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Letitia Armistead Hanson

444 THE SCIENTIFIC MONTHLY

THE BIOLOGY OF DEATH. TI—THE CHANCES
OF DEATH’

By Professor RAYMOND PEARL
THE JOHNS HOPKINS UNIVERSITY

1. Tse Lire TaBLe

P to this point in our discussion of death and longevity we have,
for the most part, dealt with general and qualitative matters,
and have not made any particular examination as to the quantitative
aspects of the problem of longevity. To this phase attention may now
be directed. For one organism, and one organism only, do we know
much about the quantitative aspects of longevity. I refer, of course,
to man, and the abundant records which exist as to the duration of his
life under various conditions and circumstances. In 1532 there began
in London the first definitely known compilation of weekly “Bills of
Mortality.” Seven years later the official registration of baptisms,
marriages and deaths was begun in France, and shortly after the open-
ing of the seventeenth century similar registration was begun in
Sweden. In 1662 was published the first edition of a remarkable book,
a book which marks the beginning of the subject which we now know
as “vital statistics.” I refer to “Natural and Political Observations
Mentioned in the Following Index, and made upon the Bills of Mor-
tality” by Captain John Graunt, Citizen of London. From that day to
this, in an ever widening portion of the inhabited globe we have had
more or less continuous published records about the duration of life in
man. The amount of such material which has accumulated is enor-
mous. We are only at the beginning, however, of its proper mathe-
matical and biological analysis.. If biologists had been furnished with
data of anything like the same quantity and quality for any other
organism than man one feels sure that a vastly greater amount of atten-
tion would have been devoted to it than ever has been given to vital
statistics, so-called, and there would have been as a result many funda-
mental advances in biological knowledge now lacking, because material
of this sort so generally seems to the professional biologist to be some-
thing about which he is in no way concerned.
Let us examine some of the general facts about the normal duration
of life in man. We may put the matter in this way: Suppose we
started out at a given instant of time with a hundred thousand infants,

1Papers from the Department of Biometry and Vital Statistics, School
of Hygiene and Public Health, Johns Hopkins University, No. 30.

iE BIOLOGY OF DEAT 445

equally distributed as to sex, and all born at the same instant of time.
How many of these individuals would die in each succeeding year, and
what would be the general picture of the changes in this cohort with
the passage of time? The facts on this point for the Registration
Area of the United States in 1910 are exhibited in Figure 1, which is
based on Glover’s United States Life Tables.

UNITED STATES LIFE TABLE - IHO

SMSO Teall iil
ee

SCC ae
FEES

re a a C7 Ho 7560 Bas ‘o DO 79

VEARS OF LIKE

FIG. 1. LIFE TABLE DIAGRAM. FOR EXPLANATION SEE TEXT

NUMBER
8

In this table are seen two curved lines, one marked 1, and the
other d,. The /, line indicates the number of individuals, out of the
original 100,000 starting together at birth, who survived at the be-
ginning of each year of the life span, indicated along the bottom of
the diagram. The d, line shows the number dying within each year
of the life span. In other words, if we subtract the number dying
within each year from the number surviving at the beginning of that
year we shall get the series of figures plotted as the J, line. We note
that in the very first year of life the original hundred thousand lose
over one-tenth of their number, there being only 88,538 surviving at
the beginning of the second year of life. In the next year 2,446 drop
out, and in the year following that 1,062. Then the line of survivors
drops off more slowly between the period of youth and early adult life.
At 40 years of age, almost exactly 30,000 of the original 100,000 have
passed away, and from that point on the J, line descends with ever
increasing rapidity, until about age 80, when it once more begins to
drop more slowly, and the last few survivors pass out gradually, a few
each year until something over the century mark is reached, when the
last of the 100,000 who started so blithely across the bridge of life
together will have ended his journey.

