CTFJARIAL STUDIES No.

Ji ,'CRS and characteristics

OF THE

MOR1MITY TABLES
VmNRY MOIR

ACTUARIAL SOCIETY OF AMERICA

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ACTUARIAL STUDIES NO. i

SOURCES AND CHARACTERISTICS OF

THE PRINCIPAL MORTALITY TABLES

PRINCIPAL CONTRIBUTOR

HENRY MOIR

ASSOCIATE CONTRIBUTORS

J. D. CRAIG A. T. MACLEAN
L. K. FILE H. H. WOLFENDEN

PUBLISHED BY
THE ACTUARIAL SOCIETY OF AMERICA
346 BROADWAY, NEW YORK

1919

528140
 Copyright 1919, by

The Actuarial Society of America

NEW YORK

PRESS OF
THE NEW ERA PR.NTING COMPANY
LANCASTER, PA.
9 *) 6 .
/
o
Ui
a

GENERAL INTRODUCTION.
In view of the fact that, with the exception of a very few
modern text books, the literature of Actuarial Science is con-
tained in scattered original papers, The Actuarial Society of
America proposes to volumes upon im-
issue a series of small
portant actuarial subjects. Each volume is intended to bring
together, as far as space permits, the more important points of
information on the subject discussed. The objects in issuing
the series are twofold: (1) to assist students of Actuarial Science,
and (2) to furnish a means of ready reference for Actuaries. The
various subjects are allocated to Fellows of the Society by the
Committee in Charge; and, associated with the principal con-
tributor, who is primarily responsible for the matter included
and the views expressed, are one or more “ Associate Contrib-
utors.” These are appointed for the purpose of aiding and
criticizing the work before publication. It is proposed to avoid
discussing subjects already covered in the Text Book of the
Institute of Actuaries except as continuity of thought may make
occasional references necessary. The title chosen to represent
the character of this series is “Actuarial Studies.”
The thanks of the Society and of the Committee in Charge
:*>
are due to all the contributors who have freely given of their
/s|' time and labor, with the sole purpose of helping others —especially
students.
N

in
 ORIGINAL COMMITTEE.
Arthur Hunter Wendell M. Strong
Henry Moir A. A. Welch
P. C. H. Papps A. B. Wood
John K. Gore, Chairman.

COMMITTEE NOW IN CHARGE.

Robert Henderson Wendell M. Strong
J. M. Laird J. S. Thompson
A. T. Maclean Hugh H. Wolfenden
A. H. Mowbray Henry Moir, Chairman.

IT
 SOURCES AND CHARACTERISTICS
OF THE PRINCIPAL

MOETALITY TABLES

The mortality table is the scientific basis of all life insurance

contracts. By means of it the probabilities of living and of dying
can be ascertained, on the presumption that what has taken place
in the past will be approximately reproduced in the future. A
mortality table consists of a schedule showing for each age the
number of persons who die and the number who survive out of a
known number under observation. Usually the table starts with
an arbitrary number, such as 100,000 at the youngest available
v
age, this arbitrary number being called the radix and gives for ,

each year of age the deaths and the survivors from this original
number. By adopting a radix the varying numbers which may
have been under observation from year to year are reduced to a
common basis suitable for comparisons, and convenient for com-
putations of annuity values, premiums, and other functions.
The older mortality tables were formed from population statis-
tics, but for nearly seventy years the tables which have been most

valuable for insurance purposes have been derived from the records
of life insurance companies. The information available to com-
panies is usually accurate as well as complete in the numbers under
observation at each age and the numbers dying, so that the rates

of mortality represented by the ratio can be correctly stated

for insured lives. The accuracy of this ratio is the fundamental

requirement of a good mortality table; and it is of more importance
that the deaths be stated at the proper ages and times than that
the record of the number living should be so strictly correct, since
any error in the numerator of the fraction has much more effect
—
than a similar error in the denominator at the younger ages
the effect is more than one hundred times greater.
1
2 SOURCES AND CHARACTERISTICS OF

In forming a mortality table from population statistics, it is

necessary, in order to get trustworthy figures, to have a census of

the people showing the numbers living at each age, as well as the
mortuary registers giving the numbers who have died at each age.
The mere death rate, without distinguishing the age distribution
of the people, is of practically no scientific value; the ages at death
of those dying and also the ages of all who are included in the
observations are essential factors. In order to ensure greater
accuracy, a census at the beginning and a^econd census at the end
of the period over which the observations extend should be taken;
but good approximate results can be obtained from one
fairly
census only, if it be carefully made, and if the ages and deaths be
accurately recorded. The mortality of nations and of cities
fluctuates from year to year, and accordingly the observations
should extend over a sufficient time to yield good average results.

Early Mortality Tables.

The earliest mortality tables of which we read were those in
use by the Romans for determining the values of life estates.
Under the Roman law a man could not bequeath more than three-
fourths of his property away from the direct heir; and it was a
common practice to bequeath annuities or life interests, the values
of which had to be determined by computation. As the Romans
made a careful census and recorded deaths with great accuracy,
it is usually supposed that they had satisfactory mortality tables,

but no proof of this supposition has been forthcoming. The taking

of a census has now become a regular custom with civilized nations,
having indeed become absolutely necessary for many purposes,
such for example as the rearrangement of the methods of repre-
sentation under all systems of popular government. In ancient
days, however, such an act was regarded with superstition, as for
example when the census of the Jews was taken by the Army of
David. He believed that the pestilence from which the Jews
afterwards suffered was a direct punishment for this act.
No records have been disclosed, from the days of the Romans
until the close of the seventeenth century, of any reliable tables
of mortality. In 1693 Dr. Halley (of comet fame), the British
Astronomer Royal, published the first tables of any importance,
which are now known.* He formed them from the registers of
* See J. I. A., Vol. I, pp. 43-46.
 THE PRINCIPAL MORTALITY TABLES. 3

deaths in the city of Breslau inSilesia, taken for a period of five

years, and they were published in the Transactions of the Royal

Society (Great Britain). Before the middle of the eighteenth
century a table of mortality was formed from observations made in
the city of London, and from this table the original premiums
adopted by the old Equitable Society were computed. The
mortality rates were very high.
In 1746 M. De Parcieux published his “Essai sur les probability
de la Duree de la Vie Humaine” in which several tables of mortality
were given, constructed from the lists of nominees in the French
tontines and from the mortality registers of different religious
houses. The mortality shown by this table is generally higher
than that of the Carlisle Table, fully described hereafter, with
which in other respects it agrees quite closely. This table was
never freely used by English-speaking people, although it was more
accurate than any of the other tables published in the eighteenth
century. It has now only a historical interest.
In the early development of scientific mortality tables we owe

more to Dr. Richard Price than to any other individual; yet he is

popularly remembered as the author of the Northampton Table
which is held out as an example of faulty construction. Dr. Price
himself was well aware of the difficulties with which he had to
contend and he strongly urged the adoption of better systems of
registration so that accurate mortality tables could be formed.
Amongst other tables formed by Dr. Price were the Chester
Tables,* which gave the rates of mortality separately for males
and females, and for the time at which they were prepared gave a
fair conception of human life. The tables were formed from the
birth and burial registers of the small town of Chester, in Eng-
land, and the accuracy of the assumptions was tested by an
enumeration of the people which included a record of the num-
bers living at each age. Unfortunately the tables never came
into general use, and the Northampton Tables became much bet-
ter known.
* See the later editions of “Price on Annuities.”
4 SOURCES AND CHARACTERISTICS OF

Northampton Table.
The first tables used to any great extent for life insurance
purposes were the Northampton Tables, detailed information
regarding which is here given as the mode of construction calls
attention to one or two errors which should be avoided. Moreover
they are still prescribed under certain old statutes as the basis
for determining the values of life estates for taxation purposes.
There were two tables formed by Dr. Price, the first published
in 1771 in his “ Observations on Reversionary Payments,” and
the second, a more complete table, in 1783, the latter being known
as The Northampton Table. The following extract from Dr.
Price’s remarks will partially explain the Tables:

“In the parish of All Saints, containing the greatest part of the town of
Northampton, an account has been kept since 1735 of the ages at which all
have died, also an account of the number of males and females that have been
christened.
Christened 4220 Buried 4689
“Of these died under 2 yrs. of age 1529
aged 2 to 5 362
5 to 10 201
10 to 20 189
20 to 30 373 (351)
30 to 40 329 (351)
40 to 50 365
50 to 60 384
60 to 70 378
70 to 80 358
80 to 90 199
90 to 100 22
4689

“In the fourth edition of this treatise, the following corrections were made:
“1st.The table printed in the first three editions having been formed
from the Northampton Bills (of Mortality) for 36 years (i. e., the first North-
ampton Table 1735-1770) this table was rendered a little more correct in
consequence of being formed from the same Bills for 46 years (1735-1780).
“2nd. The Bills give the number dying between 20 and 30 greater than
between 30 and 40, but this being a circumstance which does not exist in any
other register of mortality, and undoubtedly owing to some accidental and
local causes, the decrements were made equal between 20 and 40, preserving
the total of deaths the same that the Bills have them.
“3rd. The Bills giving only the total of deaths under two years of age
and between 2 and 5, the proportion of deaths for every particular year between
2 and 5, and for every quarter of a year after birth till one year of age, were
made the same nearly that the Chester register makes them.”

Dr. Price formed the table by taking account only of the deaths
and without using any enumeration of the population. If a census
 THE PRINCIPAL MORTALITY TABLES. 5

had been used a different result would have been reached, and the
tables would have been much more accurate. In view of the
difference between the number of christenings and of burials
(469 or 10% of the burials) he assumed that not only 10% but 13%
of the deaths were those of persons who immigrated to Northamp-
ton at the age of twenty; his reason for adopting the higher
percentage is not stated. The excess of deaths over births was
probably caused almost entirely by deaths among Dissenters, whose
children were not entered in the Parish Register of Christenings.
Dr. Farr pointed out that if effect had been given to the increas-
ing nature of the population, the table would have shown lower
and more accurate mortality rates, and would have been much
more valuable. The mortality amongst male children appears
heavier than amongst females, a feature which has been confirmed
in other tables.

Construction of the Northampton Table.*

Numbers Liy- Column 5

ing at First Numbers in Column 4 Less Raised in the
Age. Deaths. Age in Group Column 3 1300 up to Age Proportion of
(if Population Raised to 20 (i. e. 13 i
had been Radix of 10000. of Radix). fsM up to
Age 20.
Stationary).

(1) (2) (3) (4) (5) (6)

0- 2 1529 4689 10000 8700] 11649

2- 5 362 3160 6739 5439 7283
5-10 201 2798 5967 4667 6249
10-20 189 2597 5538 4238 5675
20-30 373 (351) 2408 5135 3835 5135
30-40 329 (351) 2057 4387 4387
40-50 365 1706 3638 3638
50-60 384 1341 2860 2860
60-70 378 957 2041 2041
70-80 358 579 1235 1235
80-90 199 221 471 471
90-100 22 22 47 47
4689

The figures given by Dr. Price differ very slightly from those
given in the last column, and are probably the result of an arbitrary
adjustment.
The mortality shown by the Northampton Table was excessively
high,and this led to large profits being made by the early insurance
companies, in which a much lighter rate of mortality was experi-
* See J. I. A., Vol. XVIII, p. 107 et seq.
6 SOURCES AND CHARACTERISTICS OF

enced than the table led them to expect. On the other hand,
annuity companies and the government through their annuities,
lost heavily. Dr. Price was himself sensible of the very high
mortality rates shown by the Northampton-Table, and in 1782 he
recommended the Equitable Societyto adopt the lower rates given
in the Chester Experience; butan excess of caution on the part
of the society gave the Northampton Table a standing which it
never deserved.
The mortality shown by this table has been found to correspond
roughly to the mortality of certain colored races; and, as very
complete tables of monetary values are available on the Northamp-
ton basis, the tables may in rare instances still be used with ad-
vantage, when investigation shows that some class of substandard
mortality approximates to that of the old table.
As far back as 1823 the faults of these tables were well known,
as the following quotation shows:

“Dr. Price did as much as the nature of his materials would allow. For
in those days no census or enumeration of the population had been made; and
without a comparison of a census (in which the ages are carefully distinguished)
with the Bills of Mortality, an accurate Table of Observations cannot possibly
be obtained.” Farren on Life Assurance 1823 ,

The Carlisle Table of Mortality.*

(.Published 1815.)

This table was formed by Joshua Milne, Actuary to the Sun

Life Office, London, from materials contained in a tract published
by Dr. John Heysham at Carlisle in 1797. These materials con-
sisted of a careful census in January, 1780, and a less accurate
enumeration in December, 1787, of the two parishes in Carlisle,
St. Mary and St. Cuthbert, together with the Register of the
deaths in those parishes during the nine years, 1779 to 1787.
The original statistics were divided into male and female; and
the deaths showed also the condition of each sex as regards marriage;
but the graduated tables dealt only with the total of both sexes,
details of which are given in the table quoted on the next page.
It has been pointed out that in the second enumeration the ages
do not appear to have been taken, but that the increment 1000
seems to have been proportionately added to the first enumeration,
* Milne on Annuities and Assurances, London, 1815, Article 704, p. 404
et seq. See also King, J. I. A., XXIV, 186.
 ,

THE PRINCIPAL MORTALITY TABLES. 7

Population Population
Between Deaths in Between Deaths in
the 9 years the Ages. the 9 years
the Ages. in Jan., in Dec., in Jan., in Dec.
1779-1787. 1779-1787.
1780. 1787. 1780. 1787.

0- 1 .390 3327 3761 979

1- 2 173 20-30 1328 1501 96
2- 3 128 30-40 877 991 89
3- 4 70 40-50 858 970 118
4- 5 51 50-60 588 665 103
60-70 438 494 173
0- 5 1029 1164 812 70-80 191 216 152
5-10 908 1026 89 80-90 58 66 98
10-15 715 808 34 90-100 10 11 28
15-20 675 763 44 100-105 2 2 4
3327 3761 979 7677 8677 1840

i.e., in the ratio 1000 -f- 7677. This increment looks like an approxi-
mation to the true population and Dr. Heysham said of it, after
correcting some errors, “I am persuaded the enumeration is
now pretty exact 11 .

Adding the totals together (7677 + 8677) the result was multi-
plied by four in order to place the population and the deaths on a
common basis for comparison, the latter being reduced by one-
ninth in order to effect this. The result was an approximation to
the sum of the total population exposed during eight years, and
this was compared with an approximation to the sum of the deaths
during those eight years.
The following table shows the results thus obtained:*

Between the Population. Deaths. Between the Population. Deaths.

Ages. Ages.

0- 1 347.0 28352 870.5

1- 2 153.7 20-30 11316 85.3
2- 3 113.9 30-40 7472 79.1
3- 4 62.2 40-50 7312 104.9
4- 5 45.3 50-60 5012 91.6
60-70 0790
O 4iJO
IRQ Q
lOo.o
0- 5 8772 722.1 70-80 1628 135.1
5-10 7736 79.1 80-90 496 87.1
10-15 6092 30.2 90-100 84 24.9
15-20 5752 39.1 100- 16 3.6
28352 870.5 65416 1635.9

The results given in the above table were graduated by a

graphic method of adjustment, two graphs being prepared, one for
* Sutton, J. I. A., Vol. XXIV, pp. 110-122.
 :

8 SOURCES AND CHARACTERISTICS OF

the population and one for the deaths. The following is a geo-
metrical illustration of the population graph

The base line represents the age attained while the upright lines
(called ordinates) represent the numbers alive at the various ages.
The areas of the parallelograms represent the total population in
the several groups; thus, the base of the first parallelogram being
5 years, and its area 8772, its altitude is 8772 -f- 5 = 1754. Similarly,
the 'altitudes of the next 3 parallelograms are 7736 -f- 5, 6092 -f- 5,
and 5752 -f- 5 respectively, but the base of the fifth being 10, its
altitude isll316-v-10, and so on for the other altitudes.
A curved line was then drawn through the parallelograms pro-
ceeding smoothly from the one to the other, adding a portion to
each, and cutting off an equal part. The areas were then sub-
divided into fifths or tenths as the case required, each sub-
division representing a period of one year. These years were
bisected, and the length of the ordinate then erected gave the
graduated population at the middle of the year, i. e., Lx which ,

X
Mr. Milne wrote L. The deaths were treated in exactly the same
X
way, and D, i. e., the mean number that died between the ages
x and x + 1, was obtained. From these mean values Mr. Milne
formed the values of dx . The radix was taken as 10,000 and the
figures after age 100 were adjusted arbitrarily.
 THE PRINCIPAL MORTALITY TABLES. 9

Females represented about 55% of the population, and this had

the effect of showing light mortality at the older ages, one of the
characteristics of female mortality being that it is much lighter
than male after the age of 50. Amongst insured lives, only about
10% are females, so that the table was never a good one for life
insurance premiums, or valuations; and it is not now used for such
purposes. The original statistics and remarks published by Mr.
Milne in 1815 contain a great deal of valuable information, includ-
ing comparative mortality —
(1) from different diseases, (2) during
different seasons of the year, and (3) of the two sexes. The original
publication is well worthy of careful perusal even at this date.
The results of the graduation left several irregularities, especially
at the older ages. For example, at age 91, the expectation of life
is 3.26 years, while at age 95,when it should be less, it is 3.83.
This was caused by the system of graduating separately the
population and the deaths, whereas a regraduation should have
been made of the ratio ra x The irregularities were completely
.

removed in a graduation which was successfully accomplished

by Messrs. King & Hardy* in 1880 by applying Makeham’s
Formula. This formula gives a perfectly smooth curve when the
results are presented graphically and the general characteristics
of the original Carlisle Table were maintained from childhood till
old age. It is only when approaching age 90 that the difference
between the two tables becomes considerable. Facilities were thus
given for the calculation of the more intricate benefits.
The table has been very extensively used, and even yet is of
considerable value in calculating the values of Reversions, etc.
As the published tables based on Carlisle Mortality are unusually
extensive, it is often adopted as a matter of convenience in connec-
tion with special calculations.

English Life Table No. I.f

The compulsory registration of births, marriages, and deaths

was introduced in England in 1836, and this requirement of law,
which became operative from July, 1837, gave a proper basis for
the formation of a national table of mortality.
Dr. William Farr was appointed Compiler of Abstracts in the
* J. I. A., Vol. XXII, p. 221.
Registrar General’s Returns as quoted.
t Walford’s Encyclopedia.
Farr's “Vital Statistics, 1885.”
 —

10 SOURCES AND CHARACTERISTICS OF

General Register Office in 1839 and for the next forty years he was
engaged in developing a national system of vital statistics. He
had no official connection with the census enumeration of 1841,
the observations being then made on a plan recommended by
Professor de Morgan and Mr. Griffith Davies. But Dr. Farr
used the census enumeration in conjunction with the Registers of
deaths to compile the first English Life Table which was published
in the Registrar General’s fifth annual report, 1843. This table
was based upon the Census Returns for England and Wales made
on June 6, 1841, and the deaths taken from the Registers of that
year. As the deaths related to the calendar year, it was necessary
to make a correction in the population for the period from June 6
to July 1 —
the middle of the year. An increase of 1.334% had
taken place in the ten years from 1831 and it was assumed that
this rate of increase continued during the 25 days, or .07 of a year,
until July 1st. The population as adjusted to July 1st was
15,927,867 and the deaths 343,847. In the census enumeration
some of the ages were not specified; and in such cases they were
assumed to be in the same proportion as those whose ages were
given. In like manner the ages at death in 521 cases were not
given and were similarly treated.
The rates of mortality in a single year cannot be viewed as a
proper basis for a national table, because even with a large popula-
tion of nearly 16,000,000 the variations caused by climatic condi-
tions, epidemics, etc., are great. however, from subse-
It appears,
quent results that the year 1841 did prove to be a fair average one.
Owing to the tendency for persons at any age between 30 and
40 to state their age as 30, Dr. Farr said that in quinquennial
groups the death ra/te for the period from age 30 to age 35 would

be too small and for the period from 35 to 40 too large. He further
said “ It
: is my opinion that the ages of the people have been returned
with sufficient accuracy for all practical uses in decennial 'periods”
To overcome such difficulties and obtain rates of mortality for
each age, Dr. Farr dealt with the statistics as they were two
if

series of geometric progressions —the first from age 15 to age 55

and the second from age 55 to age 95. He obtained the ratios
for these geometric series by comparing the increase in the mortality
in the groups
*
First 15-20 25-30 35-40 etc.
Second 20-25 30-35 40-45 etc.
 THE PRINCIPAL MORTALITY TABLES. 11

Since the errors in these two series would be of a similar nature

there was a great probability that the ratio would be satisfactory.
From such quinquennial grouping a central death rate was ob-
tained and treated as the death rate applicable to the central age
of the group. The table was based upon 100,000 births of whom
51,274 were males and 48,726 females —being the proportion in
which the births of the two years 1840 and 1841 were distributed.
The table therefore represents a generation of 100,000 individuals
born at the same instant and shows the relative number of males
and females at each age, as well as their probabilities of living and
expectations of life.

The period of infancy was differently treated and Dr. Farr

explained the method as follows:

“The two years 1840-41 amounted to 520,157; which

births of boys in the
was at the rate whence it may be assumed that 260,078
of 260,078 a year;
were born in the year, of which 1 January, 1841, was the middle or that the —
mean date of their birth was January 1, 1841. We can then reason upon the
—
assumption that 260,078 boys the mean ann. number of boys born in 1840
—
and in 1841 were bom 1 January, 1841. But all the boys who died in
1841, under 1 year of age, must have been boys born in 1840 and in 1841.
— —
The deaths occurred in the year 1841 in one year and they must therefore
be compared with the births in one year, viz., with the births in the year of
which January 1, 1841, was the middle. We have then this result, that
41,444 of 260,078 boys bom died in the first year after birth. . . .

“All the births are not registered: the deaths in the first year must have
occurred out of more than the number of births returned; and the mortality
in the first year must have been less than that given in the table, which is,
however, lower than the mortality deduced immediately from the children
stated at the enumeration to be living at the first year of age, and the deaths
registered at the same age. As it is, the mortality in the first year stands lower
than in any other authentic table.”

As large masses of figures were involved in each age-group a

graduation of the group results was neither necessary nor desir-
able. To get results at individual ages, “the mortality at every
age was interpolated by the log which expresses the ratio of
increase in the mortality at every year of life, and the chance of

living each year was deduced from \ .”

1
12 SOURCES AND CHARACTERISTICS OP

English Life Table No. II.

This table was published in the 12th Report of the Registrar

General, 1853, the census of 1841 again furnishing the basis for
the exposures, but the deaths were taken for a period of seven
years from January 1, 1838, to December 31, 1844, inclusive, the
total deaths in this period being 2,436,648. During that time
there were no epidemics of any consequence. Dr. Farr calls
attention to the rapid variation in the rates of mortality in infancy,
“when the rate of mortality varied so rapidly that every year
and even month is marked by a change.” At the earlier ages
the mortality rates were directly taken from the return but after
age five, quinquennial, and after age fifteen decennial periods were
used. The is of little importance in comparison with the
table
later compilation with which the results are in general agreement.
The final tables were based upon a radix of 10,000,000 persons—
5,126,235 males and 4,873,765 females.

English Life Table No. III.*

Published in 1864 as a distinct work by Dr. Farr. Several

improvements were introduced in construction and the Table
is worthy of description in greater detail than either No. I or No. II.

—
Two censuses were used those of 1841 and 1851, comprising
15,929,492 persons as adjusted to the middle of 1841 and 17,982,-
849 in 1851, while the deaths extended over the 17 years from
—
1838 to 1854 that is V/2 years approximately before the first
census and a similar period after the second census. During that
time there were 6,470,720 deaths.
The population was carried back to the beginning of 1838 by
using the ratio of increase in the population from 1841 to 1851,
assuming that such increase is in geometrical progression. Thus,
having obtained the ratio from the formula

= log Pel- log P„

!°gr ,
jo

where Phi represents the population in 1851, the population at the

* “English Life Table/' Longman, Green & Co., London, 1864.
Walford's Insurance Cyclopaedia. Farr's “Vital Statistics/’ 1885.
Important J. I. A., Vol. XLII, p. 228 et seq.
. (King).
 THE PRINCIPAL MORTALITY TABLES. 13

beginning of 1838 was estimated by the formula

log P = 38 log P - 3H
4i log r.

The following table shows the population of England and Wales

estimated in the middle of 1841 and 1851, in Dr. Farr’s groupings.

Persons. Males. Females.

Ages.
1841 1851 1841 1851 1841 1851

All 15,929,492 17,982,849 7,784,883 8,808,662 8,144,609 9,174,187

ages.

0- 2,107,008 2,355,345 1,048,270 1,180,430 1,058,738 1,174,915

5- 1,865,856 2,098,808 953,235 1,053,510 912,621 1.045.298
10- 1,772,913 1,919,255 880,567 967,007 892,346 952,248
15- 3,145,541 3,418,488 1,511,602 1,671,634 1,633,939 1,746,854
25- 2,450,322 2,740,919 1,174,473 1,323,621 1,275,849 1.417.298
35- 1,778,737 2,089,629 875,874 1,017,018 902,863 1,072,611
45- 1,270,178 1,516,324 617,113 734,314 653,065 782,010
55- 832,692 1,010,973 399,490 482,788 433,202 528,185
65- 483,593 579,187 224,310 268,052 259,283 311,135
75- 190,443 220,618 86,736 97,008 103,707 123,610
85- 30,541 31,754 12,635 12,745 17,906 19,009
95 1,668 1,549 578 535 1,090 1,014
and

wards

By arranging the groups in this way a correction is applied to

the tendency in census returns to state the ages at the nearest
decennial, as 30, 40, etc. The deaths for the same years were
arranged to correspond and thus average annual rates of mortality
were obtained by dividing the deaths during the 17 years by
S }/2 times the sum of the populations in 1841 and 1851. This
was apparently a departure from the principle of geometric
increase; butit was found by actual trial that the geometric

mean (1838-1854) was almost identical with the method adopted.

Having thus obtained the Central Death Rate for the middle
age of each group Dr. Farr calculated the probabilities of living
by a logarithmic method which gave results he said nearly
identical with the formula
2 —m x
^x
+m
'

2 x

Values of p x for intermediate ages were then interpolated by

finite differences; this method of construction made graduation
unnecessary.
 :

14 SOURCES AND CHARACTERISTICS OF

As in Table No. I the statistics were scheduled in three parts

1. Persons —Male and Female.

2. Males.
3. Females.

The radix of the first part was 1,000,000 children born alive;
of the second part 511,745, and of the third part, 488,255, being
the proportions in which boys and girls were bom during the
seventeen years under observation. The male and female tables
were constructed independently; that of the “ persons’ 7
was
obtained by combining the other two in one.
Out of 1,000,000 persons born, it was shown that 149,493 died
in the first year; 53,680 in the second; with decreasing numbers
of deaths until the age of 13, when 3,382 died between that age
and 14; then this number increased steadily for each age until
it reached 15,469 who died between 73 and 74. Thereafter,
although the rates of mortality increase rapidly the annual deaths
diminish; 92 died at the age of 100 and the last one at the age of
108 — “so 109 years is the limit of age of this table.”
\ So far as such census tables can be computed from data which
are admittedly imperfect, being based on voluntary unverified
statements, the table is looked upon as a great advance on older

methods, and many of the ideas used for the first time in that
table have since been copied and adopted by other statisticians.
Dr. Farr in all three tables assumed that the average value of the
death rate for an age interval gave the true value for the central
point of age.
Census tables represent the mortality of all classes mixed. This
means a preponderance of the laboring and industrial classes; but
the table cannot be said to represent even these classes, because of
the percentage of well-to-do people. For financial calculations
applicable to individuals the tables do not meet with present-
day requirements.
Mortality in Infancy . —
From birth until the age of 1 the deaths
were given for each month of age. They were extracted from the
registers of births and deaths directly, the census figures being of no
value for this particular purpose. For the 17 years under observa-
tion the deaths under age 1 were given for (a) the first 3 months, (6)
the second 3 months, and (c) the next 6 months; but for 8 years
of the period Dr. Farr abstracted the deaths for each one of the
 THE PRINCIPAL .MORTALITY TABLES. 15

first three months, and then distributed in the same proportions

the deaths during the 17 years occurring in the first three months.
The other figures for the first twelve months were obtained by
interpolation. These deaths in conjunction with the total number
bom admitted of a good approximation to the probabilities of
living and dying.
The English Life Table No. Ill shows slightly higher mortality
rates than either No. I or II, as indicated by the Expectations of
Life at age 30 (male). The cause of this slight difference lies
probably in the processes employed, rather than in reduced
vitality.
English Life No. I = 33.13 years.
No. II = 33.21
“
= “
No. Ill 32.76

The volume published in 1864 not only explained the construc-

tion of the experience but gave also about 600 pages of tables with
monetary values and commutation columns from 3% to 10%,
also complete joint-life values at 3% for (1) two males, (2) two
females, and (3) male and female. The tables have been freely
used by Industrial Insurance Companies.

Healthy English Life Table.*

After the completion of the English Life Table No. Ill Dr. Farr
set himself to the construction of another table based upon the
experience of 63 of the healthiest English districts inhabited by
nearly a million people, dividing the experience into males and
females. He gave a brief description in his “ Vital Statistics”
as follows:

“The Healthy District Life Table was constructed in 1859 from the Census
enumeration of 1851 and from mortality observations extending over the five
years 1849 to 1854 in 63 districts of England and Wales which showed during
the ten years 1841-50 a mean annual death-rate not exceeding 17 per 1,000
persons living. It has been found by experience that this Healthy District
Life Table expresses very accurately the actual duration of life among the
clergy and other classes of the community living under favourable circum-
stances.”

In general, the methods of construction were those used in

compiling the English Life Table No. Ill, with slight modifications.
* J. I. A., Vol. IX, pp. 124, 188, etc. Farr’s “ Vital Statistics.”
Transactions of the Royal Society, 1859, pp. 838-^tl.
16 SOURCES AND CHARACTERISTICS OF

The probabilities of life for the first four years, namely p 0 p if

,

p if andpz, were also obtained from the births and deaths without
reference to the census figures. For example, half the number of
births in two calendar years was taken as the number exposed to
risk from January 1 of the second year, while the death records
gave the numbers dying under age 1, from 1 to 2, from 2 to 3, etc.,
in the subsequent years, whence it was easy to form lx and dx
columns, and get the early values of p x Three such computations
.

were independently made by using different years, and the values

finally adopted were the mean of the three. Values of p 7 pn and ,

Pi o were obtained from the census figures, and the intervening

figures were computed by mathematical interpolation from pz to p 2o-
Dr. Farr pointed out that if there were much emigration from a
community this would result in an understatement of the death
rates, because the births would be properly recorded, but children
would be taken away by their parents and would die elsewhere.
This effect would be heightened each year after birth, and at ages
4 and 5 the death rates might be appreciably affected. On the
other hand a failure to register births might have the opposite
effect.
Later English Life Tables.
The fourth* English Life Table was based on the mortality for
the decennium 1871 to 1880 and founded upon the preceding
table (No. 3) by making allowance for the different rates of
mortality in the new period. Details regarding it are of little
interest.
The fifth* and sixth* English Life Tables were prepared by Dr.
John Tatham and the improvements in construction, as well as
the increased healthiness at the younger ages to which they direct
attention, are so considerable as to demand adequate mention
notwithstanding the fact that Dr. Tatham himself said in 1907
“The scheme devised by Dr. Farr in 1864 has been in all essential
points adhered toby his successor.” The fifth Table was based
upon the mortality in the ten years 1881 to 1890 and the — —
methods of construction were the same in principle as the sixth
Table, differing only in minor matters, such as the groupings from
* These Tables are all published in the supplements to the annual reports
Deaths and Marriages in England and
of the Registrar General of Births,
Wales and appear in the 45th, 55th, and the 65th, (1907) annual reports
respectively.
 THE PRINCIPAL MORTALITY TABLES. 17

ages 5 to 25, and the functions used for interpolation. The new
methods are free from the serious error of Dr. Farr's assumption
mentioned on p. 14, and Mr. George King says, “The principles
underlying them can scarcely be improved upon."
The facts collected by the census enumeration and those taken
from the death registers were grouped round decennial points from
ages 20 to 90. Thus, the decennial point 30 was the center of
the grouped facts from age 25 to age 35. Each group therefore
represented the population living between ages x and x + n and
the deaths between the same ages. In actuarial notation these
groups can be expressed as Tx — Tx+ ny or for the population
and l x — l x+n or lX n|, for the deaths.
,

By summing all the groups from x to the oldest age we obtain the
values of T x and lx for certain ages, 25, 35, 45, etc., and from these
we can deduce successively the intermediate values of Tx and lX)
as well as complete values of L x dXJ mxy p X} and other functions as
,

desired. Mr. King* recommends that T x and lx be interpolated

separately by a formula of osculatory interpolation to get the
intermediate values. But the method actually employed in the
English Life Table No. 5 was to interpolate by ordinary differences
between the successive decennial values of log (2 Tx + l x) and
log (2 T x - lx) so as to get log (2Tx+ i+lx+l ) and log (2 Tx+X -Ix+1 )
whence by differencing the natural numbers, decennial values of
(2 Lx + d x ) and (2 L x — dx ) were found. From these functions
the decennial values of p x were obtained from ages 25 to 65.
Other methods were employed at younger and older ages. Then
the logs of decennial values of p x from age 5 to age 85 were inter-
polated to obtain the figures for each age.
Overlapping values were used in the interpolation, and two sets
of probabilities were obtained for each age. A more regular curve
can be obtained by using an overlapping series rather than an
abutting series. From
the values at ages 25, 35 and 45 one set
of probabilities for 35 to 45 was obtained, and from ages 35, 45,
and 55 another set. The junction between these two partial
curves is generally smoother than the junction between two partial
—
curves 25, 35, 45, and 45, 55, 65 the former being overlapping
and the latter abutting. Each probability in the first series was
then multiplied by an empirical fraction so as to give greater
weight to the terms nearest the central decennial value. Nine
* J. I. A. XLII, p. 236.
18 SOURCES AND CHARACTERISTICS OF

factors were derived from the “Curve and ranged from

of Sines”
.02447 to .97553, the central value being .50000. The same prob-
ability in the second series was multiplied by the complementary
fraction, and the addition of the two gave the final value. For
example, p 3 6 would be derived from two sets of interpolations, the
first set having its central decennial point at age 35, and the second

set its central decennial point at age 45; accordingly the first
value of £>36 would be multiplied by .97553 and the second by
—
.02447 the sum of the two giving the final result.
For English Life Table No. 6 based on the mortality of the ten
years 1891-1900, the functions interpolated were log 2 Tx and log lx ,

these functions being developed apparently with the view of using

the formula

_ 2Lx — dx
~
Px
2 r + dj
x

but there is no apparent advantage in either the No. 5 or No. 6

plan, Mr. King’s suggestion giving more direct results with greater
ease.
The values above age 85 were obtained by extrapolation from
the five values 45, 55, 65, 75, and 85, because census returns at
the older ages are unreliable. The system of extrapolation cannot
be considered as satisfactory, but it was a case of choosing the
better of two doubtful methods.
Probably the most important innovation in the Mortality
Statistics of the 5th and 6th English Life Tables deals with the
Mortality by Occupation . —
The varying rates of mortality in
different occupations first formed the subject of an inquiry by Dr.
Farr about 50 years ago, and his ideas have been developed and
improved upon until a very complete analysis of this nature has
now been given for the triennial period 1900 to 1902, based upon
the census figures of 1901. The numbers living in 1901 were
obtained from the census, and the deaths in each occupation from
the registers. The information which relates only to male lives
was then divided into four principal areas:
1. London,
2. Industrial districts,
3. Agricultural districts, and
4. Other parts.
 THE PRINCIPAL MORTALITY TABLES. 19

Comparisons of this nature are generally made in other countries

“
from crude ” death rates, which show the number of deaths per
1

1,000 of population without giving effect to age or sex distribution,

and are thus often misleading; but the recent publications of
English Mortality give “corrected” figures. A standard table is

adopted showing the numbers alive in decennial periods in an

average population, and a corrected death rate for the particular
occupation or locality is then deduced by reducing the population
to the standard basis for comparison. The system is not perfect,
but shows a great advance towards scientific accuracy, and the
it

necessity for such treatment is well illustrated in the case of

farmers. The crude death rate amongst farmers, ages 15 and
upwards, for 1900-2 was 16.44 per 1,000, whereas the general
death rate amongst all males of 15 and upwards was only 16.23.
From this it would appear as if farmers were subject to a higher
death rate than males generally; yet at each age group the death
rate amongst farmers is much lower than the death rate of males
generally, and the high crude death rate is caused by the large
number of farmers at the older ages, and, relatively, the small
number at the younger ages.
The principal comparisons were made during the active working
period of life, in four decennial age groups from 25 to 65. Over
100 occupations were dealt with —in some instances industries of
like character being grouped under the same heading. The census
tables of 1901 also supply information about those who had retired
—
from any particular calling the word “retired” covering those
who had retired in comfort as well as those whose health had
broken down and had thus lost the ability to earn a living. The
occupation dealt with is that which has last been followed, and
no system has yet been devised for dealing with changes.
In the period from ages 25 to 65 there had been a consistent
decline in mortality between 1890-2, and 1900-2, this decline
varying from 11 per cent, at ages 55 to 65 to 17 per cent, at ages
25 to 35. Graphic illustrations are given showing the gradations
of the mortality for the age group 25-65 in' different occupations
commencing with clergymen, gardeners, game keepers, and far-
mers, who show the lowest corrected death rates, and ending
with hotel servants, costermongers, tin miners, and general
laborers, who show the highest death rates.
In some instances the figures must be used with great caution
20 SOURCES AND CHARACTERISTICS OF

because the classified numbers become so small that accurate

deductions from them are not warranted. Moreover, some occu-
pations requiring muscular strength and vigor are forsaken in favor
of an occupation of lighter character when a man falls into ill
health in the former. These occupations, therefore, exercise a
species of selection favorable or adverse by attracting to them-
selves either the unusually vigorous or the weak. This probably
had much to do with the heavy death rates in the miscellaneous
occupations like costermongers and general laborers. During the
period 1890-1892 there was prevalent a serious epidemic of in-
fluenza, which made the mortality at that time abnormally high.
Accordingly the lower rates shown ten years later are probably
not caused solely by improvement in longevity. The census date
— 1st April, 1901 —was not exactly in the middle of the three
elementary years during which the deaths were computed, but it
was thought better to neglect the small error thus introduced rather
than to make estimates of the subdivided populations in various
occupations to the exact middle of the year 1901, and it was found
impracticable to take the deaths otherwise than for the three
complete calendar years.
In the statistical tables the deaths in the various occupations
are not only given in seven age groups, but are given under “causes
of death,” and are also* published separately for those who are
occupied and those who are “occupied and retired.” The mor-
tality of industrial districts is above, and of agricultural districts
below, the average.

Healthy English Life Tables Nos. II and III.

The utility of a mortality table deduced from healthy districts

only, as recommended and originated by Dr. Farr, has been
confirmed and approved by later statisticians. Dr. Farr based
his table upon those districts in England and Wales whose crude
death rates did not exceed 17 per 1,000, one district with larger
death rate having been included through error. As the death
rates were tabulated to the nearest whole number, this practically
meant under 17.5 per 1,000.
A second Healthy English Table was formed after the census of
1891, and at that time a “corrected” death rate was used showing
the number of deaths per 1,000 in each registration district if the
ages and sex distribution had been in the same proportion as the
 THE PRINCIPAL MORTALITY TABLES. 21

general population at the preceding census.The second Healthy

Districts Table was formed from the statistics of England
and Wales over the period from 1881 to 1890, and a third
Healthy Districts Table was formed for the period from 1891 to
1900.
Lower rates of mortality were recorded during each of these
decennial periods than had been shown in Farr’s earlier table,
and in forming the second table those districts only were used
where the corrected death rate was 15 per 1,000 or less. There were
263 of such districts with an aggregate mean population of 4,603,-
055, representing during the ten years over 46,000,000 years of life,

or more than nine times as many as the older table.

In forming the third table the standard of healthiness was again
raised and 260 districts were included whose aggregate population
was 4,477,485 with corrected death rates not exceeding 1£ per 1,000.
Of the 260 selected districts 222 were common to the second as well
as the third table. Accordingly 41 of the districts used for the
second table were excluded in forming the third table, and 38 new
districts were included. When reduced to a common standard,
after making allowance for age and sex distribution, the corrected
death rate of the entire group of healthy districts for the third
table was .85 per 1,000 lower than that of the second table. Had
the corrected death rate of 15 per 1,000 been used (in 1891-1900)
there would have been 352 districts (with an aggregate mean
population of 7,326,280 persons) qualifying under such standard
for the third table.
The districts which experienced the low death rates were almost
exclusively those which are rural in character or contain only small
towns with rural surroundings. No part of London is represented
in the new table, yet of the healthy districts, a large proportion is
in the section of England of which London might be taken as the
center. The progress of healthfulness in England and Wales may
be partly indicated by Tables of Expectations as herein submitted;
but it should be borne in mind that the figures are affected by
the inaccuracies already discussed.
 ...

22 SOURCES AND CHARACTERISTICS OF

Expectations of Life.
Table.—Males.
AgeO. Age 20. Age 35. Age 50. Age 65.

English Life No. 3 (1838-1854) 39.91 39.48 29.40 19.54 10.82

“ “ “ 4 (1871-1880) 41.35 39.40 28.64 18.93 10.55
“ “ “ 5 (1881-1890) 43.66 40.27 28.91 18.82 10.31
“ “ “ 6 (1891-1900) 44.13 41.02 29.24 18.90 10.34

Healthy Districts No. 1 (1849-1853) . 48.56 43.40 32.90 22.03 12.00

“ “ “ 2 (1881-1890) . 51.48 44.41 32.70 21.53 11.60
“ “ “ 3 (1891-1900) . 52.87 45.37 33.32 21.74 11.61

Expectations of Life.
Table.— Females.
AgeO. Age 20. Age 35. Age 50. Age 65.

English Life No. 3 (1838-1854) 41.85 40.29 30.59 20.75 11.51

“ “ “ 4 (1871-1880) 44.62 41.66 30.90 20.68 11.42
“ “ “ 5 (1881-1890) 47.18 42.42 31.16 20.56 11.26
“ “ “ 6 (1891-1900) 47.77 43.44 31.52 20.64 11.27

Healthy Districts No. 1 (1849-1853) . . 49.45 43.50 33.46 22.87 12.58

“ “ “ 2 (1881-1890) 54.04 45.62 34.16 22.75
. 12.36
“ “ “ 3 (1891-1900) . 55.71 46.93 34.79 22.92 12.36

English Life Tables Nos. 7 and 8.

These two tables were published at the same time, in 1914, in

the form of a Supplement to the 75th Annual Report of the
Registrar General of Births, Deaths, and Marriages in England
and Wales. In an Appendix all of the statistics are published
which were used to form the final tables; also the mathematical
formulas employed.
Table No. 7 consists of the experience during an intercensal
period of ten years from 1901 to 1910 inclusive. Table No. 8
deals with the deaths in three calendar years 1910, 1911, and
1912, grouped around the census point in 1911, the population
being adjusted to 1st July, 1911. Both investigations were made
by Mr. George King, and his report on the work contains a lucid
description of the tables and of the reasons for the decisions which
were reached on points of difficulty.
Table No. 7 follows in its general principles the main lines of
investigation which characterized, and developed from, the earlier
English Life Tables; but a radical change in mode of con-
struction was made in the adoption of King’s method. The
population for each year to age 4 inclusive was enumerated, then
in quinquennial groups 5 to 9 last birthday, 10 to 14, etc. The
deaths from 1901 to 1910 were given in decennial groups from
 THE PRINCIPAL MORTALITY TABLES. 23

age 25 onwards; but were subdivided into quinquennial groups

in the proportions existing among the deaths of 1910 to 1912.
From the said quinquennial values pivotal values of population
—
and deaths were obtained, ages 12 to 97 inclusive hence m x etc. ,

From these central death rates, quinquennial values of qx were

deduced. Then by osculatory interpolation, using the function
log ( Qx +-1), the values from 18 to 97 were obtained.

The rates of mortality at ages 0 to 4 inclusive were determined

from the death returns at individual ages and the readjusted
average population. This readjustment was found necessary
because the census returns indicated a deficiency of population
at ages less than two last birthday.* The theoretical population
for each attained age was accordingly calculated from the birth
and death returns and each age was then reduced in the propor-
tion necessary to bring the total exposed to risk under age 5 down
to the total derived from the census returns. The assumption
that the total population at ages under five was correctly given
in the census returns was made because a similar assumption had
been made in the construction of English Life Table No. 6, and
it was desired that the two should be comparable. The birth
and death returns, however, indicate that the deficiency at the
two younger ages was an absolute one and not a transfer to older
ages. The rates of mortality at ages 5 to 16 inclusive were then
inserted by Lagrange’s interpolation formula from the values for
ages 3, 4, 12, 17 and 18.
At the extreme old ages no assumption was made with regard
to the termination of the table. The were used to
original data
age 92, with a pivotal value at age 97. A fourth difference series
of values of log p x was determined from the values at ages 89,
90, 91, 92 and 97, and projected onwards. While there is no
theoretical limit the practical limiting age is about 110 for men,
and 114 or 115 for women. It is claimed that the new tables are
more accurate than previous English Life Tables at the older
ages
Important changes in methods of construction were made in
forming Table No. 8. These may be briefly summarized as fol-
lows:
* The accuracy of these deductions by Mr. King has been questioned by

Dr. J. C. Dunlop’s able analysis, with verification of the ages of nearly

12,000 children. See Journal of the Royal Statistical Society Vol. 79, p. 309.
,
 —

24 SOURCES AND CHARACTERISTICS OF

1. The reduced period gives a more definite measure of the

mortality;
2. The census of 1911 gave numbers for individual ages instead
of quinquennial or decennial age periods. It was possible
therefore to group these in a more scientific theway and
groupings adopted were ages 4 to 8, inclusive, 9 to 13,
etc., instead of 5 to 9, 10 to 14, etc., as formerly.

3. Marital condition was given in tabulating the deaths of

women during that period. Wives show lighter mor-
tality rates than widows, and spinsters lighter than
wives, except between ages 45 and 55, though in the
latter case the differences are not very marked.
4. The rates of mortality for the first six years of life were cal-
culated from the birth and death returns without refer-
ence to the census figures.
5. Healthy Districts Tables were discontinued in favor of
Tables based upon the mortality in
a. London;
b. County Boroughs;

c. Urban Districts; and

d. Rural Districts.

These four groups represent approximately varying degrees

of urbanization.
census population in 1911 was approximately 17,400,000
The
males and 18,600,000 females. Under the general title of English
Life Table No. 8, there are published the following:

1. Life table for the entire area of Englandand Wales males —

and females respectively, with the usual mortality func-
tions.

2. Life tables for females only according to marital condition

(a) Spinsters, (b) Wives, and (c) Widows.

3. Sectional life tables —

males and females respectively
(a) Administrative County of London; ( b ) Aggregate of
County Boroughs; (c) Aggregate of Urban Districts;
(d) Aggregate of Rural Districts.

Throughout the greater part of fife London shows lighter mor-

than the County Boroughs; both of these show heavier
tality
 —

THE PRINCIPAL MORTALITY TABLES. 25

mortality than the Urban Districts, while the Rural Districts

show the lightest mortality of all. Female mortality in London
up to age 25 shows be'tter than any of the others.
The effect of the emigration of young adults, and of immigra-
tion caused by the return of older British subjects from overseas;
also the effect of old age pensions on the statements of age; de-
liberate misstatements by women, etc., are discussed with other
minor criticisms in a review of the Tables J. I. A., XLIX., pp.

96-107. The suggestion is made to attempt elimination of such

errors —a dangerous proceeding unless based on carefully ascer-
tained facts.*
The notation was changed from the old system used in English
Life Tables to the regular actuarial notation Text Book form.
If Mr. King had done nothing in actuarial science except to
standardize our notation all future generations of actuaries would
be in his debt.
An interesting part of the report is the mortality shown by the
various tables reduced to one common basis for comparison.
The rate is lower at all ages and for both sexes by the English
Life Tables No. 7 than by No. 6, and lower at practically all ages
in No. 8 than in No. 7.

Expected Deaths per Annum in a Population Distributed According

to the Census Returns of 1911 Ages 0 to 89, Inclusive.

Ages Last Birthday. No. 6. No. 7. No. 8.

Males 0- 4 106,677 92,197 79,357

5-59 122,830 101,995 91,628
60-89 94,369 87,114 84,216

0-89 323,876 281,306 255,201

Females 0- 4 89,394 76,879 65,980

5-59 112,806 93,667 81,497
60-89 108,344 94,472 91,091

0-89 310,544 265,018 238,568

* See further discussion by Mr. King and others. J. I. A., XLIX., p. 297
et seq.) also J. I. A., XLVIII, p. 207, on “Graduation of Ages.”
 26 SOURCES AND CHARACTERISTICS OF

U. S. Life Tables 1910.

These tables are the first of any scientific value prepared by
the U. S. Government from Census returns. When the census
of 1910 was taken the Bureau of the Census called into consul-
tation a committee of the Actuarial Society of America and this
committee gave general advice, both with reference to the taking
of the census and the tabulation of the data. Although the
recommendations were not in every case followed, the general
results, and the tables now available, prepared under the super-
vision of Prof. James W. Glover, mark a notable epoch in the
history of mortality investigations in the United States.
The which were published in 1916, are based upon the
tables,
census of the population taken in 1910 and the deaths during
the calendar years 1909, 1910, and 1911 for the original regis-
tration states comprising: Maine, New Hampshire, Vermont,
Massachusetts, Rhode Island, Connecticut, New York, New
Jersey, Indiana, Michigan, and the District of Columbia. Ac-
cordingly the tables do not exhibit the mortality of the entire
area of the United States, but deal chiefly with the northeastern
section.
The census was taken as of April 15, 1910. The data were
entered on the schedules by the enumerators, and the people
were recorded as of their usual place of abode. The work of
enumeration
1909
commenced on April 15, and in cities had to be
completed
1910 within two weeks; in country districts within thirty
An estimate of the population was
days.1911 made as of July 1,

1910, being the central point of the three calendar years 1909,
1910 and 1911. The estimated population in these original
registration states was 24,131,759, and the reported deaths for
the three years were:

353, 576
377, 015
368, 087

The area covered contained roughly one quarter of the popu-

lation of the U nited States. In much of the remaining area the
system is either faulty or practically non-existent.
registration
—
Twenty-five tables were published the first being a general
 :

THE PRINCIPAL MORTALITY TABLES. 27

table dealing with both sexes and covering the entire area, the
second and third being the same except for division into male
and female; the next twelve for males and females separately in
subdivided classes of the population —namely:
1. White, 4. Foreign-Born White,
2. Negro, 5. Cities,
3. Native White, 6. Rural.

The with place of residence, giving male and

last ten tables deal
female mortality separately in five individual states: Indiana,
Massachusetts, Michigan, New Jersey and New York.
The lowest mortality rate amongst white males is shown at

age 11 —viz: 2.28 per 1,000; amongst white females, it is 1.98

per 1,000 also at age 11. The mortality amongst foreign-born

white males is lighter than that of native white males between
ages 21 and 38; but at other ages is heavier. This may indicate
selection on the part of healthy immigrants and the immigration
authorities. In general the mortality of men is greater than that
of women. The rate of mortality in cities is much higher than
in rural districts during practically the whole of life, and negro
mortality is very pronouncedly higher than that affecting Cau-
casians.
The following tables give some indication of the relative mor-
tality rates

United States Life Tables — 1910.

Death Rates per 1,000 of Population — 1,000 q
i. e.: x.

Native White Foreign-Born Native

Age. Male. White M ale. Negro Male. White Female.

10 2.37 2.47 5.02 2.06

30 7.14 5.80 14.96 6.13
40 10.02 10.53 21.03 7.76
60 27.21 36.81 50.79 22.06
80 132.43 141.76 131.27* 121.23

Corresponding Values of ex .

10 51.93 50.30 40.65 54.43

30 35.61 33.71 27.33 37.98
40 28.33 26.03 21.57 30.33
60 14.58 13.06 11.67 15.78
80 5.15 4.98 5.53* 5.47

*
Ages probably exaggerated.
28 SOURCES AND CHARACTERISTICS OF

The
tables dealing with different states indicate that mortality
in Indiana and Michigan is notably lower than in the older com-
munities of Massachusetts, New Jersey, and New York. This
may partly be accounted for by the larger proportion of rural
population in the former and the industrial centres with larger
proportion of foreign born in the latter. Other sections of the
United States are understood to show still lower death rates,
while the South is not represented at all in the compilation herein
described.
On account of the importance of infant mortality, and the
rapid decline from birth during the first year, a separate table is
given in conjunction with each of the life tables showing the rates
of mortality and their derived values for each month during the
first year. The most cases were based upon the
calculations in
enumerated population and reported deaths. This method is
generally found unsatisfactory, yet in this instance was adopted
in preference to using the birth registration statistics, which are
also unreliable. The figures should be used with caution —they
show significant differences in mortality conditions in the various
classes of the general population, as, for example, the usual
higher rate affecting male babies, and a very high rate in infancy
amongst negroes.
From ages 15 to 85 the method of adjustment was that of
osculatory interpolation with fifth differences, the ages being
grouped in quinquennial sets 4-8, 9-13, 14-18, etc. For the
first five years a more direct method was employed, and the

interval from 5 to 13 was bridged over by ordinary fourth dif-

ference interpolation formulae. At the advanced ages Witt-
stein’s formula was employed, the rate of mortality being taken
as unity at age 115. This is an unusually advanced age for the
limit of life, yet it finds precedent in the English Life Tables
Nos. 7 and 8. In order to join the osculatory interpolation with
the Wittstein Graduation, Spencer’s 21-term formula was em-
ployed over a range, usually small, sufficient to insure a smooth
junction.
life tables, where the above summary
In the explanation of the
of graduation methods is given, it is stated that powerful smooth-
ing formulas were not used, as it was not always easy to distin-
guish the irregularities which are characteristic of the population
from those which are merely due to defective enumeration and
 THE PRINCIPAL MORTALITY TABLES. 29

it was therefore deemed better to present the life tables in an

approximately unadjusted form. It is intended to publish all
the original data in a later report with a detailed account of
methods employed in constructing the life tables.
The tables are valuable as being the first of the kind prepared
in the United States but in studying the difference in the various
rates of mortality, those factors likely to produce differences
should not be forgotten, as, for instance, in comparing the expec-
tation oflife of people living in the cities with those living in the

country, it must be remembered that the cities contain a larger

proportion of foreign born, while hospitals and sanitariums are
mostly situated in towns and cities. The tables having been
prepared from an estimated population and from reported deaths,
the errors likely to have occurred in registration and tabulation,
even as late as 1910, may be considerable. Where all the deaths
are not recorded, as is generally the case in registration statistics,
the error tends to decrease the death rate, and this factor may
have caused part of the difference between rural and urban com-
munities, since town and city registration is more complete than
rural. The statutory obligation to register any death before a
burial permit will be granted can be better enforced in city dis-
tricts.
30 SOURCES AND CHARACTERISTICS OF

TABLES FORMED FROM

THE EXPERIENCE OF LIFE INSURANCE COMPANIES.

Davies’ Equitable Table.

The Equitable Society was formed in 1762, and is the oldest
Life Office at present having a separate existence. Some years
adopted the Northampton Table
after its formation this Society
as the basis of premiums, and Dr. Price recommended that the
actual deaths experienced should be compared with those ex-
pected by the Northampton Table; this was accordingly done
annually.
In 1800, Mr. Morgan, then Actuary of the Equitable, stated
that the deaths among the members for the preceding thirty years
had been as follows:

Ages 10-20 One-half of the number expected by the Northampton Table.

Ages 20-30 One-half do. do.
Ages 30-40 Three-fifths do. do.
Ages 40-50 Three-fifths do. do.
Ages 50-60 Five-sevenths do. do.
Ages 60-80 Four-fifths do. do.

This table shows that the actual deaths were very much less
than the expected, and Mr. Griffith Davies adjusted the North-
ampton Table to follow the experience of the society, his results
being published in 1825. The methods he used are now un-
important; but he obtained the numbers living for each tenth age,
and interpolated by finite differences for the intermediate ages.
His table was not properly a mortality experience, deduced from
the facts; but only a modification of the Northampton Table to
obtain figures more nearly in conformity with actual conditions.

Morgan’s Equitable Table.*

This table, published in 1834, was formed by Mr. Arthur
Morgan, Actuary of the Equitable Life Office, from the experience
of the society from its commencement in September, 1762, to
January 1, 1829. It is the first table deduced on correct principles
from the records of a life insurance company.
* J. I. A., Vol. XXIX, pp. 113-7, by James Chatham.
 :

THE PRINCIPAL MORTALITY TABLES. 31

There were 21,398 lives, of whom 6,930 were living on January 1,

1829; 9,324 had surrendered, forfeited, or discontinued their

policies; and 5,144 had died. Altogether there were 266,872 years
of life under observation and the average period of exposure was
1234 years.* The effect of the selection of lives was discussed
and the rapid increase in mortality after date of entry was re-
ferred to.
The following shows the way in which the facts were tabulated

Age Attained 30. Age Attained 31.

Age at
Entry. Attained Living on Discontinued Attained Living,
the Above Jan. 1, 1829, their Assces, Died. the Above etc.
Age. at Above Age. at Above Age. Age.

24
25 421 10 29 2 380 etc.
26 #

27
• etc.

Thus opposite each age at entry under the Column headed “ Age
Attained” were put:
1. The number living who attained that age.
2. Those who were existing at that age on January 1, 1829, and
who thus passed out of observation.
3. The number who ceased to be members at that age, and

who thus also passed out of observation.

4. The number who died between that age and the next.
Under Age Attained 30 opposite age 25, we find 421 in the column
showing the number living, which is the number out of those
entering at age 25 who continued members of the society until
they attained age 30; of these, 10 were existingf on January 1,
1829, while 29 ceased to be members between the ages 30 and 31,
and 2 died. Deducting 10 + 29 + 2, or 41, from 421, gives 380,
the number who entered upon their thirty-second year of age,
which was placed under “Age Attained 31” opposite 25, etc.
Members were assumed to attain the age stated at entry (i. e.,
age next birthday) on the first of January following entry. This
was therefore the first “Calendar Year” investigation.
* J. I. A., Yol. II, p. 202.

t The word “existing” is used with an unusual meaning, the letter E being
used in mathematical formulas.
 :

32 SOURCES AND CHARACTERISTICS OF

The table is now of historic interest only, and it is therefore

unnecessary to describe the processes in full.

Actuaries’ Table; Combined Experience Table; or

Seventeen Offices’ Experience 1843.
As it was felt that the rate of mortality among insured lives
must be different from that of the general population on account
of the former having to pass a medical examination, it was resolved
at a meeting of actuaries and others connected with life insurance,
held in London in 1838, to ask various companies to contribute
their experience. A committee was formed and issued schedules
in the following form to the contributing offices

Year of Distinction Special

For Use Current If by Sex, if into Cause of Risks
of Age at Death, Female, Town, (T). Death. and Re-
Office. Entry. D. F. Country, (C).
Entry. Exit. marks.
Irish, (I).

The forms were thus confined to a record of the 'policies issued;

but the Equitable and Amicable Societies apparently furnished
their observations on lives only, so the general results were mixed.*
It was believed that the rate of mortality would not be sensibly
affected by the fact that a man might often effect several policies
at various ages, and might at death be treated as several different
persons. It has been said that this has the effect of diminishing
the rate of mortality at the early ages, and increasing it at the
old ages; but the extent of this tendency must be slight.

The returns embraced 83,905 policies, of which 44,877 were

existing at the close of the observations (December 31, 1837),
25,247 had discontinued, and 13,781 had died.f
The committee state that the tables represent a lower rate of
mortality than can be expected during a longer period of time
than that over which the observations extended, for the average
duration of all the policies was less than 83^ years, notwithstanding
that the two oldest companies then existing (the Amicable and
the Equitable) were included. The average duration of policies
embraced in nearly one-half of the experience was under 5)^ years.
More than one-half of the policies effected were existing at the close
of the observations, and nearly one-third had been discontinued.
* J. I. A., Vol. II, p. 203. f J. I. A., Vol. X, p. 197.
 —

THE PRINCIPAL MORTALITY TABLES. 33

The tables were constructed by a “ calendar year” process, and

were adjusted according to a formula given by Mr. Woolhouse.
The mortality amongst Irish lives was found to be heavy as com-
pared with those resident in Great Britain. The mortality
amongst assured females from ages 20 to 50 was considerably
greater than amongst males of the same ages. From 50 to 70,
it was less, while above 70 it was found to be sometimes greater

and sometimes less, but at the advanced ages the statistics were
quite inadequate to enable one to form a reliable opinion.
The Table was adopted as the standard for valuation purposes in
Massachusetts about 50 years ago, and continued in very general
use till 1901, as it was considered a “safe” table. Industrial
policies were also valued on this basis, so it became necessary to
extend the mortality rates down to age 0, and the National
Convention of Insurance Commissioners in 1883 adopted the
following rates for ages 0 to 9, recommended by D. P. Fackler,
W. S. Smith, D. W. Whitney and A. F. Harvey:
Age. lx d* Qx

0 143,400 22,184 .1547

1 121,216 7,697 .0635
2 113,519 4,030 .0355
3 109,489 2,617 .0239
4 106,872 1,892 .0177
5 104,980 1,428 .0136
6 103,552 1,123 .0108
7 102,429 922 .0090
8 101,507 792 .0078
9 100,715 4 715 .0071

Institute of Actuaries Tables Published 1869

( H
m and Others).

In 1862, the Council of the Institute of Actuaries, aided by a

joint committee of the Faculty of Actuaries and the Managers*
Association (The Associated Scottish Life Offices), undertook to
collect and tabulate the materials requisite for investigating the
rate of mortality among insured lives, and 20 companies agreed
to furnish their experience. The particulars of the lives were fur-
nished on cards, which gave the following particulars, and 180,000
of which were sent in:
Policy No. Healthy or diseased Age at Entry Cause of Death
Life Year of Entry Age at Exit Remarks.
British, Irish or Year of Exit Mode of Exit
Foreign
34 SOURCES AND CHARACTERISTICS OF

There were 10 English and 10 Scottish companies contributing

their experience, and on the Scottish card, the following particu-
lars in addition to the above were given:

Sum Assured.
Class.
Exact dates, and
English, Scotch, instead of British.

The office age at entry (i. e., next birthday age) was inserted in
the card, which afforded the means of approximating to the actual
age by the assumption that the insured attained that age at the
end of the year of entry.
The cards were first of all sorted into four divisions, viz.: (1)
Hm ,
(Healthy Males); (2) Hf ,
(Healthy Females); (3) Dmf ,

(Diseased Male and Female); and (4) those exposed to extra risk
from climate, occupation, etc.
The cards in each of these divisions were then arranged according
to the name of the life, with the view of bringing together all those
relating to the same person and eliminating duplicates. The next
step was to sort the cards in each division into three groups accord-
ing as they had passed out of observation —(1) by death, (2) by
discontinuance of their insurance, and (3) by surviving the period
at which the observation closed, briefly termed “died,” “discon-
tinued,” and “existing.” All those of the same age at entry
were next brought together, and finally arranged according to
age at exit. The number of cards was reduced by elimination of
duplicates to 160,426 persons, of whom 26,721 died, 45,376 dis-
continued, and 88,329 were existing at the close of the observations.
The average duration of exposure was more than 9 years. Females
formed about 11% of the total. The Hm table started at age 10,
with a radix of 100,000.
The tables were formed by the calendar year method, it being
assumed that the entrants in any year came under observation on
the average at the middle of the year, and would attain the age at
entry (i. e., age next birthday) at the close of the calendar year.

This short period from the date of entry to end of the year of
entry (assumed to be six months) was called the year “0 ”; and in
keeping the mortality separate for each age at entry, as already
explained, the mortality during this period was assumed to apply
to the previous age. Thus, those who entered at age 30 next
birthday, were assumed to be on an average exposed to risk for
 THE PRINCIPAL MORTALITY TABLES. 35

six months in the year “0”; and the mortality for this six months
was set down as applying to age 29. Later investigation showed
that the average period of risk in the calendar year of entry was
less than six months, also that the average true age at issue was
less than six months younger than the age next birthday as
stated.
The method of keeping the various ages at entry separatefrom
each other was adopted in order that future investigators might
make use of the facts in forming “ select” tables, afterwards
described. The committee made no immediate use of this arrange-
ment, but combined in the H
m table all those of the same attained
age whether they had been insured for only a year or two, or for
many years. The effect of selection ceased to be of any practical
importance after the expiry of 5 years, and accordingly the m(b) H
table was formed, the experience of the first five calendar years
after entry (approximately years) being neglected.
The effect of forming a table in the way the m was formed H
(known technically as an “aggregate” table, as opposed to a
“select” table) i. e., entering new or select lives at each age with
the general body of policy-holders at that age, some of whom must
of necessity be unhealthy, has the effect of making the apparent
mortality at the older ages higher than would be shown by a table
taking account only of the new entrants at such higher ages, be-
cause the unhealthy lives are brought forward and included. The
method has the opposite younger ages, because a body
effect at the
of lives, selected at a relatively young age, becomes “mixed” and
contains a proportion of unhealthy lives; but the proportion of
such unhealthy lives is reduced by the introduction of more healthy
lives year by year, so that the lighter mortality amongst these
newly selected entrants reduces the rate in respect of those who
entered at the younger age. Premium rates computed from such
a table are lower at young ages and higher at old ages than a select
experience shows to be correct.
At ages under 45, the Hf table shows much heavier mortality
—
than the H m but after that age lighter thus confirming previous
,

investigations. The tables were graduated by W

oolhouse’s formula.
These tables came to be very generally employed in Great
Britain, and were also adopted as a standard for all life insurance
purposes in Canada. They were never officially recognized and
have been very seldom used in the United States.
 :

36 SOURCES AND CHARACTERISTICS OF

The American Experience Table, 1868.*

The American Experience Table of Mortality, now recognized

as the standard table in the United States, was formed by Sheppard
Homans and was first published under its present name in a
schedule attached to an Act passed by the legislature of the State of
New York on May 6, 1868. The author never gave full particulars
of the data employed. He used mortality statistics deduced from
the experience of the Mutual Life Insurance Company of New
York, but the figures were inadequate at the older ages and accord-
ingly he arbitrarily adjusted the table. The table starts at age 10
with a radix of 100,000 and ends with three deaths between ages
95 and 96, the latter being therefore the limiting age of the table.
It has been much used, and has grown in popularity because it
has furnished a safe basis of measurement of American mortality
amongst insured lives after the first effects of selection have dis-
appeared.
At the first dinner of the Actuarial Society of America, April
25, 1889, f Mr. Homans said
“The result was that after I had collated the experience of the
Mutual Life I drew a curve representing the approximate rates
of mortality at different ages; and then found by a simple
method of adjustment the rates of mortality now called The 1

—
American Experience Table’ a name, however, that was not
given by me. The table has for its basis the experience of the
Mutual Life; but it is not an accurate representation of that
individual company. In other words, it is not intended to be,
and never was claimed to be an accurate interpretation of the
experience of the Mutual Life.”
He further stated that the American Table was prepared
simply as a study, and that he had made the limiting age 96
because in the records in different countries he could find no
instance of any insured individual attaining the age of 100 years.
The Mutual Life experience, also prepared by Mr. Sheppard
Homans, was published in 1858 and dealt with a period of fifteen
years from the commencement of the company in 1843. Mr. D. P.
Fackler has pointed out that premiums based upon the new tables
were adopted in 1861 so that the modifications contained in the
* Walford’s “Insurance Cyclopaedia,” T, A. S. A., Vol, X, pp. 509-514.
t T. A. S. A., Vol. I., pp. 33-34.
 THE PRINCIPAL MORTALITY TABLES. 37

American Experience Table as compared with the mortality rates

of the earlier table of 1858 must have been made about the year
1860. They must therefore have depended on the additional ex-
perience of the Mutual Life for the years 1858 and 1859 only, or in
other respects have been adjusted by Mr. Homans arbitrarily from
a study and comparison of other tables. The new table “was
intended to represent the death rate among insured lives resid-
ing in salubrious districts after the effects of medical selection were
eliminated.”
The graduation of the Mutual Life Table of 1858 was by a
graphic process, but no particulars are given of the method used
by Mr. Homans in graduating the American Experience Table.
Recent investigations* would seem to indicate that the follow-
ing maybe considered as established facts:
1. The American Experience Table is based on a table of the

values of the reciprocal of qx to three decimal places for each age

from 10 to 95 inclusive. The method by which this table was
derived from the original data is unknown.
2. From the values of the reciprocal of qx the value of the
logarithm of the rate of mortality was taken out to seven decimal
places.
3. Starting with a radix of 100,000 at age 10, the value of log l 10

was taken out to seven decimal places. The logarithm of qx was

added to it to form log di 0 The natural number of dio was ex-
.

tracted to the nearest unit and subtracted from ho to form ln ,

&c.j the process being repeated for each age.

In 1902 Mr. Arthur Hunter made a very successful graduation of
the American Experience Table by the application of Makeham’s
Law of Mortality, and this Makehamized Table is of great value
in simplifying the calculation of benefits depending upon two or
more lives.

The table is now generally prescribed by State Laws for valuation

purposes and has been adopted almost universally in the United
States.
* T. A. S. A., XII, p. 253; XIV, pp. 27-37, and 354-363.
 ;

38 SOURCES AND CHARACTERISTICS OF

Thirty American Offices’ Tables.*

Tables were compiled in 1881 by Levi W. Meech from the
returns of 30 American Offices, dealing with 1,027,529 lives,
of which 549,418 were existing at the close of the observations
(1874), 46,543 having died, and 431,568 having discontinued.
The returns were furnished on cards, which gave:
Residence, Amount, Class, Calendar year of entry,
Calendar year of exit, Age at entry, Sex, Cause of death.

Male and female lives were investigated separately, and each

subdivided into the three classes — existing, discontinued, and died.
Less than 5% of the lives were female. These classes were again
subdivided into durations of Policies, 0, 1, 2, 3, 4, . . . ,
and these
again into still smaller groups ‘according to the age at entry.
Policies were assumed on the average to be taken in the middle
and were treated as exposed for half of the first
of the initial year,
calendar year. Those who passed out of observation were also
assumed to do so at uniform intervals. Average policy years
thus begin and end with the middle of the calendar year, while
the average birthday is assumed to be at the middle of the initial
year, the general assumptions being similar to those made in
forming the Institute of Actuaries’ Table. The office age at entry
was “nearest” birthday; and the entry ages were diminished by
for the period of exposure in the year of entry, i. e., as if the
ages were changed from the middle to the beginning of the calendar
year of duration. The average age at entry was 35.23 years, and
the mean duration of the policies was 4.36 years. The mortality
was investigated by lives, but the principal tables were based
upon amounts insured and claims, with slight adjustments towards
the extremes of the table. The rate of financial loss was greater
than the rate of mortality, showing that the claim rate was higher
amongst policies of large amount. The effect of medical selection
was stated to disappear within 2}^ years.
At ages under 45, the mortality of females was found to exceed
that of males, indeed the excess from ages 20 to 35 was over 35%
from the age of 45 to 65 the order is reversed, though by a much
smaller difference relatively, and again at the older ages (ages 67
to 95 inclusive) the mortality amongst females exceeds that
amongst males.
* System and Tables of Life Insurance, by Levi W. Meech.
 THE PRINCIPAL MORTALITY TABLES. 39

As 549,418 of the policies were existing at the close of observa-

tions, the record ceased before the real experience had developed.
Had the investigations been deferred 15 or 20 years many more
policies would have passed to their termination. The defect from
having so many existing at the close of the observations was
approximately supplied by assuming the existing to be carried
forward until they should pass out of observation by discontinuance
or death, the ratios of mortality and discontinuance for this purpose
being taken as those actually experienced on Select Mortality and
Withdrawal bases down to 1874. This was called the method of
“Final Series”;* of course it is effective only when the real and
the assumed statistics are combined in an aggregate table, since
it increases the proportion which the non-select lives at any age
bear to the total under observation at that age.
The figures from 10 to 90 in the male table were graduated by
Makeham’s Law of Mortality, taking the ungraduated values of
^ 25 , ho, hs, and 1 7q as data. Notwithstanding that previous tables
showed considerable deviations from Makeham’s Law, the results
in this caseshowed close agreement with the ungraduated values,
and this was explained by Mr. Meech as follows:
1. The observations were more numerous than those of any

previous collection.
2. They were nearly homogeneous.
3. The statistics were accurately deduced.
4. The construction was improved by “ Final Series.”
5. The observations were free from misstatements of age
common to census returns.
But as more recent experience has shown that many tables can
be graduated by Makeham’s Law, including even old tables like
the “Carlisle,” the suggestions as to the causes why this table
should follow the law probably show a lack of familiarity with the
adaptability and flexibility of the Law as afterwards developed.
The graduation life, on account of the
of the table for female
small numbers above 70 was aided by comparison with larger
collections, and then adjusted by Woolhouse’s method. A very
complete set of monetary values was published.
The statistics were also analyzed by states and territories of
the United States, and tables were given of the actual and expected
claims in each state or territory. These figures are less valuable
* See J. I. A., Vol. XXXII, p. 9 et eeq.
40 SOURCES AND CHARACTERISTICS OF

than they would have been if the effect of selection had been taken
into consideration, because in some states the business may be
relatively recent whereas in others there may be much old business.
In some of the Southern states the expected and actual claims
are given for each county in the state separately a desirable —
separation. There are also tables showing the causes of death
from diseases which are grouped under the following heads:
Zymotic, Constitutional, Nervous, Circulatory, Respiratory, Di-
gestive, and Miscellaneous.

Standard Industrial Mortality Table.

Prior to 1907 the Policy Liabilities on Industrial Insurance were
based on the same tables as were used for ordinary policies.
Mortality tables had been compiled by individual companies from
their own experiences and used in calculating premium rates; but
as the statutes did not differentiate between the two classes the
valuation of industrial policies was based upon the Actuaries, or
Combined Experience for policies issued prior to January 1, 1901,
and upon the American Experience Table for policies issued there-
after. Early in 1907, after modification of the New York laws,
the Superintendent of Insurance fixed as the legal basis for New
York State a table based exclusively upon the experience of
industrial policies, called the “ Standard Mortality
Industrial
Table”; and, while permission has since been granted by the
New York Legislature to use other tables, this one is still recognized
as a standard.
The Standard Industrial Mortality Table was based upon the
experience of the Metropolitan Life Insurance Company during
the ten years 1896-1905. The policies at riskand the death claims
were obtained from data contained in registers in which were kept
a record of all Industrial premium paying policies, classified accord-
ing to year of issue and age at entry. The experience included
48,508,562 years of risk and 767,552 death claims.
The unadjusted data were first graduated by Woolhouse’s
formula for graduation from age 2 up to age 35 inclusive, also by
Makeham’s formula from age 20 to the end of life, using the groups
of ages 27-39, 40-52, 53-65, 66-78 for obtaining the constants.
The ages under 30 as obtained by the Woolhouse graduation were
merged into the Makeham graduation by means of a second
 THE PRINCIPAL MORTALITY TABLES. 41

Woolhouse grading, the resulting probabilities being retained

from ages 12 to 35 inclusive, the Makeham graduation being
followed from age 36 upwards. The original figures from ages 2
to 6 inclusive were retained without graduation, while for ages
7 to 11 an interpolation formula was used.
The table starts at age 2 with a radix of 100,000, and age 99 is
the limit of life, there being 1 living at age 98. The rate of
mortality qx is lower than the American Experience from ages 10
to 21, then higher to age 87 inclusive; and at the very old ages it
of necessity becomes lower again since the limit of life in the
American experience is age 96. Medical selection is not such
an important factor in case of industrial as of ordinary risks,
since the applicants in most cases are subjected only to a medical
inspection, and accordingly the tables were based upon the entire
experience, thus being “aggregate” in form. The mortality curve
does not agree at all closely with any known table; but probably
comes nearer the English life experience than any other.

National Fraternal Congress Table of Mortality.

The fraternal organizations meet annually in convention, and
at the National Fraternal Congress held in 1897 the feeling was
expressed that the Actuaries’ Table of Mortality which was then
the standard table for old line life insurance companies showed
higher mortality rates than was necessary according to the past
experience of the better class fratemals. Accordingly a com-
mittee was appointed to look into the subject, and this committee
made a report at Baltimore in 1898, accompanying their report
by a table of mortality which was afterwards adopted as the
National Fraternal Congress Table.
One of the principal objects in view was, as stated by the com-
mittee, to prepare a standard table which would bring out premium
rates as low as practicable, apparently even taking into account
the profit from lapsing, no surrender values being paid, since the
committee reported that the problem in the preparation of the
table “involved the basis of a minimum rate, with the elimination
of cash, paid-up, and extended values .” The mortality rates are
Committee stated that many
therefore low; yet a year later the
fraternal ordershad had an even more favorable experience, al-
though others may have encountered a higher death experience
than the tables indicate.
42 SOURCES AND CHARACTERISTICS OF

Details of the number of lives exposed to risk and of the number

of years’ exposure are not given, the statement made by the com-
mittee being

“The experience examined and available embraced the mortality experi-

ence of the Old Line companies in the United States, England, Canada, and
Australia; of the Fratemals, the experience of the two oldest and largest in
this country.”

Apparently, therefore, the table consists of the arbitrary judg-

ment of the members of the committee; this judgment was con-
firmed by a continuing committee one year later, the report in

1899 stating that the committee “has had opportunities for

extending its research somewhat, as new data have been compiled
of the actual experience of the fraternal orders, members of this
Congress, which were not available one year ago.” After a careful
investigation nothing was disclosed which would lead the com-
mittee to recommend a change.
The two “oldest and largest fratemals in this country” at that
time were The Royal Arcanum and the Ancient Order of United
Workmen, “and it is generally understood that the experience of
the Royal Arcanum largely controlled in fixing the data agreed
upon by the committee.” The table was tested still further and a
voluminous report submitted to the National Fraternal Congress
in 1906, when the congress considered that it was justified in
continuing endorsement as originally given.
its

The table was graduated by Mr. George D. Eldridge, who states

that the material was placed in his hands “late on the afternoon
of November 16, 1898, the day before the committee having the
matter in charge was to report to the congress then in session.
The work of graduating qx was completed during that night.”
The table was graduated on the assumption that qx could be repre-
sented by a function of the form A +
Bc x+ *; and as a preliminary
step the value of qx was determined experimentally from the
material at certain ages “taken at fifty or over, with a view to
dealing first with that part of the table only which, under the
general limitation of fratemals, is not affected by the admission of
new lives.” From these experimental values of qx the three con-
stants, A, B ,
and c were obtained. These constants gave a rate
of mortality at age 20 of .0052511; but it was the judgment of
the actuaries that, excluding the savings from selection during
 THE PRINCIPAL MORTALITY TABLES. 43

the three years immediately succeeding admission, a rate at age 20

of .005 was a far more justifiable minimum. The latter was there-
fore adopted and a subtractive series formed from ages 20 to 45.
It will be observed generally with reference to the above table
that while the results may be practical as a standard of measure-
ment from the fraternal standpoint, representing minimum mor-
tality rates for adoption by such orders, nevertheless the processes

adopted in deducing the table were largely empirical.

44 SOURCES AND CHARACTERISTICS OF

SELECT LIFE TABLES.

Insurance companies do not accept all the applicants who offer
themselves, but reject a small proportion of the lives proposed for
insurance, taking the great majority at the usual premium rates,
charging others an increased premium, and declining entirely a
few whose prospects of longevity appear to be much below the
average. The necessity for this distinction arises from the fact
that if the benefits of insurance were free to all comers, there would
be an undue proportion of under-average lives, more than the
normal proportion in the population, since an unhealthy man needs
insurance more than a healthy one. Moreover the healthy would
with reason object to be classified with the diseased and to pay
the same premium rates. Selection is effected by means of medical
and other reports on the health, family history, personal history
and habits of the individual whose life is proposed for insurance,
with due regard also to occupation and habitat.
For the first two or three years after entry the effect of this
selection is quite apparent, the death rate amongst recent entrants
being very low as compared with the rate amongst those who have
been insured for several years, or as compared with the general
population; but, as years pass the rate of mortality approaches
nearer to that of non-select lives, although it is the general opinion
that the effects of the first selection never entirely disappear. Mr.
Sprague held* that the mortality among select lives gradually
increased until it attained a maximum, after which it diminished;
this he attributed to two counterbalancing causes:
1. The selection as exercised by the Office when insurance is

effected, and
2. The selection exercised by the lives insured in having the
right to withdraw, and the consequent withdrawal of a
considerable proportion of the healthy lives during the
early years of insurance.
More recentlyf it has been urged that withdrawals do not have
the effect of reducing the proportion of healthy lives; indeed the
* J. I. A., Vol. XV, p. 328.
f J. I. A., Vol. XXIX, p. 81; also XXXII, p. 117, etc.
 THE PRINCIPAL MORTALITY TABLES. 45

direct contrary is sometimes accepted on the ground that with-

drawal from a company in good standing is more frequently a result

of financial embarrassment or irregular habits. The opinion that
discontinuances have not an adverse influence on the mortality
—
seems to be gaining ground even Mr. Sprague stating that he
had “considerable doubt” as to whether the lives which withdraw
are on the average better than those which remain. Until the
point is settled by convincing statistics, which are difficult to pro-
cure, it remains a matter of opinion with plausible arguments on
both sides.
To investigate the effect of selection properly, it is desirable
to trace a large number from each age at entry until
of entrants
they all pass out of observation; this has been done on several
occasions, the first important investigation being made by Mr. J. A.
Higham prior to the year 1850. In that year he read a paper before
the Institute of Actuaries on “The Value of Selection among
Assured Lives, etc.” This consisted of an analysis of the expe-
rience of the Equitable Society. In 1851 he submitted another
paper on “The Value of Selection as Exercised by the Policy
Holders against the Company.”* His deductions were based
upon the Actuaries or Seventeen Offices' Experience, but his
figures were not much used for practical purposes. Mr. Higham
said “the probability of surviving the year immediately after
selection is a quantity which we have not at present the means of
measuring”; and the means of measuring this quantity accurately
was not obtained until about the year 1900.
After the observations from which the H m Experience Table
was compiled were published, Messrs. King and Sprague devoted
themselves to a careful analysis of selection and the monetary
tables published by Sprague in 1879 were widely used for the
succeeding twenty years.

King's Analysed Tables — 1876.f

The first important discussion of the rate of mortality by dura-
tion of insurance after publication of the H
m mortality experience
was opened by Mr. King in a paper “On
the Mortality amongst
Assured Lives,” read before the Institute in 1876. This paper
* J. I. A., Vol. I, p. 179.

t J. I. A., Vol. XIX, p. 385.

 ’

46 SOURCES AND CHARACTERISTICS OF

marked an epoch in the study of mortality statistics. Extracts

from Mr. King’s own description of his new mortality tables will
give an indication of his procedure:

“I have prepared and graduated ten mortality tables for ages at entry
20, 25, etc., up to 65. They were formed from the tables of ‘exposed to risk’
and ‘died/ ... by tracing separately those who entered at the ages
. . .

It was of importance to include as many of the

20, 25, etc., respectively.
observed facts as possible; I have, therefore, after the first ten years of assurance,
combined with those entering at age x those also entering for ages x — 2,
x — 1, x +
1 and x +
2, thus making x the central age of a quinary group.
... It would have been more satisfactory had larger numbers enabled us
to dispense with this grouping; but, after all, it canmake very little difference
in the mortality among persons of the same age, when they have been assured
for some considerable time, whether they entered at a period two years more
or less remote. Two slight errors are introduced which tend to neutralize
one another.
“In the early years of assurance, however, the case is different. During
the first ten years, the medical examination at entry must exercise a decided
but rapidly decreasing influence, while the selection against the company
caused by discontinuances is at its strongest. It is, consequently, of im-
portance to avoid mixing those who have been assured, say 5 years, with
those who have been assured 6 and 7 years, or only 3 and 4. The numbers,
moreover, are sufficient to render it unnecessary; and for the first ten years
of each table, I have brought into account the exposed to risk and the deaths
for that age at entry only which appears in the heading. The table for age 65
is the only one where the numbers were so small as to produce serious fluctu-

ations; but for the sake of uniformity, I have adhered to the same plan through-
out.’

At the advanced periods of life, commencing after age 60, Mr.

King combined the observations for several ages at entry:
Entry ages 20 and 25 being combined at age 60.
“ “ 20 to 45 “ “ “ “
80.
“ “ “ “
And all entry ages 89.

The tables were adjusted by a very simple method of graduation,

viz.:
j
a x
_
- d'x - 2 -r d'_ i + d + dx+1 + dx+2
x
5

where d' represents ungraduated and d the graduated number

of deaths. When the result was still too irregular the operation
was repeated.
Mr. King assumed that the rate of mortality for the fraction
of the year of entry, “year 0,” would continue for a full year,
 :

THE PRINCIPAL MORTALITY TABLES. 47

adding “perhaps by so doing the mortality is slightly underrated.”

He used the mean of 3 ages at entry, thus obtaining a simple and
rough graduation of the first years mortality.
Mr. King also analysed the rate of discontinuance which “de-
creases not only with the duration of the policy, but also with
the age at which the policy was effected.” The rates of dis-
continuance at age 35 and at all ages combined were as follows:

Rate % of Discontinuance. Rate $ of Discontinuance. Rate °!o of Discontinuance.

Year. Age 35. All Ages. Year. Age 35. All Ages. Year. Age 35. All Ages

0 2.5 2.7 5 2.7 2.8 110-14 1.4 1.4

1 6.2 7.0 6 2.2 2.4 15-19 1.0 .9
2 4.2 5.0 7 3.2 3.6 20-24 .8 .7
3 3.8 4.1 8 1.9 1.8 25-29 .4 .5
4 2.9 3.3 9 1.5 1.6 30 and .4 .4
over

Sprague’s Select Mortality Tables.*

In 1879 Mr. T. B. Sprague published the results of an investiga-
tion he H
made from the m statistics to determine the effect of
selection, and to show the uses to which Select Tables could be
put. He first reduced the figures for each age at entry to a common
radix of 100,000; and, in order to lessen the irregularities arising
from small numbers, he grouped the entrants at five ages to get
the rate of mortality for the central age of the group.
The same assumptions were made as to ages at entry as were
made 100,000
in compiling the Institute Experience, namely, that the
100,000
entrants at any age next birthday attained that age at the end of
100,000
the year, also that the initial period, “year O,” covered half a year.
100,000
50,000
To deduce the mortality for age 30, the five year group contained
50,000
of exact age 29|)
which gave 500,000
200,000 of mean age 30.
of exact age 30§ j

of exact age 28§\ which gave 200,000 of mean age 30.

of exact age 31| j

of exact age 27|1

which gave 100,000 of mean age 30.
of exact age 32£ J
of mean age 30.

The reason for taking only 50,000 at the two last named ages
was of course that the balance of 50,000 in each case entered into
the adjacent groups; i. e., the other 50,000 at age 27 were
included in the group for age 25 at entry, and the 50,000 at age
* J. I. A., Vol. XXI, p. 229 et eeq.
48 SOURCES AND CHARACTERISTICS OF

32§ in the group for age 35. By reducing the figures to a

common radix, the facts at each age had the same weight assigned
to them in the final table.
The following table indicates the method and gives the figures
used for age 30:

Assumed Age at Entry. Average Age at Entry 30.

Time Elapsed.

Survi- Total Age

27} 28} 29} 30} 31} 32} vors. Deaths. At-
tained.

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)

years
0 50,000 100,000 100,000 100,000 100,000 50,000 500,000 0 30
! 49,962 99,788 99,931 99,754 99,676 49,864 498,975 1,025 30|
H 49,550 99,346 99,394 99,316 99,115
98,347
49,609
49,256
496,330 3,670 31!
492,663 7,337 32!
2! 49,167 98,655 98,644 98,594
3* 48,672 97,940 97,490 97,839 97,573 48,818 488,332 11,668 33|
4! 48,345 96,823 96,166 96,926 96,841 48,315 483,416 16,584 34!
47,986 95,858 95,142 96,024 95,960 47,860 478,830 21,170 35!

This table gives the numbers living at the end of 1|, 2|,
etc., years; and in order to obtain the numbers at the end of full

years, Mr. Sprague divided the deaths in Column 9 of the above

table into half-years by a method of differences. The deaths in
the first and second half-years were then added together and di-
vided by the corresponding numbers exposed to risk to give the
rate of mortality for the first full year, and so on for subsequent
years.
The tables were computed on the further assumption that the
jy m(6 > table represented the ultimate rate of mortality. Accord-
ingly having deduced the Select rates for the first five years, and
having graduated them by the Graphic Method, these graduated
rates were joined to the H
m (5) rates. When the former exceeded
the latter in the years one, two, three or four, the m (5) rates were H
adopted from that year onwards; after the first five years the
#m(5> T a ble was adopted in all cases. This saved labor in calcula-
tions, because all the more useful values had been published for
the m W Table, and those for the early years only had to be
H
added.
From the rates of mortality for quinquennial ages, found as
above shown, the rates for intermediate ages were obtained by a
process of osculatory interpolation.
 : ;

THE PRINCIPAL MORTALITY TABLES. 49

These tables quickly came into general use, especially for the
calculation of premiums; and, as compared with ordinary life net
premiums under the H m Table, those by the Select Tables are
higher up to age 43, but after that age they are lower. King’s
Analyzed Tables gave similar results. As the method of com-
puting the rate of mortality for the first year introduced a function
involving the second year’s mortality, the rate deduced by Mr.
Sprague was probably too high, while Mr. King’s method left

the same factor avowedly too low.

In addition to the painstaking work of Mr. Sprague in this
investigation there were four original ideas introduced by him at
that time which deserve special emphasis
1. The facility obtained by using a Common Radix
2. The happy combination of his figures with the H m W Table;
3. The use of a new formula of Interpolation; and
4. The development of an excellent Notation for Select Tables.
Moreover, Mr. Sprague, in an elaborate and very valuable paper*
showed the many uses to which select tables could be put whereby
information could be obtained on points regarding which nothing
could be learnt from the old aggregate tables. Those uses opened
a new field of vision to many actuaries, and enabled them to solve
problems, which some had scarcely even ventured to guess at
previously. The result was the immediate acceptance by nearly
all actuaries of the Select Table Principle.

British Offices’ Life Tables, 1893.f

A growing opinion that the mortality of insured lives had de-

H
veloped on lines which made the m Table obsolete, with a strong
desire for more truly representative tables, especially Select Tables,
led to the formation of a Joint Committee and the
of the Institute
Faculty of Actuaries to compile new statistics. In 1894 cards
were issued to the contributing offices, arid sixty sent in returns.
Males and females were dealt with separately by means of colored
cards. Rated up lives and those subject to extra hazard were
excluded, the experience being confined to healthy lives resident
* J. I. A., Vol. XXII, p. 400.
t British Offices Life Tables —several volumes published by C. & E. Lay-
ton, London. See especially “An Account of the Principles and Methods,
etc.,” 1903.
 : :

50 SOURCES AND CHARACTERISTICS OF

in Britain when the policies were issued. If extra premiums were

afterwards incurred for foreign residence or occupation, the lives
were continued under observation without modification on this
account. The experience extended from the Policy Anniversary
in 1863, or subsequent date of entry, to the anniversary in 1893
or previous exit. One of the objections to the m Table was thus H
—
avoided, namely that the data for that table extended back to
the earliest history of the oldest companies when sanitary and
economic surroundings were entirely different.
The rates of mortality are shown separately for different classes
of policies, as follows

Approxi-
Symbols No. of Years No. of mate Mor-
Used. of Experience. Lives. tality
Ratio.*

Whole Life Participating OM 7,056,863 551,838 100

Whole Life Non-participat-
ing ONM 602,591 56,807 110
Endowment OEM 897,673 132,043 75
Limited payments OLM 410,251 36,839 81
Increasing scale premiums OIM 207,709 23,280 109
Temporary OTM 36,489 11,603
Contingent OCM 15,586 3,482
Joint Lives QJM 90,171 9,195

Select Tables are expressed 0 [NM1 O lM1

, ,
etc. ;
while for female lives
the letter / is substituted in the above symbols instead of m.
Select mortality tables have been accurately formed for the first

time and show the company’s and the policy holder’s

effect of the
selection. The effect of selection is shown to be of little impor-
tance after 5 or 6 years yet unadjusted tables are given which
exclude
1. The first 5 years;
2. The first 6 years;
etc., etc., up to the first 10 years.
By excluding the first ten years we probably get the ultimate
rate of mortality. Select values during the first ten years have
* This “Approximate mortality ratio” is obtained by comparing the actual

deaths between the principal insurance ages 30-50 with the expected deaths
by the 0 M(6) table. The select period (first five years) was excluded in making
the comparison. In the last three classes the non-select experience is scarcely
sufficient to make a satisfactory comparison.
 THE PRINCIPAL MORTALITY TABLES. 51

been graduated to join this ultimate table. Those tables which

exclude a portion of the data have been called truncated a word —
which does not seem expressive for the particular purpose in
view.
Duplicate lives were eliminated from the aggregate tables; but
all except simultaneous policies were retained in the select

statistics, since two taken at different dates on the

policies
same life do not come same section of a select mortality
into the
table. Accordingly the Select Tables purport to deal with a larger
number of lives and a greater number of years of exposure. In
the aggregate and ultimate tables if two policies appeared on the
same life, but with an uninsured interval between the discon-
first was treated
tinuance of the one and the issue of the other, the
aswithdrawn and the second as a new issue.
The 0 M and the 0^ (5) as compared with the American Experience
Table show the following results:

Complete Expectation of Life Rate of Mortality qx per 1000.

Age.
American. 0m 0M(5) American. 0M 0 M(5)

20 42.20 43.68 42.39 7.81 4.04 6.52

30 35.33 35.57 35.06 8.43 5.95 7.47
40 28.18 27.86 27.67 9.79 9.15 9.78
50 20.91 20.61 20.52 13.78 15.04 15.45
60 14.10 14.07 14.04 26.69 28.87 29.21
70 8.48 8.71 8.71 61.99 62.07 62.19
80 4.39 4.84 4.84 144.47 138.44 138.50

The rate of mortality qx by the American Table is higher than

the 0M at ages under 43, then considerably lower from that age to
age 70, after which it is again higher. Net premiums for Whole
Life insurance follow generally the same course; but at the prin-
cipal entry ages 25 to 40 there is never so much difference as $1.00
per thousand. At age 25 the American Experience rate is 87
cents more than the 0 M and at age 40 it is 49 cents less. The
Expectations of life by the American Experience and the 0 M(5)
show a remarkable agreement while annuity values, premium rates,
etc., also differ but slightly.
Female Experience is given for: (1) Ordinary Life participating,
(2) Ordinary Life non-participating, and (3) Minor Classes. As
compared with male mortality the same characteristics appear as
52 SOURCES AND CHARACTERISTICS OF

had been noted in earlier investigations; there is also an indication

of general superiority of female over male vitality; but medical
selection does not appear to be quite so effective. A full analysis
of female in comparison with male mortality was made by Mr.
C. W. Kenchington* and a further investigation was afterwards
made by Mr. A. J. C. Fyfe.f
Amongst the “Old Assurances” in force in 1863, there were
comparatively few recent policies, and the method whereby such
Old Assurances were included, while extending greatly the expe-
rience at the older ages, had the effect of introducing an increased
number of non-select and aged lives into the aggregate 0 M expe-
rience, as well as into the select experience. This would make the
mortality curve of the aggregate table unduly steep after middle
life; it probably accounts for the high reserves by this table.

H
Although the m net premiums are lower than Sprague’s Select up
to age 43, the 0 M are lower than the 0 [M1 Select only up to age 29
— a result possibly arising from the same cause.
Net premiums by the 0 M Table are less than those by the older
H m Table, but policy values average greater, a condition caused
by the different slope of the mortality curve. The mortality
in the various classes confirms the belief that the larger the rate
of premium paid, the lower the mortality —an effective illustration
of the selection exercisedby policy holders.
A careful study of the new statistics as compared with earlier
compilations appears to show
1. A marked improvement in vitality;

2. The influence of medical selection is more persistent, and

especially conspicuous amongst younger men;
3. Self selection by annuitants had not improved to the same

extent as medical selection of applicants for insurance.

One of the new features of this experience is the publication for
the first These are given
time of complete tables of withdrawals.
for ages at issuegrouped around quinquennial points and for
each year of duration from 0 to 9 inclusive, also for “10 and
upwards.”
The rates of discontinuance per cent, according to the 0M expe-
rience! were as follows:

* J. I. A., Vol. XLIV, p. 105. t T. F. A., Vol. VII, p. 21.

JT. F. A., Vol. IV, p. 82. § See J. I. A., Vol. XXXVII, p. 463.
 THE PRINCIPAL MORTALITY TABLES. 53

Central Age at Entry.

Year. Year.
25 35 45 55

1 3.05 2.42 2.25 1.98 1

2 8.59 6.56 5.70 5.17 2
3 5.81 4.44 3.88 3.46 3
4 4.21 3.40 2.92 2.64 4
5 3.27 2.66 2.44 1.95 5
6 2.78 2.34 2.09 1.77 6
7 2.30 2.08 1.70 1.41 7
8 2.17 1.72 1.49 1.11 8
9 1.91 1.67 1.33 1.02 9
10 1.68 1.52 1.21 1.11 10

The rates of discontinuance per cent, on non-participating whole

life policies differed materially from the above as is shown by the
following rates for central age at issue, 35, that is for the group of
ages 32-37.

Rates of Discontinuance per cent, O nm Experience.

Central Age 35.
Year. Rate.

1 4.36
2 10.13
3 7.36
4 6.57
5 4.90
6 3.88
7 3.20
8 2.72
9 2.49
10 2.31

The graduation of the entire experience was placed in charge

of Mr. George F. Hardy; and the 0 M(5) Table was graduated by
Makeham’s Law, constants being determined by a new method
somewhat similar to the method of moments. In the adjustment
of the 0 M Table the use of Makeham’s formula alone was not practi-
cable; but the graduated table was built up on the basis of the gradu-
ated 0 M(5) by a double frequency curve connecting the two tables.
As it was necessary to abandon or modify Makeham’s formula the
only object in view was to obtain a perfectly smooth curve for the
0 M Table, and to represent as nearly as possible the ungraduated
facts. But Makeham’s Law was applied to the graduation of the
qnm(5) experience,* and
was found to give good results from age 20
onwards.
* J. I. A., XXXVIII, p. 501.
54 SOURCES AND CHARACTERISTICS OF

An ultimate table, excluding the first ten years of the participat-

ing experience, was graduated by Makeham’s Law and the select
values were graduated to join this Ultimate Table by an extension
of the same law, introducing a function dependent on the duration
of the insurance.

Specialized Mortality Investigation.*

This is not strictly a mortality table but rather an investigation
into the relative mortality as affected by certain special features,
such as: nationalities resident in the United States, occupations,
personal and family histories, and localities. The work was under-
taken in 1901, under the direction of the Actuarial Society of
America, from thirty years’ experience (1870-1899) of thirty-four
life insurance companies in the United States and Canada. Its
object was to supply those officers who have to decide upon the
acceptance of risks with material for ascertaining whether a
particular class is better or worse than normal.
The investigationwas based upon policies except that if several
policies were issued on one application in the same year only one,
the longest in force, was reported.The duration of policies can-
celledwas computed by subtracting the calendar year of issue
from that of termination, and of policies in force by taking the
exact duration at the anniversaries in 1900.
The mortality experience in the different classes was compared
with a table adopted to represent Standard Mortality amongst
healthy lives. The expected deaths were computed by such
Standard Table, which was based upon Farr’s Healthy English
Male Table, modified for ages 15 to 21, inclusive, and for 52 to 61,
inclusive. For ages 15 to 21, eleven-tenths of the annual mortality
of the then new male experience O m(5) was taken, while at ages 52
to 61, five-sixths of the O m(5) mortality was adopted. In order to
allow for the effect of selection during the early years, the following
percentages of mortality by the Standard Table were used:
Percentages of Standard Mortality to Allow for Selection.
Ages at Entry.
Year 1. Year 2. Year 3. Year 4. Year 5. Year 6 and
After.

15 to 28 45 64 79 90 97 100
29 to 42 50 68 82 92 98 100
43 to 56 55 72 85 94 99 100
57 to 70 60 76 88 96 100 100

* Volume published by A. S. A., 1903, 479 pp., folio.

 THE PRINCIPAL MORTALITY TABLES. 55

The final results were published in 1903, with the actual and
expected deaths for each class in the four age groups above shown
as well as in total. The detailed facts were also published to
permit of individual study, and from which more accurate con-
clusions may be deduced.
The classes of risks may be briefly described as follows:
1. Policies for large amounts; one class over $20,000.
2. Policies granted on terms other than applied for; 2 classes.
3. Nationality; divided into 4 classes.
4. