he fays, been Certainly informed was 690.000. T h e number of cottages not rated was hot, he adds, accurately know n; but from theaccounts giyep in it appeared, that they could not amount to above 200,0O0; and, allowing 6 to a houfe, this would make the number of people in England 5.340.000. But if 5 to a hou’fe fhould be a jufter allowance,1' the number will be 4,450,000. * T he number of people in Scot4 land he reckons j , 500^000, and in Ireland i,Ooo,oeo.--'S-ee a Letter to George Lewis Scott, Efq; Phil. Tranfa^f. vo); X L I$> p. 877. i 756. ' t Vid. Gentleman’s M agatihe for 1752, and Dr. Sharps Comparative hijlory o f the incrsafe , p, 38. In page 58 of this laft work the author fays, that, in order to be fully fa- tisfied about the nUmber of perfpns to be allowed to a family, he procured the true number of families and individuals in 14 market towns, fome of them conftderable for trade and popu- Joufnefs; and that in them were 2 0 ^ 1 families, and 97,611 individuals, or but little more than 4 ! to a family. He adds, that, in order to find the difference in this refpe& between, towns of trade and country parifhes, he procured from divers parts of the kingdom the exatT: number an duals \n 65 country parifhes. T h e number of families was 17,208; individuals76,284 ; or not quite 4 ! to a family.— In the place I have juft referred to, in the Gentleman’s Magazine, there is an account of the number §{ houfes and in O x­ ford exclufiveof the colleges, and in Wolverhampton, Coventry, and Birmingham, for 1750. T h e number of perfons to a houfe was, by this account, 4+ in the two former towns, and 5 .̂ in the two latter. It feems, therefore, to appear that 5 perfons to a houfe is an allowance large enough for London, and too large for England in general. mdivi* D ow nl oa de d fr om h tt ps :/ /r oy al so ci et yp ub li sh in g. or g/ o n 05 A pr il 2 02 1 C 1 0 4 ] individuals 3 6 ,1 6 9 , which gives nearly 5 to a houfe. ------ A nother method which D r. Brakenridge took to determine the num ber o f inhabitants in L o n ­ don was from the annual num ber o f burials, adding 2000 to the bills for omilTions, and fuppofing a 3 0 th part to die every year, In order to prove this to be a moderate fuppofition he obferves th at, according to D r. Halley’s Obfervations, a 34th part die every year at Brellaw. But this obfervation was made too inad­ vertently. T h e num ber o f annual burials there, ac­ cording to D r. Halley’s account, was 1174, and the num ber o f inhabitants, as deduced by him from his T able, was 3 4,000, and therefore a 29th part died every year. Befidesf any one may find, that in reality the T able is conftru&ed on the fuppofition, th a t the whole num ber born, or 1238, die every year y from whence it will follow that a 28 th part died every year. * D r. Brakenridge, therefore, had he attended to this, would have ftated a 2 4 th part as the proportion th at dies in London every year, and this would have taken off 1 5 0 ,0 0 0 from the n u m ber h e has given. But even this rauft be lefs than the ju ft proportion. For let three fourths of all w ho either die in London or m igrate from it, be fuch as have been born in L ondon $ and let the reft be perfons w ho have removed to L on­ don from the country or from foreign nations. * Care fiiould be taken, in confidering D r. Halley’s T able, not to take the firft number in it, or 1000, for fo many ju ft born. 1238, he tells us, was the annual medium of births, and 1000 is the number he fuppofes ail living at one year and under. It was inattention to this that led D r. Brakenridge to his miftake. T h e D ow nl oa de d fr om h tt ps :/ /r oy al so ci et yp ub li sh in g. or g/ o n 05 A pr il 2 02 1 t m 1 . - TChe txpettfttion o f the former, it hasx be^n qannot exceed 20 years* and years haye been al- Ibweci to the l a t t e r . O n e w ith another, then, they will have an expeBationof 22^ years. X |iat is, one o f a 24. will die every year. ^ A n d , confequently, * Tbfe whrild5 hiiiiiber of inhabitants in Rome, in (the' year ¥761, was 1 5 7 4 5 2 ^ ofvwhoda^90,239 were males, and 67,213 females; And the annual medium of births, for 3 years from '1759 to 1761, was $,167, and of burials 7,153. According to this account, therefore, a 2MfW o f the inhabitants dte-iti Rome every year. See D h Short’s Comparative increafe and decreafe 'opmankind in England and \fiveral m n t r m abroad,p. 59, 6o.-H-r-rIn Berlin, as the fame author r e |a t^ , p. 60, in fix years, from 1734 t0 17 4 °’ We annua* medium,or births was 3,504, of burials 3,639; and the number of mha- bitants was <¥8,197; miles 32,990, and females 35>f$7j*f ** m th part,therefore*ofithe inhabitants pf Berlin are buried every year. As numbers, taken, by a d u a l furvey are generally too little, fuppofe, in the jjrefent.inftance, an error committed m reckoning the .number o f Inhabitants,; equal to a lOtH of the whole num ber,’ or to the whole number of children under 3} and fuppofe liteevkife ho omiflirins in the burials; T h e conje- Ueence will.be* that about 1 in 21 are buried at Berlin every year>—— At Dublin, in the year 1695, the numbfr of kihabit- ants was found, by an e x a a furvey; to be 46,508 (febPhilof. Tranfe&ions, N ° 261 )¥ •' I find no I account of the anntal burials juft thatitiinefjjIbufe friom i6 6 i to t 6 8 i , the medium had been 16131 a n f from 1715 to 1748 it was 2123. can, therefore, be n a material error in fuppofing that in focjjj lt was 1800; arid this makes i in 22 to die annually.