This diagram is a graphic representation of that important type of
document known as a life or mortality table. It puts the facts of mor-
tality and longevity in their best form for comparative purposes. The

446 THE SCIENTIFIC MONTHLY

first such table actually to be computed in anything like the modern
fashion was made by the astronomer, Dr. E. Halley, and was pub-
lished in 1693. Since that time a great number of such tables have
been calculated. Dawson fills a stout octavo volume with a collection
of the more important of such tables computed for different countries
and different groups of the population. Now they have become such
a commonplace that elementary classes in vital statistics are required to
compute them.

2. CHANGES IN EXPECTATION IN LIFE

I wish to pass in graphic review some of these life tables in order
to bring to your attention in vivid form a very important fact about
the duration of human life. In order to bring out the point with
which we are here concerned it will be necessary to make use of an-
other function of the mortality table than either the J, or d, lines
which you have seen. I wish to discuss expectation of life at each age.
The expectation of life at any age is defined in actuarial science as
the mean or average number of years of survival of persons alive at the
stated age. It is got by dividing the total survivor-years of after life
by the number surviving at the stated age.

In each of the series of diagrams which follow there is plotted the
approximate value of the expectation of life for some group of people
at some period in the more or less remote past, and for comparison
the expectation of life either from Glover’s table, for the population
of the United States Registration Area in 1910—the expectation of life
of our people now, in short—or equivalent figures for a modern Eng-
lish population.

Because of the considerable interest of the matter, and the fact that
the data are not easily available to biologists, Table 1 is inserted giv-
ing the expectations of life from which the diagrams have been plotted.

HEV BIOLOGY OF DEATH 447

fy ABE ile
Changes in expectation of life from the seventeenth century to
the present time.

Average length of life remaining td/ Average length of life remaining to
cock lone alive at beginning of age Fey One alive at beginning of age
Age : Age
Breslau, Carlisle, Breslau, Carlisle,
17th 18th U. S. 1910 17th 18th U. S. 1910
CLUS PIN IAA WLAN Gir Oh AMALIA COND ee heen Cea a UN Heol Ne century. century. century.

Ova 33.50 38.72 51.49 o-1 | sgs0 | 3872 | srg || sos | 168 | arar | 2098 50-51 16.81 ZT 20.98
I-2 38.10 44.67 57.11 51-52 16.36 20.39 20.28
Pas) 39.78 47.55 57.72 52-53 15.92 19.68 19.58
Sint 40.75 49.81 57-44 53-54 15.48 18.97 18.89
ANS 41.25 50.76 56.89 54-55 14.99 18.27 18.21
5 - 6 41.55 51.24 56.21 55-56 14.51 17.58 17.55
6-7 41.62 51.16 55.47 50-57 14.02 16.89 16.90
7-8 41.16 50.79 54.69 57-58 13.54 16.21 16.26
S19 40.95 50.24 53.87 58-59 13.06 15.55 15.64
9-10 | 40.50 | 40.57 | 53.02 59-60 12.57 14.92 15.03
IO-II 39.99 48.82 52.15 60-61 12.09 14.34 14.42
II-12 30.43 48.04 51.26 61-62 11.62 13.82 13.83
12-13 38.79 47.27 50.37 62-63 11.14 13.31 13.26
13-14 38.16 46.50 49.49 63-64 10.67 12.81 12.69
14-15 37.51 45.74 48.60 64-65 10.20 12.30 12.14
15-16 36.86 44.99 47.73 65-66 0.73 11.79 11.60
16-17 36.22 44.27 46.86 66-67 9.27 11.27 11.08
17-18 35.57 43.57 46.01 67-68 8.81 10.75 10.57
18-19 34.92 42.87 45.17 68-69 8.36 10.23 10.07
19-20 34.26 42.16 44.34 69-70 7.91 9.70 9.58
20-21 33.61 41.46 43.53 70-71 7.53 9.17 Q.II
21-22 32.05 40.75 42.73 71-72 7.17 8.65 8.66
22-23 32.34 40.03 41.94 72-73 6.85 8.16 8.22
23-24 31.67 39.31 41.16 73-74 6.56 7-72 7:79
24-25 31.00 38.58 40.38 74-75 6.25 7-33 7.38
25-26 30.38 37.86 39.60 75-76 5.09 7.00 6.99
26-27 20.76 37.13 38.81 70-77 5.79 6.69 6.61
27-28 20.14 36.40 38.03 77-78 5.71 6.40 6.25
28-29 28.51 35.68 37.25 78-79 5.66 6.11 5.90
29-30 | 27.03 | 34.090 | 36.48 79- 5.67 5.80 5.56
30-31 27.35 34-34 | 35.70 80-81 5-74 5.51 5.25
31-32 26.76 33.68 34.93 81-82 5.86 5.20 4.96
32-33 26.18 33.02 34.17. j| 82-83 6.02 4.93 4.70
33-34 25.50 | 32.30 33.41 83-84 5.85 4.65 4.45
34-35 25.05 31.68 | 32.66 84-85 4.39 4.22
35-36 24.51 31.00 | 31.90 85-86 4.12 4.00
36-37 23.97 | 30.32 31.16 || 86-87 3.90 3-79
37-38 23.43 29.63 30.42 87-88 3-71 3.58
38-39 22.88 28.95 29.68 88-89 3.59 3.39
39-40 22.33 28.27 | 28.94 89-90 3.47 3.20
40-41 21.78 27.61 28.20 90-91 3.28 3.03
41-42 21.23 26.97 27.46 QI-92 3.26 2.87
42-43 | 20.73 | 26.33 | 26.73. || 92-93 3.37 2.73

