I am not in the least acquainted with the subject on which your
papers[148] treat, but that is no reason why I should not mention what
appears to me defective. In page 8[149] you add 1/6 to the births for
probable omissions, and 1/12 for deaths; but you do not tell your reader
why these proportions are taken rather than 1/4 or 1/3, nor can I
discover on what grounds those numbers are chosen.
You sometimes take averages from the known facts of certain years; but
your averages are formed on an arithmetical ratio while your application
is to a geometrical series. I submit whether this is correct.
If, as you say in page 14[150], births are to burials as 47 to 30, and
the mortality as 1 to 47, the addition to the population would be little
more than 1/82 instead of 1/83, for out of every 1410 persons 30 would
die and 47 would be born, and consequently there would be an increase of
17; but 1410 divided by 17 is 82.94, or 83 nearly; and therefore, if
1410 gives an increase of 17, 9,287,000 will give an increase of
111,970, or 1,119,700 in ten years, which will raise the population
9,287,000 + 1,119,700 = 10,406,700 instead of 10,483,000[151].
In page 16[152] the mortality is supposed to be as before, 1 in 47, and
the births to the population as 1 to 29-1/2, and the population to be
9,287,000. This latter sum divided by 29-1/2 gives 314,813 the annual
number of births, and divided by 47 gives 197,595 the annual number of
deaths; deduct one from the other (197,595 from 314,813) gives 117,218
for the annual increase, which in ten years would be 1,172,180, which
added to the former population of 9,287,000 gives 10,459,180 instead of
10,531,000.
I have marked in pages 35 and 36 some very trifling errors. These are
all I can discover with the facts which are before me.
Ever truly yours,
DAVID RICARDO.
_8 Feb., 1817._