— M 1745 the-number account laid before the ;jLord ;to be ^,244* It is pro­ bable, this number of families did not confift of more thart 50,ocb individuals. Suppofe them, however, 5 5 ,0'cb; and, as at this time the rnedium of annual-burials appears to have been 1 in 23 died a n n u a l l y f e e D r. Short’s- Comparative Hi/hry, p. 15, and NewObfermtiom, ^ 2 2 8 ; know not bow far thefe fa^ls may be depended on; If they come at all neaif the tru th , they dembnftrate that I have been very moderate in making V o t . L I X . P fuppofing D ow nl oa de d fr om h tt ps :/ /r oy al so ci et yp ub li sh in g. or g/ o n 05 A pr il 2 02 1 [ 106 I fuppofing the annual recruit from the country to be 7 0 0 0 , the num ber o f births 3 times 7 000 or 2 1 ,0 0 a, and the burials and m igrationiz^^ooo (w hich feern to be all high fuppofitions), the num ber o f inhabitants w ill be 22_* multiplied by 28,000, or 6 3 0 ,0 0 0 . I will ju ft mention here one other inftance o f ex­ aggeration on the prefent fubjedl. M r. Corbyn Morris, in his Obfervations on pajl only 1 in 2 2 f, including emigrants, to die in London annually. — — In 1631 the number of people in the city liberties o f London was taken, by order of the Privy Council, and found to be 130^178.— T his account was taken five years after a plague that had fwept off near a quarter of the inhabitants ; and* when, therefore, the town being full of recruits in the vigour o f life, the medium of annual burials muff have been lower than ufual, and the births higher. Could, therefore, the medium o f annual burials at that time, within the walls and in the 16 pa- fifties without the walls, be fettled, exclufive of thofe who died in fuch parts of the ibparifhes without the walls, as are not in the libertiesthe proportion dying annually obtained from bence might be depended on, as rather lefs than the common and juft- proportion. Rut this medium cannot be difeovered with any accuracy. Graunteftimates that two thirds of thefe i<6 pariflies are within the libertiesj and, if this is right, the medium of an­ nual burials in the city and liberties in 1631, was 5,500, and 1 in 2 3 I died annually j or, making a fmall allowance for defi­ ciencies in the bills*, 1 in 22*1......M r. M aitland, in his Hiftory- of London, vol. II. p. 744, by a laborious, but too unfatisfadlory, inveftigation, reduces this proportion to 1 in 2 4 ! } and on the fuppofitions, that this is the true proportion dying annually, a t all times, in London, and that the deficiencies in the burials amount to 3,038 annually, he determines that the number of in­ habitants within the bills was 725,903 in the year 1737. T h e number of burials not brought to account in the bills is probably, now much greater than either D r. Brakenridge or M r! M aitland fuppofe it. I have reckoned it fo high as 6000, in order to include emigrants, and alfo.to be more fare of not falling be­ low the truth.. D ow nl oa de d fr om h tt ps :/ /r oy al so ci et yp ub li sh in g. or g/ o n 05 A pr il 2 02 1 [ 10 7 ] growth afid prefent Jiate of the city of London, pub-' iifhed in 1751, fuppofes that no more than a 6 0 th part of the inhabitants o f London, who are above 20, die every year, and from hence he determines that the number of inhabitants was near a million. In this fuppofition there was an error o f at lead one half. According to D r. Halley’s Table, it has been {hewn, that a 34th part o f all at 20 and upwards, die every year at Breflaw. In London, a 29th part, according to M r. Simpfon’s T able, and alfo according to all other Tables o f London Obfervations. A nd in Scot­ land it has been found for many years, that o f 9 7 4 minifters and profeffors whofe ages are 27 and upwards, a 33d part have died every year. H ad, therefore, M r. Morris ftated a 30th part of all above 20 as dying annually in London, he would have gone beyond the truth, and his conclufion would have been 4 00,000 lefs than it is. D r, Brakenridge obferved, that the number o f in ­ habitants, at the time he calculated, was 127,000 lefs than it had been. T h e bills have lately ad- vancedj but ftill they are m uch below What they were from 1717 to 1743. T h e medium o f the an­ nual births, for 20 years, from 1716 to 1736, was 18,000, and o f burials 26,529 ; and by calculating from hence on all the fame fuppofitions w ith thofe which made 651,580 to be the prefent num ber o f inhabitants in London, it will be found that the number then was 735,8 4 0 , or 84,260 greater than the number at prefent. London, therefore, for th e lif t,$6 years, has been decreafing; and though now it is increafing again, yet there is reafon to think that the additions lately made to the number o f P 2 buildings D ow nl oa de d fr om h tt ps :/ /r oy al so ci et yp ub li sh in g. or g/ o n 05 A pr il 2 02 1 E 108 J buildings round it, are ow ing, in a great measure,, to the incre^fe o f luxury,, and the inhabitants re­ quiring more room to live upon*. It fhould be rem em bered, that the num ber o f in h a­ bitants in London is now fo m uch lefs as I have made: it, than it was 40 years ago, on the fuppofition that th e proportion o f the omiffions in the births to thofe in the burials was the fame then that it is now. But it appears th at this is n o t i b e fid:.-------From 1728, the year when th e ages Mth e dead was firft given in th e bills, to 1742, near five-fixths of thofe who were born died under 1 o, according to the .------- F rom 1742 to 1752 three quarters y and ever finee 1752 this proportion has flood nearly as it is now,, or at fomewhat more than two-thirds* T h e omif- fions in the births,therefore, compared w ith thofe in the burials were greater fo rm e rly ; and this m u ft render the difference between the num ber o f inhabit­ ants now and formerly lefs confiderable than it may ieem to be from the face o f the bills,. O ne reafbn w h y th e proportion of the amounts o f the births and burmk in the bills comes now nearer than it did to $ medium of annual burials in the 07 parifhes within the walls was, From 1655 to 1664, From 1680 to 1690, From 1730 to 1740* From 1758 to 1768, 3264 3^39 2316 1620 T h is account proves, that though, fince 1655, London has, doubled its inhabitants, yet, within the walls, they have de- creafed; and fo rapidly for the laft 30 years as to be now re­ duced to one half.