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36
Annual Report of the London County Council, 1914.
the cases of cerebro-spinal fever giving a history of suffering from influenza, within 7 days of onset of
symptoms of cerebro-spinal fever, reveals the fact that of 27 such cases all except 5 were within the age
period 15—45; it is therefore obvious that any correction which might be made, to eliminate as far as
possible sources of error arising from the lack of precise knowledge of the age incidence of attack of influenza,
would tend to reduce the "probability" values which it is desired to obtain. The figures shown
in column 2 of the following table have therefore been calculated on the assumption that the cases of
influenza occurring in the London population were proportionate to those occurring among members
of the Council's staff.

In explanation of the table, it may be stated that column 2 shows the number of cases of influenza
occurring among 3,000 of the Council's staff in each week; column 3 shows the result of applying the
figures in column 2 to the London population, and gives the estimated number of cases of influenza in
each week which might be expected to have occurred in the London population; column 4 shows the
proportion of the London population attacked in each week, based on the figures shown in column 3,
the fractions representing this proportion express the probability that a case of cerebro-spinal fever
selected at random in the corresponding week will give a history of recent attack by influenza; column
5 shows the number of cases of cerebro-spinal fever occurring in each week and column 6 the number of
these cases giving a history of suffering from influenza within 7 days; column 7 shows the probability
of each of the occurrences shown in column 6. The facts shown in columns 5 6 and 7 of the table are
exhibited graphically in sections I. and II. of diagram (Y).
It will be seen from the table that in 13 out of the 20 weeks investigated cases of cerebro-spinal
fever occurred giving a history of suffering from influenza within a week of attack by cerebro spinal fever.
The probabilities of such occurrences are shown in column 7 and the values of (p) calculated on the
data it has been possible to collect are so small as to raise question whether the occurrence of influenza
and cerebro spinal fever in the same person within the limited period can be regarded as independent
events.
If the figures for the whole period under review be taken it will be seen that of 462 eases of cerebrospinal
fever 27 gave a history of suffering from influenza within seven days of the onset of this illness.
The probability of the occurrence of so large a number of cases assuming attack by influenza and
cerebro-spinal fever within the limited period to be independent events works out at a figure
which is practically infinitesminal. It will be seen from section 111. of diagram (Y) that the
most probable number of cases giving a history of recent attack by influenza is 2, and that the
successive probabilities of obtaining 3, 4, 5, etc., cases rapidly decline, the probability of obtaining 7
cases for instance falls as low as .0077; beyond this point it is unuecessary to calculate the ordinates of
the probability curve, but the sum of the probabilities of the first 8 ordinates gives a figure of .9964, the
probability of obtaining 8 or more cases with an influenza history is therefore the difference between
•9964 and unity—viz. '0036. It will thus be seen that the probability of obtaining more than 7 such cases
is less than 4 in 1,000, whereas the number of such cases actually recorded reaches the high figure of 27.
The facts set out in the preceding paragraph may perhaps be more clearly appreciated if presented
as follows: suppose that 462 persons are chosen at random from the London population in groups of
from 20 to 30 during each week of the first five months of the year 1915, one would expect, having
regard to the prevalence of influenza during these months to find that some 2 or 3 of the 462 persons
thus chosen would either be suffering from or recently recovered from an attack of influenza ; turning,