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distance between the three peaks in the former epoch is 97 weeks, and between the valleys approximately
the same. In the later epoch, the interval between the two peaks is about 100 weeks. These
two epochs are separated by an interval of some 290 weeks, which is nearly three times 97 weeks ; hence
the periodogram shows a very high amplitude for the 97 week period, firstly because the intervals
between the peaks in both epochs do not greatly differ from 97 weeks, and secondly because the two
epochs are separated by an interval which is very nearly an exact multiple of this period. Actually,
however, during this interval (of three times 97 weeks), there were only two waves of measles, and this
fact demonstrates the independence of the periodicities in the interval and those of the two epochs
respectively.
In the 20 years 1874—1893 the table shows high amplitudes at 87, 89|½, and 97 weeks; the last
being the highest. The diagram shows there were two measles epochs with high peaks, one in 1875—1880,
and the other in 1888—1893. In the latter epoch, the three peaks have an average distance of 88 weeks;
in the former, the average distance is about 94 weeks. The distance between the two epochs is about
580 weeks (97 X 6), and to this fact is due the high amplitude shown for a period of 97 weeks. This is,
therefore, a spurious period.
The 19 years 1893 to 1912 are marked by a number of high peaks in the opening years 1893 to
1898, while another group of high peaks occurs in the years 1908 to 1912. The peaks of the two groups
are separated by a period of about two years. The distance between the centres of the two groups is
approximately 680 (7 x 97) weeks; hence the periodogram shows high amplitudes for periods of 97
weeks and over; it also shows a high amplitude for a period of 87 weeks, but this is due to the fact that
the interval between the two groups is nearly a multiple of 87 weeks. The period of 87 weeks has no
relation to the true periodicity of measles in these years.
In the diagram on page 89 a somewhat different grouping of years from that shown in Dr. Brownlee's
Table is adopted. In place of Dr. Brownlee's four periods of eighteen years, five periods of ten years
have been selected, containing as nearly as possible all the principal epidemics of the past 77 years. The
year has been divided into 13 four-weekly periods (or approximately " lunar " months), and the average
mortality for each of these months for the 10-year period has been found. The deviations per cent, of
the mortality in any given month for the 10-year average for that month have been calculated and plotted.
The resulting contour thus represents as nearly as practicable the progress of the epidemic after the
elimination of merely " seasonal " variations.
It will be seen that in the contour for 1888—1898 there were six epidemics, while in earlier and
later years there were five. The average interval between the epidemics in each series of years is shown
on the diagram.
Broadly speaking, therefore, it is found that the interval between the predominant " peaks " in
successive years has decreased generally from approximately 108 weeks in the forties to a minimum of
about 88 weeks late in the eighties (i.e., just between the third and fourth contours of the diagram), and
thereafter has increased roughly speaking, to about 104 weeks in recent years.
It should be added that the epidemics which occur in the winter are marked by sharper " peaks "
than in the summer. In part, these irregularities are accounted for by the effect upon the measles
mortality of abnormally cold weather or other winter conditions tending to increase the deaths from
respiratory diseases.
In summary of the whole matter it may be pointed out that, as Dr. Brownlee's Diagram of
Amplitudes shows, in London epidemics tend to recur at half-yearly, yearly and round about the twoyearly
interval—the highest amplitudes (Diagram II. in his paper) are, roughly speaking, at 26 weeks,
52 weeks, and then follows the group round about the interval of two years, viz., 87, 89½, 97, 105½,
109½ and 114 weeks. These periodicities have not always obtained in London (see the table on p. 37
and a number of quite different periodicities occur in other large towns. It is very important to realise
that too much stress should not be laid upon the precise length of the periods. Thus, Dr. Brownlee says
elsewhere (Phil. Trans. Series B., Vol. 208, p. 236) with regard to a low amplitude for the period of
114 weeks : " The period of 114 weeks, however, has not necessarily disappeared. The amplitudes for
the periods of 112 and 113 weeks are respectively 197 and 199. This difference between 112.5 and 114
weeks is not beyond the variation already found in the examination of the figures for the sub-epochs
between 1838 and 1914. During that epoch the 97 weeks period varied from 95 to 97-5 weeks. In
like manner the 87 weeks period may be represented by a period of 86 weeks. Large amplitudes are
found for several long periods—117, 122, 130, 136 and 144 weeks—periods for which no evidence
exists in data since the year 1838."
There is, moreover, the serious difficulty caused by the confusion resulting when the intervals
between succeeding groups of epidemics happen to correspond roughly with some multiple of the observed
periods of each of the groups.
A further striking phenomenon to be taken into account is that of seasonal distribution. Dr.
Brownlee has observed : "In the description of the epidemiology of measles in London, it is constantly
remarked that there are two well-marked seasons in the year at which an excess of deaths from
measles may be expected." This fact had led to wide acceptance of the view that the time of occurrence
of measles outbreaks was largely determined by season and that the period tended to range in London
about a two-yearly interval; but in certain instances it was found to be something shorter than this,
and in some cases an interval of approximately eighteen months had been observed. Sir A. Whitelegge
had, indeed, in his Milroy Lectures (1892) suggested that this tendency, to an interval of shorter duration
than two years, might be due to increasing aggregation of susceptible children in London; and, in the
Milroy Lectures (1906), I pointed out that this view was confirmed by the influence apparently exerted
by an increasing birth rate in certain towns.
Do Dr. Brownlee's carefully prepared statistics carry the question after all very much further than