— —T h e like may be obferved of the „ p a . m m immediately without the walls. Since 1720 thefe oa- iiflies have been decreafing fo faft, that the annual b u r ia h m 1 th e D ow nl oa de d fr om h tt ps :/ /r oy al so ci et yp ub li sh in g. or g/ o n 05 A pr il 2 02 1 [ I 0 9 ] tht true proportion, may, perhaps, be that the num ­ ber of DilTenters is confiderably leffened. T h e Foundling Hofpital alfo may have contributed a little to this event, by leflening the number given in the biila as having died under io> without taking off any from the births-, ior ail that die in this hofpital are buried at Pctncrctjs church, which is not within the Sills. See the preface to a collection of the yearly bills of mortality from 1657 to 1758 inclufive,p. 15. 1 will add, that it is probable that London is now become lefs fatal to children than it w a s a n d that this is a further circumftance which mu ft reduce the difference I have m entioned; and w h ich is likewife- neceffary to be joined to the greater deficiencies in the births, in order to account for the very fmall propor­ tion of children who furvived 10 years of age, during, the two ftrft of the periods I have fpecifiedi Since 17 52, London has been thrown more open. T h e cuftom o f keeping country-houfes, and of fending:children to be: nurfed in the country, has prevailed more. But, particularly, the deftrudtive ufe of fpirituous liquors; among the poor has been checked. I have fhewn that in London,, e v e n in its prefent: them have funk from 8^672 to $ 4 3 % and are now lower than they were before the year 1660.* In Weftminfter,.. on the con­ trary, and the 23:out-pariflies in Middlesex arid Surrey, the an­ nual burials have, fince .16:60, advanced from about, 400O to i 6 ,oqo. —- —T hefe fa£ls prove that the inhabitants of Lon­ don are aow much lefs c ro w d s together than they were* I t appears, in particular, that within the inhabitants take as m uch.f06m.to live upon as double their number did formerly. — T he VeryTame'concluTicins may be drawn from an examina­ tion of th e 'christenings..; ftatej. D ow nl oa de d fr om h tt ps :/ /r oy al so ci et yp ub li sh in g. or g/ o n 05 A pr il 2 02 1 [ 1 1 0 ] ftate, and according to the m o d modefate compute}* tion, h a lf the num ber born die under three years o f age ; and I have oblerved that at Breflaw half live to 26. A t E dinburgh, if I may judge from fuch o f its bills as 1 have feen, almofl as great a propor­ tion of children die as even in London. But it appears from Graunfs*accurate account o f the births, weddings, and burials in three country parifhes for 90 years; and alio, w ith abundant evidence, from D r. Short’s collection o f obfervations in his parative Hijlory, and his treatife entitled, New - Jermtions on Town and Country Mortality + 5 that in country villages and pariihes, th e major part live to mature age, and even to marry. So gieat is the difference, efpecially to children, between living in great towns and in the country. But no­ thing can place this obfervation in a more fin k in g light than the curious account given b y .D r. T h o m as H eberden, and publifhed in the Philofophical T ra n f- v * Political O the Bills o f M orta­ lity^ by Captain John Graunt, F . R. S. . J f T h e public is much obliged to this author for the pains he has taken m c o l l i n g obfervations on the. mortality and increafe ^ m a n k in d , m different countries and fix atio n s, Jn his N ew Ubiervations, p. 309, he mentions an ingenious parifh clerk, in the country, who, by a particular account which he took, found that of 314, who had been baptized in his parifh in one year, 80, or nearly a quarter part, died under four years of age! Fortjvfix died the firft y e ar; thirteen the fecond; fixte^n the th ird ; and five the fourth. After four, life grows more liable, and at ten acquires its greateft {lability; and in this cafe it cannot be reckoned that above a iOth, or, at rnoft, an 8th more than the quarter that died under four, would die under t m h y and thereforC> Probab]y> near two-thirds arrived at m a- a&ioits D ow nl oa de d fr om h tt ps :/ /r oy al so ci et yp ub li sh in g. or g/ o n 05 A pr il 2 02 1 [ XXI } actions (vol. L V IL p. 461 J>, oj mortality, of the inhabitants of the ijland of . In this ifland, it feems, the weddings have been to the births> for 8 -years, from 1759 to 1766, as i a to 46.8 j and to the burials as 1 0 ^ 0 2 7 .5 . Double thefe proportions, therefore, or the proportion of 20 to 46.8, and of 20 to 27.5 are the proportions of the number marrying annually,, to the number born and the number dying. L et 1 marriage in 10 be a 2d or 3d marriage on the fide of either the man or the woman y and 10 marriages will imply 19 indi­ viduals who have grown up to maturity, and lived to- marry once or oftener; and the proportion of the number marrying annually the firft time, to the num ­ ber dying annually, will be 19 to 27.5, or near 3 to. 4 . It may feem to follow from hence, that in this iiland near three-fourths o f thofe who die have been married, and, confequently, th a t not many more than a quarter of the inhabitants die in childhood and celi­ bacy 5 and this would be a ju ft conclufion were there no increafe, or had the births and burials been equal. But it muft be remembered, that th e general effedt o f an increafe, while it is going on in a country, is to render the proportion o f perlbns marrying annually to the annual deaths greateryand to the annual births lefs than the true proportion marrying