43-44 | 20.23 | 25.71 | 25.99 93-04 3.48 2.59
44-45 19.72 25.08 25.26 94-95 3.53 2.47
45-46 | 19.22 24.45 24.54 95-96 3.53 2.35
46-47 18.72 23.81 23.82 || 96-907 3.46 2.2

47-48 | 18.21 23. LOW) 2370) ili vo7eo8 3.28 2.14
48-49 | 17.71 2.50 | 22.30 | 98-99 3.07 2.04
49-50 | 17.25 aby 21.69 |! Q9-100 hetere 1.95

Figure 2 gives the results from Halley’s table, based upon the mor-
tality experience in the City of Breslau, in Silesia, during the years
1687 to 1691. This gives us a picture of the forces of mortality towards

448 THE SCIENTIFIC MONTHLY

HALLEYS GRESLAY I687- 1692) LIFE TABLE

EXPECTATION OF LIFE
&,
y
S
RY
A
.

: lil
ins
aa

(2) I ORME DM ZOM RLS INE OWES PAO NTS IN SOM S SOOM OOH NTO SMIN CO > Mh 0 MR mn CN

YEARS OF LIFE.
FIC. 2. COMPARING THE EXPECTATION OF LIFE IN THE 17TH CENTURY WITH THAT

OF THE PRESENT TIME
the end of the seventeenth century. From this diagram it appears that
at birth the expectation of life of an individual born in Breslau in the
seventeenth century was very much lower than that of an individual
born in the United States in 1910. The difference amounts to approxi-
mately 18 years! At 10 years of age, however, this difference in ex-
pectation of life had been reduced to just over 12 years; at age 20, to
a little less than 10 years; at age 30 to 7-1/3 years; at age 50 to just over
4. years; at age 70 to 1-1/2 years. At age 80 the lines have crossed.
The individual 80 years old in Breslau could expect to live on the aver-
age a half year longer than the individual of the same age in the United
States in 1910. At age 83, the last year covered by Halley’s table, the
17th century individual could expect on the average to live approxi-
mately a year and a half longer than his twentieth century brother.
So then what the diagram shows is that the expectation of life at early
ages was vastly inferior in the seventeenth century to what it is now,
while at advanced ages the chances of living were distinctly better—
relatively enormously better—then than they are now. Let us defer
the further discussion of the meaning and explanation of this curious
fact until we have examined some further data.

