in which P 0 is the population today
and ris the rate of increase. These equa-
tions are further modified for population
growth statistics, but such intricate cal-
culations are not within the scope of this
book. (For more about population growth
and biology, see above.)
Who were John Grauntand Sir
William Petty?
English statistician John Graunt (1620–
1674) is generally considered to be the
founder of the science of demography,
which is the statistical study of human
populations. In 1661, after analyzing
some major statistics of the London pop-
ulace, he wrote what is considered the
first book on statistics, Natural and Polit-
ical Observations upon the Bills of Mor-
tality.
The “Bills of Mortality” refers to the
collections of mortality figures in London, a city that had suffered greatly from the out-
break of several plagues. Because the king wanted an early warning system of new out-
breaks, weekly mortality records were kept, along with the causes of death. Based on this
information, Graunt made an estimate of London’s population that is thought to be the
first time anyone interpreted such data; it is therefore considered by some to mark the
beginnings of population statistics.
Graunt’s work influenced his friend, Sir William Petty (1737–1805). (He also
influenced Edmond Halley, the astronomer and discoverer of Comet Halley; for more
about Halley, see “Mathematics in the Physical Sciences.”) Petty’s work was a bit more
practical (and political): he wanted to set up a central statistical office for the English
crown in order to make estimates about the sum of England’s overall wealth. His unusual
approach was to assume that the national income was the same as the total national con-
sumption. He didn’t forget about the plague, but added estimates of losses to the national
economy due to the plague. From there, he suggested that modest investment by the
state to prevent deaths from plague would produce abundant economic benefits.
What is a logistic equation?
A logistic equation (resulting in a curve on a graph) represents the exponential
increase in numbers of a species until it reaches the carrying capacity in its specific 319
MATH IN THE NATURAL SCIENCES
Sir William Petty was a practical mathematician who
wanted to establish a national statistics office in
England that, among other studies, could calculate
economic losses and benefits due to the plague.
Library of Congress.