out of any given number born. This proportion generally lies between the other two proportions, but always neared: to the firft * . and, in the prefent cafe, it is fufficiently evident that it cannot be much lefs than two-thirds. * if 3 country where there is no increafe or decreafe of the. ^ a Hants, and where alfo life, in its firft periods, is fo ftablc,, In D ow nl oa de d fr om h tt ps :/ /r oy al so ci et yp ub li sh in g. or g/ o n 05 A pr il 2 02 1 [ 1 1 2 3 ' .m ' t i l L ondon, then, h a lf die under three years o f age, and in M adeira about two-thirds of all w ho are and marriage To much encouraged, as that half all who are born live to be married, the annual births and burials mu ft be equal * and alfo quadruple, the number of weddings, after allowing for 2d and 3d marriages.: Suppofe in thefe circumftanees (every th in g elfe remaining the fame) the probabilities o f , during its ilirft ftages, to, be improved. In this cafe, more than h a lf the born will live to be married, and an iricreafe will take place. T h e births will exceed the burials, arid both fall below quadruple the weddings ; or, which is the fame, below double the number annually married. ----- S u ppofe next ( the and the encouragement to inarritigt- remaining th e fame) the only of the marriages to be improved. In this cafe it .is plain, that an increafe alfo will take place ; but the annual births and burials; inftead of being lefs; will now both rife above quadruple the weddings, and therefore the proportion of the born to that part of the born who marry ( being by fuppofmon two to one) will be dels than the proportion of either the annual births or the annual burials to the number marrying annually.——^-Suppofe again (the encouragement to ■ marriage.remaining./ the fame) that the lities o f life and the prolifeknefs of are both improved. In this cafe, a fnore rapid increafe will take place, or a greater excefs of the births above the burials,; but at the fame time they will keep nearer to q̂uadruple, the weddings, than if the latter caufe only had operated, and produced the fame increafe.— -—I ihould be too minute and tedious, were I to explain thefe obferva- tions at large. It follows from them , that, in every country or fituation where, for a cotirfe of years', the burials have been either equalto or left.than the bifibstand both under quadruple the m arriages; and alfo that wherever the burials are than quadruple the annual marriages, and at the fame time the births greater) there the major part of all th a t are born live to marry. In the inftance which I have confidered above, and which occa­ sions this note, the annual births are fo much greater than quadruple the marriages, and at the fame rim e the annual burials fo much lefs,that the proportion that lives to marry of thofe who are born can fcarcely be much lefs than I have faid, or tw o- thirds. borfi D ow nl oa de d fr om h tt ps :/ /r oy al so ci et yp ub li sh in g. or g/ o n 05 A pr il 2 02 1 t “ S 3 borft live to be married. Agreeably to this, it ap­ pears alfo from the account I have referred to, that th e exp ecta tio n of a child ju ft born in Madeira is about ( o years, or near double the exportation of a child tuft bom in London. For the num ber o f inha­ bitants was found, by a furvey made in the beginning of the year 1767, to be 64,614. T h e annual me­ dium of burials had been, for eight years, 1293 j of births 220 r. T h e num ber of inhabitants, divided by the annual medium of b, gives 49.89, or th e expeBation nearly o f a child juft born, fuppofmg th e births had been 1293, and conftantly equal to the buriahy the number o f inhabitants remaining the fame. A n d the feme num ber, divided by the annual I have {hewn how the allowance is to be made for t i and 3d marriages 5 but it is not fo conftderable as to be of “ m a c u l a r confequerrce •, and,' betides, it is, in part, compenfaml by the na- tufal children which are included in the births* and which raife the proportion of the births to the weddings higher than it ought to bev and therefore bring it nearer to the true proportion of the humber bom annually, to thofe who marry annually, after de- du&m? thofe Virho marry a dd or J d trm e ; In drawing conclufions from the proportion of births and burials in different fixations* fonir^Writers on the increafe Of mankind have not given due attention to the difference m thefe proportions arifing from the different drcumftances o f i n * ereafe or deereafe among a peoples O ne inftance of this I nave m w mentioned * and erne further infhnce of it ti neceffary to be mentioned. T h e proportion- of annual births to weddings has beenconfidered as giving the true number of children derived from each marriage, taking all marriages one with another, feut this is true only when, for rnatty years* the births and bu­ rials have kept nearly, equal. W here there is an excefr of the births occafioning an. increafe, the propottion of mt» s weddings muff be lei's than the proportion of children crive from each marriage * and the contrary hwift take place w ere there is a decreafek V o l . L I X . CL m e d iu m D ow nl oa de d fr om h tt ps :/ /r oy al so ci et yp ub li sh in g. or g/ o n 05 A pr il 2 02 1 f 4 * 4 ] m edium of* births,-gives 29.35, or the expectation of* a child ju ft born, fuppofing the burials 2201, the num ber o f births and o f inhabitants rem aining th e fame 5 and the true expectation of life mu ft be fom e- w here near the mean between 4 9 .8 9 and 2 9 .3 5 . A g ain : A 50th part o f the inhabitants o f M adeira, it appears, die annually. In L ondon, I have fhewn, that above twice this proportion dies annually. In fmaller towns a fmaller proportion dies, and th e births alfo com e nearer to the burials. A t Breda w, I have obferved, that, by D r. H alley’s T ab le , Part dies an n u a lly ; and th e annual m e­ dium o f births, for a complete century, from *®33 Jo 1734> has been 1 0 S 9 ; of burials 1256. J A t N orw ich, the annual m edium o f births, dif- fenters included, for four years, from 1751 to 1 7 5 4 , A 1* 0 y 1214* A nd as the num ber o f inhabitants was at that tim e 36^169 /fee pag. 1 0 5 ) a 30th part o f the inhabitants died annually. In ge­ neral, £ there feems reafon to. think that in tow ns (allow ingforparticular advantages o f fituation, trade, police^ cleanlinefs, and opennefs, w hich fome towns may have), the excels o f the burials above the births and the annual deaths are m ore or lefs as the towns are greater or fmaller. In L ondon itfelf, about 160 years ago, when it was fcarcely a fourth part o f its pre- lent bulk, the births were nearly equal to the burials. ? 