The elements of vital statistics / by Arthur Newsholme.

  • Arthur Newsholme
Date:
1899
Catalogue details

Licence: Public Domain Mark

Credit: The elements of vital statistics / by Arthur Newsholme. Source: Wellcome Collection.

    22/380 (page 8)
    previous iuterceusal period, that is, that the population increases in geomelrical progyession, Tlie problem is therefore one in compound interest. Let the net Jvnnual rate of increase per unit of population he represented by r. Then 1 at the l)eginning of a year will be 1 + r at tlie end of the same year or the beginning of the next year. Similarly, if the same rate of increase contiiuie, the population at the end of the 2nd year = (l +?)^, „ ,. „ 3rd year = (1+r)3, ,, ,, ?ith year = (1 + If Ave commence with population P, the population at the end of the ni\\ year = P(l + r). , The value of r can be ascertained if we know the population at the two last consecutive census enumerations. Tims if P'= population at the census 1891, P ^- „ „ „ 1881, P =P(1 Taking the logarithm of each side of the equation, log. P' = log. P+lOlog. (l+r), :. log. (l+ r) = TVaog.P'-log.P). Whence 1 + r is easily obtained from a table of logs. For example, if the census population of a town is 32,000 in 1881, and 36,000 in 1891, what is the mean population in 1895 ? (a) First find the rate of increase in 1881-91. Here P= 32000, P' = 36000, log. P' = log. 36000 = 4-556303, log. P =log. 32000 = 4-505150, log. P-log. P=-051153, ^VUog P'-log. P) =-0051153 = log. l+r. {!)) Aptply this to the increase in the next i\ years. Here P--P (l+r) V' (isn5) (1891) log. P = log. 36000 + Y- log. (1 4 r), (1895) = 4-556303 +V (-0051153), = 4-556303 +-0217400, = 4-578043. And from the table of logs, the population corresponding to this number = 37848 = population at the middle of 1895.