Figure 3 compares the expectation of life in England at the middle
of the eighteenth century, or about a century later than the last, with
present conditions in the United States. Again we see that the expecta-
tion at birth was greatly inferior then to what it is now, but the differ-
ence is not so great as it was a century earlier, amounting to but 12-3/4
years instead of the 18 we found before. Further it is seen that, just
as before, the expectations come closer together with advancing age.
By the time age 45—middle life—is reached the expectation of life was
substantially the same in the eighteenth century as it is now. At age
47 the eighteenth century line crosses that for the twentieth century,

THE BIOLOGY OF DEATH 449

MILNES CARLISLE 1780 - 787 LIFE TABLE

EXPECTATION OF LIFE

5) —

[eae Ret Me cota [aes [vee ol >=
fo) | |

{e) 5 10 iS LOE 2S FESO SS tO AO SO. 55 60 OS 7O ETS COM GS; 90 25 0

YEARS OF LIFE

FIG. 3. COMPARING THE EXPECTATION OF LIFE IN THE 18TH CENTURY WITH THAT
OF THE PRESENT TIME

and with a few trifling exceptions, notably in the years from 56 to 62,
the expectation of life for all higher ages was greater then than it is
now. Or we see in the eighteenth century the same kind of result as
in the seventeenth, only differing in degree.

The changes in expectation of life from the middle of the seven-
teenth century to the present time furnish a record of a real evolution-
ary progression. In this respect at least man has definitely and dis-
tinctively changed, as a race, in a period of three and a half centuries.
This is, of course, a matter of extraordinary interest, and at once stim-
ulates the desire to go still farther back in history and see what the
expectation of life then was. Fortunately, through the labors of Karl
Pearson, and his associate, W. R. Macdonell, it is possible to do this,
to at least a first approximation. Pearson has analyzed the records as
to age at death which were found upon mummy cases studied by Pro-
fessor W. Spiegelberg. These mummies belonged to a period between
1900 and 2000 years ago, when Egypt was under Roman dominion. The
data were extremely meager, but from Pearson’s analysis of them it
has been possible to construct the diagram which is shown in Figure
4. Each circle marks a point where it was possible definitely to cal-
culate an expectation of life. The curve running through the circles is
a rough graphic smoothing of the scattered observed data. Unfortu-
nately, there were no records of deaths in early infancy. Either there
were no baby mummies, or if there were they have disappeared. For
comparison, the expectation of life from Glover’s 1910 United States
life table is inserted.

It will be seen at once that the general sweep of the line is of the
same sort that we have already observed in the case of the seventeenth
century table. In the early years of life the expectation was far below
that of the present time, but somewhere between ages 65 and 70 the