10r£ f Q p p m t m i pt 63. And the, n $ \ ^ T r , v o h V /I. part iv, s a t e s a s M i . « 2 *• But D ow nl oa de d fr om h tt ps :/ /r oy al so ci et yp ub li sh in g. or g/ o n 05 A pr il 2 02 1 t I But in country pariflies and villages the births almoft always exceed the burials f a n d I believe it feldom happens that fo many as a 30th, or much more than a 40th part o f the inhabitants die annually*. ' In the four provinces o f N ew England there is a very rapid increafe of the inhabitants: but, notwithftanding this, at Bofton, the capital, the inhabitants would decreafe were there no fupply from the c o u n try : for, if the account I have feen is juft, from 1731 to 1762, the burials have all along exceeded the births+. So remarkably do towns, in confequence of their un- favourablenefs to health, and the luxury which ge­ nerally prevails in them, check the increafe o f countries. * la 17 3^ there was art account taken of ihe number of fa ­ milies and inhabitants in the Prulfian dominions. T h e number of inhabitants was 2,138,465. T h e medium of annual births, weddings, and burials was nearly 8 4 ,0 0 0 ; 21,000, and 5 5,481. Near a 40th part, therefore, died every year. Vid. D r. Short's Comparative Hi/lory, p. 69, and Abridgment Tranfaftions, ibid. -T h e proportion of weddings and burials to the births (hews that, in thefe countries, there was a quick in­ creafe, notwithftanding the wafte in the cities.------ In the year 1733 a furvey was taken of the inhabitants of the parifbof Stoke' Damerel in DevonJhire,and the number of men, women, and children, was found to be 3361."-*- T*he chrijlenings for the year were i22— — the weddings- 28—— burials62.-——N om ore,there­ fore, than the 54th part of the inhabitants died in the year.-___ \ n o f this year an epidemical fever prevailed in the parifli. See Martyn’s Abridgment o f the Tranfaflions> vol. IX . P*325*7 According to Graunt's account of a parilh in Hampfinre, not reckoned, he fays, remarkably healthful,, a 50th . part of inhabitants had died annually for 90 years. Natural and Political Obfervations> bV. Chap. xii. f See a particular account of the births and burials in this ' town Irom 1731 to 1732 in the Gentleman's Magazine for 1753, F’ 4' 3' Q H ealth- D ow nl oa de d fr om h tt ps :/ /r oy al so ci et yp ub li sh in g. or g/ o n 05 A pr il 2 02 1 [ 3 H eakhfulnefs and Prolificknefs arc, probably, caufes o f increafe feldom feparated, In conform ity to this obiervation, it appears from com paring th e births and weddings, in countries and towns w here regifters of th em have been kept, that in the former, marriages* one w ith another, feldom produce lefs th a n four children each j generally between four and five, and fometimes above five* But in tow ns feldom above f o u r ; generally between three and four and fometimes under three % I h a te fometimes b eard the great num ber o f o ld people in L ondon mentioned to prove its favourable- nefs to health and long life. But no obfervation can be m uch more erroneous* T h e re ought, in reality, to be more old people in London, in proportion to th e num ber o f inhabitants, than in any fmaller to w n s, becaafe at lead one quarter o f its inhabitants are perfons w ho come into it, from th e country, in th e m o d robuft part o f life, and w ith a m uch greater probability o f attaining old age, than if they had com e into it in -the weaknefs o f infancy. But, no tw ith - ftanding this advantage, th e re are m uch fewer per­ fons w ho a tta in to great ages in L ondon th a n in any other place w here obfervatioos have been made.— - A t Vienna, of 2 2 ,7 0 4 w h o died in the four years * A nyone may fee what evidence there is for this, by con- fulling the accounts in I > . Short’s tw o books already quoted* and iV the AbMgment o f the Philof , vol. V I I . part iv. p. 4 6 .—Inconlidering thefe accounts, it fhould not be forgotten that allowances m u l be made for the different circum - ftances of increafe or decreafe in a place, agreeably to the obfer­ vation a t the end of the note in pag* 113. I7I7> D ow nl oa de d fr om h tt ps :/ /r oy al so ci et yp ub li sh in g. or g/ o n 05 A pr il 2 02 1 [ » 7 ] 171 Jr, 1718, 1724, 1725 J 09 readied 90 years* that is, 48 in 20,000. But in London, for the k ft 30 years, only 35 o f the faihe num ber have reached this age.----- - A t Breflaw it appears, by Halley's Table, that 41 o f 1238 born, or a 30th part, live to be 80 years o f age.-------In the parifla of Jitt-faiffis in N ortham pton an account has been kept for m any years of the ages at which all d ie ; and, I £nd, that of 1377, w ho died there in, 13 years, 59 have lived to be 8o, or a 23d part.--— - According to M r. Kerffeboom’s Table of Obferva- tions, published at the end o f the laft-edition o f Mr. D e Motvre’s Treatife on the D o d rin e of Chances, a 14 th part of all that are born live to be 8 0 ; and, had we any obfervations in country purifhcs, this, probably, would not appear to be too high a proportion But in London, for th e Jaft 30 years, only 2.5 o f every to b o * Vid* Abridgment of the Pkilofbphical TrjmfaAioBs, v d . VII. part iv. p*. 