he doctrine marks a critical point in political economy. Malthus's
opponents, as Mr. Bonar remarks,[217] attacked him alternately for
propounding a truism and for maintaining a paradox. A 'truism' is not
useless so long as its truth is not admitted. It would be the greatest
of achievements to enunciate a law self-evident as soon as formulated,
and yet previously ignored or denied. Was this the case of Malthus? Or
did he really startle the world by clothing a commonplace in paradox,
and then explain away the paradox till nothing but the commonplace was
left?

Malthus laid down in his first edition a proposition which continued
to be worried by all his assailants. Population, he said, when
unchecked, increases in the geometrical ratio; the means of
subsistence increase only in an arithmetical ratio. Geometrical ratios
were just then in fashion.[218] Price had appealed to their wonderful
ways in his arguments about the sinking fund; and had pointed out that
a penny put out to 5 per cent. compound interest at the birth of
Christ would, in the days of Pitt, have been worth some millions of
globes of solid gold, each as big as the earth. Both Price and Malthus
lay down a proposition which can easily be verified by the
multiplication-table. If, as Malthus said, population doubles in
twenty-five years, the number in two centuries would be to the present
number as 256 to 1, and in three as 4096 to 1. If, meanwhile, the
quantity of subsistence increased in 'arithmetical progression,' the
multipliers for it would be only 9 and 13. It follows that, in the
year 2003, two hundred and fifty-six persons will have to live upon
what now supports nine. So far, the case is clear. But how does the
argument apply to facts? For obvious reasons, Price's penny could not
become even one solid planet of gold. Malthus's population is also
clearly impossible. That is just his case. The population of British
North America was actually, when he wrote, multiplying at the assigned
rate. What he pointed out was that such a rate must somehow be
stopped; and his question was, how precisely will it be stopped? The
first proposition, he says[219] (that is, that population increased
geometrically), 'I considered as proved the moment that the American
increase was related; and the second as soon as enunciated.' To say
that a population increases geometrically, in fact, is simply to say
that it increases at a fixed rate. The arithmetical increase
corresponds