450 RHE SCLENTLEIG VM ON GEE,

ENPECTATION OF LIFE

| | | | | n
(2) 5 10.15 20. 25 30 35 40 45 50 55 60.65 710 75 80 G5 90. 95 100

YEARS. OF AGE
FIG. 4. COMPARING THE EXPECTATION OF LIFE OF ANCIENT EGYPTIANS WITH THAT
OF PRESENT DAY AMERICANS. Plotted from Pearson’s and Glover’s data
Egyptian line crosses the modern American line, and from that period
on the individuals living in Egypt at about the time of the birth of
Christ could look forward to a longer remaining duration of life, on
the average, than can the American of the present day. Pearson’s com-
ment on this fact is worth quoting. He says: “In the course of those
centuries man must have grown remarkably fitter to his environment,
or else he must have fitted his environment immeasurably better to
himself, No civilized community of to-day could show such a curve
as the civilized Romano-Egyptians of 2,000 years ago exhibit. We
have here either a strong argument for the survival of the physically
fitter man or for the survival of the civilly fitter society. Either man
is constitutionally fitter to survive to-day, or he is mentally fitter, i. e.,
better able to organize his civic surroundings. Both conclusions point
perfectly definitely to an evolutionary progress. . . . That the ex-
pectation of life for a Romano-Egyptian over 68 was greater than for
a modern English man or woman is what we might expect, for with the
mortality of youth and of middle age enormously emphasized only
the very strongest would survive to this age. Out of 100 English alive
at 10 years of age 39 survive to be 68; out of 100 Romano-Egyptians
not 9 survived. Looking at these two curves we realize at a glance
either the great physical progress of man, which enables him far more
effectually to withstand a hostile environment, or the great social and
sanitary progress he has made which enables him to modify the en-
vironment. In either case we can definitely assert that 2,000 years
has made him a much ‘fitter’ being. In this comparison it must be re-
membered that we are not placing a civilized race against a barbaric
tribe, but comparing a modern civilization with one of the highest

types of ancient civilization.”
Macdonell was able to continue this investigation, on much more

RAE BIOLOGCYAOR DEBATE 451

extensive material extracted from the Corpus Inscriptionum Latinarum
of the Berlin Academy, which gives records as to age of death for many
thousand Roman citizens dying, for the most part, within the first three
or four centuries of the Christian era. His material may, therefore,
be taken to represent the conditions a few centuries later than those of
Pearson’s Romano-Egyptian population. Macdonell was able to cal-
culate three tables of expectation of life—the first for Roman citizens
living in the city of Rome itself; second, for those living in the provinces
of Hispania and Lusitania; and third, for those living in Africa. The
results are plotted against the United States 1910 data, as before, in
Figures 5, 6 and 7.

|

|UNITED STATES
| jl

EXPECTATION OF LIFE

YEARS OF AGE
FIG. 5. COMPARING THE EXPECTATION OF LIFE OF ANCIENT ROMANS WITH THAT OF
PRESENT DAY AMERICANS. Plotted from Macdonell’s and Glover’s data

Figure 5 relates to inhabitants of the city of Rome itself. The
populations from which the expectations are calculated run into the
thousands, and fortunately one is able to separate males and females.
As in Pearson’s case, which we have just examined, modern American
data are entered for comparison. It will be noted at once that just as
in the Romano-Egyptian population the expectation of life of inhabi-
tants of ancient Rome was, in the early years of life, immensely in-
ferior to that of the modern population. From about age 60 on, how-
ever, the expectation of life was better then than now. Curiously
enough, the expectation of life of females was poorer at practically all
ages of life than that of the males, which exactly reverses the modern
state of affairs. Macdonell believes this difference to be real, and to
indicate that there were special influences adversely affecting the health
of females in the Roman Empire, which no longer operate in the
modern world. Up to something like age 25 the expectation of life
of dwellers in the city of Rome was extremely bad, worse than in the
Romano-Egyptian population which Pearson studied, or in the popu-

452 Wels, SOMBIN IIMA G WA OUNITIEUESY

lations of other parts of the Roman Empire as we shall see in the fol-
lowing diagram. Macdonell thinks that this difference is real and due
to circumstances peculiar to Rome.

LIFE

EXPECTATION OF
N
Q

fa) Sie OT Stee ZOOL ZS BGO SO) 0 ASST SORTS ONE CORE OSE ORR /SEROO RNG Sn SOME OS OO)

YEARS OF AGE

FIG. 6. COMPARING THE EXPECTATION OF LIFE OF THE POPULATION OF THE ROMAN
PROVINCES HISPANIA AND LUSITANIA WITH THAT OF PRESENT DAY AMERICANS. Plotted
from Macdonell’s and Glover’s data

The general features of the diagram for the population of His-
pania and Lusitania (Figure 6) are similar to those that we have seen,
with the difference that the expectation of life up to age 20 or 25 is
not as bad as in the city of Rome itself. Again the females show a
lower expectation practically throughout life than do the males. The
lines cross the modern American lines at about age 60 and from that
point on these colonial Romans had a better expectation of life than
the modern American has. |