46* ——— It appears-aHo that more than three-fifths of all who died in thefe years at Vienna were boys and girls, by whom, I fuppoffc, are meant perfons under f6 . About the fame proportion dies under r6 at Berlin. t In this town, us in molt other tow ns of any magnitude, the births, including Di{Tenters, fall fhort of .the- burials 4 ' and the greater part die under age, X T his, however, will appear Itfelf ittconfiderable, when horn- pared with the following accdunt: “ In the burials in ** thediftrifl; of ChrifHana, in Norway, amounted to 6,929, and “ the chriftenings to 11,024. Among thofe who died, 294, or w i in 18, had lived to the age of 90 ; 63. to the age of 100, and “ fevento the age of 101.------ In thedioqcfe ofB ergen^the per- K fobs who died amounted only to 2,580, of whom r8 lived to- the age of 100 j one woman to the age of 204, and another M womain to the age of to8.** •See the Annual Rtgifiet, for 17^ 1, p. t o x. ; D ow nl oa de d fr om h tt ps :/ /r oy al so ci et yp ub li sh in g. or g/ o n 05 A pr il 2 02 1 C 118 ] w ho have died, have lived to be 80, or a 4 0 th part $ w hich may be eafily difcovered by dividing the fum o f all who have died during thefe years at all ages, by the fum of all who have died above 80. A m ong the peculiar evils to which great towns are fu b jed , 1 m ight further mention the plague, Be­ fore the year 1666 this dreadful calamity laid L o n ­ don altnoft w ade once in every 15 or 20 y ea rs; and there is no reafon to think that it was not generally bred within itfelf. A moft happy alteration has taken place, w hich, perhaps, in part, is owing to the greater advantages o f cleanlinefs and opennefs, which London has enjoyed fince it was rebuilt, and which lately have been very wifely im proved. T h e fad s I have now taken notice of are fo im ­ portant that, I think, they deferve more attention than has been hitherto bellowed upon them . Every one knows that the d ren g th of a date confifts in the n u m ­ ber o f people. T h e encouragem ent o f population, therefore* ought to be one o f the firft objeds o f policy in every d a te ; and fome o f the w o rd enemies o f population are the luxury, the licentioufnefs, and debility produced and propagated fey great towns. I have obferved that London is n o w * increafing. But it appears that, in truth, this is -an event m ore to be dreaded than defired. T h e more London in- * T h is increafe is greater than the bills (hew , on account o f the omiflion in them of the two parifhes which have been molt* encreafed by new buildings; I mean Marybone and Pancrafs pa-v rilhes. T h e former of thefe parilhes is, I fuppofe, now one of the largeft in London. creafes, D ow nl oa de d fr om h tt ps :/ /r oy al so ci et yp ub li sh in g. or g/ o n 05 A pr il 2 02 1 C ” 9 3; creafes, the more the reft o f the kingdom muft b ed e - ferted; the fewer hands m uft be left for agriculture ; and, consequently, the Jefs muft be the plenty and the higher the price of all the means of fubfiftejice. - ■— Moderate towns, being feats of refinement, emu­ lation, and arts, may be public advantages* But great towns, long before they grow to half the bulk of London, become checks on population of too hurtful a nature, nurferies of debauchery and volup- tuoufnefs; and, in many refpe&s, greater evils than can be compenfated by any advantages * T h e mean annual births,weddings ̂ and burials in the fol­ lowing towns, for fome years before 1768, were nearly, Births* Weddings. Burials. A t Paris, — 19,200 — 4 300 — 19,500 Vienna, — 5,600 ~ — 6,800 Amfterdam, — 4,500 — 2,400 — 7,600 Copenhagen, — 2,700 — 868 —> 3,100 In the Paris bills there is, I am informed, an omiffion o f all that die in the Foundling Hofpital,amounting to above 2000 an­ nually. T h e excels, therefore, of the burials above the births’' is greater than the bills fhew. T his excefs, however, is mtich leis than could have been expected in f o l a t e a town. I am not Jure to what caufe this oughtxto be afcribed ; but Icannot wonder at it, if it be indeed true* th a t a fifth of all born in Paris ^re fent to the Foundling Hofpital, and that a third of the inhabitants die in hofpitals, and alfo that all married men are excufed from fervirig in the militia, from whence draughts are made for the army. Thefe are encouragements to marriage and population, which no other city enjoys j and it is ftrange that in this kingdom fome policy of the fame kind with that laft mentioned ftiould not be purfued.-—— A further fingularity in the ftate of Paris is, that the births in it are above four times the weddings, nothing like which is the cafe in any other town wbofe bills 1 have feen. It may feem, therefore, that here, as well as in the moft healthful D r. Heberdeu D ow nl oa de d fr om h tt ps :/ /r oy al so ci et yp ub li sh in g. or g/ o n 05 A pr il 2 02 1 [ 1 2 0 ] D r. H eberden obferves fhat, tn Madeira* the in* habitants double their own num ber in 8 4 years. But and Increafing country parishes, each marriage produces more than four children j but this is a cohcfufion which, in the pre­ sent cafe, cannot be depended on. I t fhould be confidered that, probably, fame who leave the cou ntry to fettle at Paris, come it already marned j and th at no fmall proportion of th e births may be illegitimate* Thefe caufes, however, may only* balance the allowance to be made for the fecond and third marriages among the annual weddings }, and, if it is indeed* fa& , that the people at Paris are fo prolific as they appear to be in the bills, it will only prove more ftrongly th at, like other great towns, it is very unfavourable to h ealth ; for the more prolific a people are, the greater muft be the mortality aftipng thenf if they do ndt increafe* “ — — L et us fuppofe the true number of deaths at Paris, in* eluding emigrants and fuch as die in the Foundling , to be 2 J,000} th e number married annually 2 .