date

[154b-420] Numbers Assumptions
[154b-420]

Numbers

Assumptions

7. The ratio of the numbers of the different ages taken out of the community by death to the numbers left remaining in it alive, is not the same as between age and age: some of the ages losing from this cause, within a given portion of time more of their numbers than others, in the proportions observed is according to the rate of mortality in France, as reported by D r Hutton in his Mathematical Dictionary.

8 The number assumed for the total number of the numbers of the given community of all ages is 500,000 supposed for the purpose of calculation to be 500 000.

9. The proportional numbers as between age and age are those which are exhibited in the ensuing Table now given in Column [\ZS\] the same being respectively the observed numbers observed to be in existence /found existing/ in a total of 851 Paupers, composing the stock of 31 Parishes, according to a Census reported by Sir Frederic Eden in his Book intitled The State of the Poor 3 Vols 4 to London 1797.
Similar Items
  • Title: [[154b-418] Numbers Assumptions]
    Description: [154b-418]

    Numbers

    Assumptions

    Assumptions /Suppositions/ or Positions assumed

    1. A certain community is given (viz: of the community of Paupers or Burthensome Poor maintained at the public expence throughout South Britain such part as is composed of persons of all ages from birth to one and twenty years complete inclusive)

    2. A period of 21 years is assumed (viz: from 1 Jan y 1800 to 31 Dec. r 1820 both inclusive) at the commencement of which period, all persons on that day, members of the given community, are to be placed in a certain situation, as likewise all persons successively becoming members thereof during the given period, which persons are to be discharged from the situation in question, on the several days on which they respectively attain the age of 21 years compleat, and /but/ not before.
  • Title: [Title of Accumulation Table Apprentice]
    Description: Title of Accumulation Table

    Apprentice-Accumulation-Table: Shewing the numbers of Pauper Apprentices that would be accumulated in the different Years of a Period of 21 Years from 1 Jan. 1800 to 31 Dec r 1820 inclusive on the following Suppositions viz:

    1. The whole number of Paupers existing in the Country on the 1 Jan: 1800 under the age of 21 to be taken in on that day on the footing of Apprentices.

    2. Every such Infant Pauper to continue on the footing of an Apprentice till his or her arrival at such his or her Age of maturity, and no longer.

    3. Total number that would be received on that footing on the 1 Jan. y 1800 supposing the whole number to be received of Paupers of all ages to be 500

    3. Total number of /to be 500/ Paupers in South Britain for the 1 st & every other year of the period 500,000

    4. N o of Paupers of the respective ages under 21 as in Column 1 of the Table: the same being respectively to the above /being respectively to the/ total of 500000, in a proportion deduced from a Census of 851 Paupers, standing upon the list of /belonging to/ 31 Parishes, as exhibited in [...?] on the Poor 4to Vol.II.& III. London 1797
  • Title: [[154b-436] Numbers Propositions]
    Description: [154b-436]

    Numbers

    Propositions

    Illustration

    Let that period be a year: let the day of observation be the supposed day of the opening of the supposed institution - viz: 1 Jan y 1800: and let the observed number be 36500.

    The number born in the state in question in the course of the year can not have been the 36500 and no more: had that been the case, there could have been no deaths in all that time among individuals of that tenderest of all ages. The number born must have been that number which after whatever reduction it had suffered from the defalcations made by death, still amounted to the observed number observed.

    Let the rate of mortality be as before the rate indicated by Halley's Brislane Table: according to this Table in the compass of the given period - a Year - out of every 1000 there die 145. To get the total of the numbers existing in the community in question of the age in question in the course of the year of which the day in question is that last day, we must add to the observed number viz: 36500 145 for every thousand in the observed number 145 x 362 = 52922

    which being added together makes 417922

    N.B. This therefore makes the real disproportion between the numbers born the 1 st Year and the Numbers left alive at Age 2 so much greater than what the observed numbers of those ages would give it.