LIFE

(L

OF

EXPECTATION

VEAPS AF AGE

FIG. 7. COMPARING THE EXPECTATION OF LIFE OF THE POPULATION OF THE ROMAN
PROVINCES IN AFRICA WITH THAT OF PRESENT DAY AMERICANS. Plotted from
Macdonell’s and Glover’s data

TES DIOLOCY.OR DEAE 453

The Romano-African population diagram appears to start at nearly
the same point at birth as does the modern American and in general
the differences up to age 35 are not substantially more marked from
modern conditions than they are in the seventeenth century Breslau
table. The striking thing, however, is that at about age 40 the lines
cross, and from then on the expectation of life was definitely superior
in the early years of the Christian era to what it is now.

It should be said that the curious zigzagging of the lines in all of
these Roman tables of Macdonell is due to the tendency, which ancient
Romans apparently had in common with present day American negroes,
towards heavy grouping on the even multiples of 5 in the statement
of their ages.

Summarizing the whole matter we see that during a period of
approximately 2,000 years man’s expectation of life at birth and sub-
sequent early ages has been steadily improving, while at the same
time his expectation of life at advanced ages has been steadily
worsening. The former phenomenon may be attributed essentially to
ever increasing knowledge of how best to cope with the lethal forces
of nature. Progressively better sanitation, in the broadest sense, down
through the centuries has saved for a time the lives of ever more and
more babies and young people who formerly could not withstand the
unfavorable conditions they met, and died in consequence rather
promptly. But just because this process tends to preserve the weak-
lings, who were speedily eliminated under the rigorous action of un-
mitigated natural selection, there appear now in the higher age groups
of the population many weaker individuals than formerly ever got
there. Consequently the average expectation of life at ages beyond
say 60 to 70 is not nearly so good now as it was under the more rigor-
ous régime of ancient Rome. Then any individual who attained age 70
was the surviving resultant of a bitterly destructive process of selection.
To run successfully the gauntlet of early and middle life he necessarily
had to have an extraordinarily vigorous and resistant constitution.
Having come through successfully to 70 years of age it is no matter of
wonder that his prospects were for a longer old age than his descend-
ants of the same age to-day can look forward to. Biologically these
expectation of life curves give us the first introduction to a principle
which we shall find as we go on to be of the very foremost importance
in fixing the span of human longevity, namely that inherited constitu-
tion fundamentally and primarily determines how long an individual
will live.

3. ANALYSIS OF THE LIFE TABLE

I shall not develop this point further now, but instead will turn
back to consider briefly certain features of the dx line of a life table.
Figure 1 shows that this line, which gives the number of deaths occur-

454 UAE aS GaN ele Ita Ciel O NMG eye

ring at each age, has the form of a very much stretched letter 5S resting
on its back. Some years ago Pearson undertook the analysis of this
complex curve, and drew certain interesting conclusions as to the
fundamental biological causes lying behind its curious sinuosity. His
results are shown in Figure 8.

PEARSON’S GRADUATION OF dy

I.

20

VEARS OF UFE

FIG. 8. SHOWING PEARSON’S RESULTS IN FITTING THE Dx LINE OF THE LIFE TABLE
WITH 5 SKEW FREQUENCY CURVES. Plotted from the data of Pearson’s original memoir on
“‘Skew Variation’? in the Phil. Trans. Roy. Soc.