*4,300-; or 8,6006 } and the births, as before, 19,200., 1,906 then will b e th e n u m - ber of annual recruits from the couritfy. O f thefe let only 1,200 be fupfpofed to marry : - %n d 5 8,666 lefiened by 1,200, or 7V40©, will*be the number o f fchofe born at Paris who r r a rry annually ;s and 11*800, or aboyo..tb^eerjiftht will be th e number ^Xina*n childhood and celjbacy. T h is, though it gives an un* favourable reprefentation of Paris when compared w ith the country, makes it appear to advantage when compared with fonae other g reat towns. .1 am not fofiicientl# informed of the ftate of Paris to know how near this calculation3 Gomes to the truth. E very fuch doubt would be removed, were the ages of the dead given in the Paris bills* I t is much to be wifhed this was done* T h e births and burials here come fo near to one another, that there can fcarcely be a properer place for fuch bills j and a T able of Obfervations might be formed from them that would give the values of lives much more exactly than the London Tables* I cannot help adding th at, excepting the omiffion I have mentioned in the burials, the Paris bills are complete * but it is wen known that the London bills are extremely otherwife. London, therefore, m uflbe much larger in companion of Paris than it appears to be in the bills, th k D ow nl oa de d fr om h tt ps :/ /r oy al so ci et yp ub li sh in g. or g/ o n 05 A pr il 2 02 1 C ' * ■ ] this (as you, Sir, well know) is a very flow increafe compared with that which takes place among our colonies in A m e r i c a . In the back fettlements, where the inhabitants apply themfelves entirely to agricul­ ture, and luxury is not known, they double their own number in 15 y ears; and all through the nor­ thern colonies in 25 years* T his is an inftance o f increafe fo rapid as to have fcarcely any parallel. T h e births in thefe countries muft exceed the burials m uch more than in Madeira, and a greater proportion o f the born muft reach m aturity.----- - I n 1738, the num ber of inhabitants in N ew Jerfey was taken by order o f the government, and found to be 47,369V Seven years afterwards the num ber of inhabitants was again taken, and found to be increafed, by procrea­ tion only, above 14,000, and * very near one of the inhabitants were found to be under f 16 years o f age. In 22 years, therefore, they muft have doubled their own number, and the births m uft have ex ­ ceeded the burials 2000 annually. As the increafe here is much quicker than in Madeira, we may be Hire that a finaller proportion of the inhabitants muft die annually. L et us, however, fuppofe it the fame, or a 50th part. T his will make the annual burials * See a difcourfe on Chrijlicn by D r. Styles, Bofton, 1761, p. 103.109, &c.— See alfo o f Great Britain confidered with regard to herColonies , together with Obfervations concerning the increafe o f mankind, p. 3$. 2d edit. London, 1761. * According to Dr. Halley’s Table the number of the living under 16 is but a third of all the living at all ages j and this may be nearly the cafe in all places which juft fupport themfelves in the number of their inhabitants, and neither increafe or decreafe. VolvLIX. R lo D ow nl oa de d fr om h tt ps :/ /r oy al so ci et yp ub li sh in g. or g/ o n 05 A pr il 2 02 1 [ 1 2 2 ] to have been, during thefe feven years, 1000, ®n<* the a n n u a l births 3000, or an 18th part o f the inha­ bitants.-------Similar obfervations may be made on the m u c h quicker increafe in R hode Ifland, as related in the preface to D r. Birch’s of the bilk of mortality, and alfo in the valuable pam phlet, latt quoted, on the interejl of Great Britain vpith regard to her colonies, p .'36.------- W h a t a prodigious differ­ ence m ull there be between the vigour and the h ap - ninefs o f hum an life in fuch fixations, and in fuch a place as London? — T h e original num ber o f perfons who, in 1643, had fettled in N ew E n g an , was 21,200. E ver fince it is reckoned, th at more have left them than have gone to th e m * . In the year 1760 they were increafed to h alf a m illion. T h ey have, therefore, all along doubled their ow n num ber in 25 years; and, if they continue to in­ creafe at th e fame rate, they will, 70 years hence, in N ew England alone, be fo u t m illio n s; and m all N o rth America above twice the num ber o f inhabit­ ants in G r e a t- B r ita in f .------- But I am w andering * See D r . Styles’s pamphlet juft quoted, p . i i o , &c. x T h e rate of increafe, fuppofitig tbe procreative powers the fame, depends on two caufes: T h e ‘^encouragem ent tc► mar- « r i a g e a n d the “ expectation o f a th ild juft born. W h e n one of thefe is given, the increafe will be always in proportion to the other. T h a t is j As m u c h gW tefi as the ratio is of the numbers who reach maturity, hnft o f tftofe who marry to the number boro, fb much quicker or Jfotver wfll the incream 1 * I*et us/uppofe the operaiioh d f thefe bitffes fiteh as to produce an in n u alcx cefs of the births above the equal to a 36:11 part ©f the whole number of inhabitartfM3GIt may feem to follow from hence, that the inhabitants ^ b u ld double their own number 'in 36 years * and thus fome haVe caltuktedO ‘ But the tru th is, that they would double theit own ivutnber in much lefs time, from D ow nl oa de d fr om h tt ps :/ /r oy al so ci et yp ub li sh in g. or g/ o n 05 A pr il 2 02 1 t the period of doubling will be the quotient produced by dividing the logarithm of 2 by the difference between the logarithms of r 4- 1 and r , as might be eafily demonftrated. In the prefent cafe, being 36, and r-f- t being 37, the period of doubling comes out 25 years. I f is taken equal to i 2, the period of doubling will be 15 y e ars.