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9
by compound instead of by simple interest only. Instead
of taking the difference between the population
enumerated in 1861 and 1871, the difference between
the logarithms of those numbers affords the true method
for ascertaining the rate of increase. The article
concludes with the following paragraph :—
" It is scarcely necessary to repeat in conclusion that
in an increasing population each year's increase is larger
than that of the preceding year, and that any method
of calculation which assumes that the annual increase
throughout a decade is equal must be fallacious. The
calculation of the true annual rate of increase, which
is so simple by logarithms, would cover acres of paper
by common arithmetic; this will be apparent to anyone
who realises the fact that the annual rate is the tenth
root of the rate of increase in ten years."
Now, as before stated, the population of Bethnal
Green in 1871 was 120,104, and in 1861 105,100, the
logarithms of these two numbers respectively are
5*0795574 and 5*0216030, the difference between them
is *0579544, which is the logarithm of the rate of increase
of population during the ten years 1861 to 1871.
Seven-tenths and a fortieth of this logarithm (for the
seven and a quarter years since the 1871 census)
amounts to *04201694, and this, added to the logarithm
of the population in 1871, amounts to 5'12157444,
which is the logarithm of the population in the middle
of 1878, and the number to which is 132,304.
Strictly according to the Registrar-General's plan this
would be the estimate of the population for Bethnal