He regarded the d, line of the life table as a compound curve, and by
suitable mathematical analysis broke it up into five component fre-
quency curves. The data which he used were furnished by the d, line .
of Ogle’s life table, based on the experience of 1871 to 1880 in Eng-
land. This line gives the deaths per annum of one thousand persons
born in the same year. The first component which he separated was
the old age mortality. This is shown by the dotted curve having its
modal point between 70 and 75 years, at the point lettered O, on the
base of the diagram. This component, according to Pearson’s gradua-
tion, accounted for 484.1 deaths out of the total of 1,000, or nearly
one-half of the whole. Its range extends from under 20 years of age
to the upper limit of life, at approximately 106 years. The second
component includes the deaths of middle life. This is the smooth curve
having its modal point between 40 and 45 years at the point on the
base marked O,. Its range extends from about 5 years of age to about
65. It accounts for 175.2 deaths out of the total of 1,000. It is a long,
much spread out curve, exhibiting great variability. The third com-
ponent is made up by the deaths of youth. This accounts for 50.8
deaths out of the total of a thousand, and its range extends from about
the time of birth to nearly 45 years. Its mid-point is between 20 and 25
years, and it exhibits less variability than either the middle life or the
old age curves. The fourth component, the modal point of which is at
the point on the base of the diagram marked O, covers the childhood

oO

RE ETOLOCY ORD A itt 45

mortality. It accounts for 46.4 deaths out of the total of 1,000. Its
range and variability are obviously less than those of any of the other
three components so far considered. The last, excessively skew com-
ponent, is that which describes the mortality of infancy. It is given
by a J shaped curve accounting for 245.7 deaths after birth, and an
antenatal mortaliy of 605. In order to get any fit at all for this por-
tion of the mortality curve it is necessary to assume that the deaths
in utero and those of the first months after birth are a homogeneous
connected group.

Summing all these components together it is seen that the resulting
smooth curve very closely fits the series of small circles which are the
original observations. From the standpoint merely of curve fitting
no better result than this could be hoped for. But about its biological
significance the case is not quite so clear, as we shall presently see.

Pearson himself thinks of these five components of the mortality
curve as typifying five Deaths, shooting with different weapons, at
different speeds and with differing precision at the procession of human
beings crossing the Bridge of Life. The first Death is, according to
Pearson, a marksman of deadly aim, concentrated fire, and unremitting
destructiveness. He kills before birth as well as after and may be
conceived as beating down young lives with the bones of their an-
cestors, The second marksman who aims at childhood has an extremely
concentrated fire, which may be typified by the machine gun. Only be-
cause of the concentration of this fire are we able to pass through it
without appalling loss. The third marksman Death, who shoots at
youth has not a very deadly or accurate weapon, perhaps a bow and
arrow. The fire of the fourth marksman is slow, scattered and not very
destructive, such as might result from an old fashioned blunderbus.
The last Death plies a rifle. None escapes his shots. He aims at old
age but sometimes hits youth. His unremitting activity makes his
toll large.

We may let Pearson sum the whole matter up in his own words:
“Our investigations on the mortality statistics have thus led us to some
very definite conclusions with regard to the chances of death. Instead
of seven we have five ages of man, corresponding to the periods of in-
fancy, of childhood, of youth, of maturity or middle age, and of
senility or old age. In the case of each of these periods we see a per-
fectly regular chance distribution, centering at a given age, and tailing
off on either side according to a perfectly clear mathematical law.

“Artistically, we no longer think of Death as striking chaotically:
we regard his aim as perfectly regular in the mass, if unpredictable in
the individual instance. It is no longer the Dance of Death which pic-
tures for us Death carrying off indiscriminately the old and young, the
rich and the poor, the toiler and the idler, the babe and its erandsire.
We see something quite different, the cohort of a thousand tiny mites

456 DEUS, S(CIUBINISUOMG. SK OUN IEEUESY

starting across the Bridge of Life, and growing in stature as they ad-
vance, till at the far end of the bridge we see only the gray-beard, and
the ‘lean and slippered pantaloon.’ As they pass along the causeway
the throng is more and more thinned; five Deaths are posted at different
stages of the route longside the bridge, and with different skewness of
aim and different weapons of precision they fire at the human target,
till none remains to reach the end of the causeway—the limit of life.”

This whole, somewhat fanciful, conception of Pearson’s needs a
little critical examination. What actually he has done is to get a good
empirical fit of the d, line by the use of equations involving all told
some 17 constants, Because the combined curve fits well, and funda-
mentally for no other reason, he implicitly concludes that the fact that
the fit is got by the use of five components means biologically that the
d, line is a compound curve, and indicates a five-fold biological hetero-
geneity in the material. But it is a very hazardous proceeding to draw
biological conclusions of this type from the mere fact that a theoretical
mathematical function or functions fits well a series of observational
data. I have fully discussed this point several years ago (Pearl:
Amer. Nat. Vol. XLIII) where I pointed out:

“The kind of evidence under discussion can at best have but in-
ferential significance; it can never be of demonstrative worth. It is
based on a process of reasoning which assumes a fundamental or nec-
essary relationship to exist between two sets of phenomena because the
same curve describes the quantitative relations of both sets. A little
consideration indicates that this method of reasoning certainly can not
be of general application, even though we assume it to be correct in
particular cases. The difficulty arises from the fact that the mathe-
matical functions commonly used with adequate results in physical,
chemical, biological, and mathematical investigations are comparatively
few in number. The literature of science shows nothing clearer than
that the same type of curve frequently serves to describe with complete
accuracy the quantitative relations of widely different natural phe-
nomena. As a consequence any proposition to include that two sets
of phenomena are casually or in any other way fundamentally related
solely because they are described by the same type of curve is of a
very doubtful validity.”

Henderson has put Pearson’s five components together in a single
equation, and says regarding this method of analyzing the life tables:
zs it is dificult to lay a firm foundation for it, because no
analysis of the deaths into natural divisions by causes or otherwise has
yet been made such that the totals in the various groups would conform
to those frequency curves.” The italics in this quotation are the pres-
ent writer’s for the purpose of emphasizing crucial points of the whole
matter, which we shall immediately discuss in more detail.

RAE BIOLOGVIOF.D EAR 457

Now it is altogether probable that one could get just as good a fit to
the observed d, line as is obtained by Pearson’s five components by
using a 17 constant equation of the type

y—a-+bx-+cx?-+dx?+ex! + fx’+ gx°4+_______- +nx!°
and in that event one would be quite as fully justified (or really un-
justified) in concluding that the d, line was a homogeneous curve as
Pearson is in concluding from his five-component fit that it is com-
pound.

Indeed Wittstein’s formula involving but four constants gives sub-
stantially good fit over the whole range of life.

But in neither case is the curve-fitting evidence, by and of itself, in
any sense a demonstration of the biological homogeneity or hetero-
geneity of the material. Of far greater importance, and indeed conclu-
sive significance, is the fact, to be brought out in a later paper in this
series, that in material experimentally known to be biologically homo-
geneous, a population made up of full brothers and sisters out of a
brother x sister mating and kept throughout life in a uniform environ-
ment identical for all individuals,one gets a d, line in all its essential
features, save for the absence of excessive infant mortality arising from
perfectly clear biological causes, identical with the human d, line.
It has long been apparent to the thoughtful biologist that there was not
the slightest biological reason to suppose that the peculiar sinuosity of
the human d, line owed its origin to any fundamental heterogeneity
in the material, or differentiation in respect of the forces of mortality.
Now we have experimental proof, to be discussed in a later paper in
this series, that with complete homogeneity of the material, both genetic
and environmental, one gets just the same kind of dx line as in normal
human material, We must then, I think, come to the conclusion that
brilliant and picturesque as is Pearson’s conception of the five Deaths,
actually there is no slightest reason to suppose that it represents any
biological reality, save in the one respect that his curve fitting demon-
strates, as any other equally successful would, that deaths do not occur
chaotically in respect of age, but instead in a regular manner capable
of representation by a mathematical function of age.