-— • But it is certain that this ratio may, in many fixations, be greater than j l ; and, inftead of remaining the fame, or becoming lefs, it may4iHcreafe, the confequence of which will be, that the period of doubling will be (hotter than this rule gives it.-*-— Accord­ ing to D r. Halley’s Table,, the number of perfons between 20 and 42 years of age, Is a third part of the whole number living at all ages* T h e prolific part, therefore, of a country may very well be a 4th of the whole nnfnber of inhabitants } and fup- pofing four of thefe, or every other marriage between perfons all under 42, to produce one birth every year,, tlic annual number Of births will be a 16th part of the whole number of people; and, therefore, fuppqllng tfie burials to be a ^ 8 th part, the an­ nual excefs of the births. above the burials will be a 24th part, and the period of doubling i f years.-— T h e number of inha­ bitants in New England was, as I have faid from D r. Stiles’s pamphlet, half a million in 1760. If they have gone oh in- creafing at the fame rate ever fince, they muft be now 640,000} and it feems to appear that,in Fa<5t they are now more thari this number, Fpr,, fince {h av e writ the above obfervations, t'have feen a particular | r o u n ^ | d J ohGfuffey s lately taken with 4 yiew, to4ta^aUqnVand fpr other purpofes, of the number of males, betyyeep 1 6 and 60, in the four provinces. According tob, thist Recount, the number of fuch males is 218*000. :-:: T h e p e o p l e , therefore, between 16 ai.d 60, 1^ females* rtiiuft be hearly D ow nl oa de d fr om h tt ps :/ /r oy al so ci et yp ub li sh in g. or g/ o n 05 A pr il 2 02 1 - it j] to b ^ a |t h f o l n ^ nunabec o f ̂ nhabitants, and its I in- l l ^ n c e on population.; T h e obfervations I have m od is to be made o f the lights afforded by the London bilk, and ferve as a fpecimen o f the proper m ethod o f cal­ culating from them . It is. indeed extrem ely to be (bey were lefe impferfeff than they are, p‘nd extended further. M ore pariihes round London m ight be taken into th e m ; and, by an eafy im prove­ m ent in the pariffi regiffers now kept, they m ight be 4.20,000, In order to be mere fore of avoiding excels, I will call the)n only 400,000. In p r . Halley’s T able the proportion o f all the-living under 16 and above 60, to the reft of the living, a ttt this will foake thb number of people now Jiving in the four provinces of N ew England to be 6 6 6 ,ooq. B ut, on account of the rapid increafe, this proportion mu ft be con fiderably greater in New England^, than-that given by D r. Halley s Table. In N ew jerfey, I have faid the nunfoer of r^ w a i found to be aim oft equal to the number abpvo 16, Suppofe, however^ that in N ew England, where the increafe is fomewhat flower^ the proportion I have mentioned is on y 16 to 20, and then the whole number of people will be I cannot conclude this note without adding a remark to re- move pn o ty ^ f o n w h ic h may occur to fome in reading D r. He- eipen s account pf Madeira, fo which I have referred. In that account 5945 is given as the number of children under feven in theintand, at the beginning of the year 1767." T h e medium of annual biiths, fo ̂ eight years, had been 2201 j of burials 1202;. n fix years, therefore, 13,206 muft have been born ; and if, at the end of fix years, no more th?n cqAc o f thefe were alive, l 2 i o muft hav^ died mfyear. i T K t almoffalV the b u - n a s in the ifland, for fix ydarsj muft hgve been burials of C , rf ,f tinder feven .Jears (if :;ageiij£'TM4: plainly incredible : * ere ore* 1C feems cprtaih, that the number of children under feven years of age muft, through fome miftake, be given, M itfut account,, 3000 o r4000 too little. ^ extended D ow nl oa de d fr om h tt ps :/ /r oy al so ci et yp ub li sh in g. or g/ o n 05 A pr il 2 02 1 [ I 2 5 jO extended through all the pariihes4 and towns in the kingdom. T h e advantages arifing From hence would be very con fide rable. It would give the precife law according to which human life waftes in its different ftages, and thus fupply the neceffary for com­ puting accurately the values o f all life-annuities and reverfons. It would^ like wife, (lie w the different degrees o f healthfulnefs of different fituations, mark the progrefs of population from year to year, keep always in view the number o f people in the king­ dom, and, in many other refpeds, furnifh inftruc- tion of the greatefl importance to the ffate. M r. De Moivre, at the end of his book on the. dodrine o f chances, has recommended a general regulation o f this k in d ; and obferved, particularly, that at lead ft is to be wifhed, that an account was taken, at proper intervals, o f all the living in the kingdom, with their ages and. occupations j which would, in Tome degree, anfw er modi o f the purpofes I have mentioned.— —But, dear Sir, I am fenfible it is hieh time to finifh thefe remarks. I have been carried in them far beyond the limits I at fird intended. I al­ ways think with pleafure and gratitude o f your friend- fliip* T h e world ow fs to ypu many important dis­ coveries i and your name m uff live as long as there is any knowledge of philofophy among mankind. T h at your happinefs in this, and every other refped, may continually increafe, is the fincere wifh of, Newington-Green, April 17.69. Your much, obliged,, and very humble fervant, Richard Price. X V II. Dijfertatk D ow nl oa de d fr om h tt ps :/ /r oy al so ci et yp ub li sh in g. or g/ o n 05 A pr il 2 02 1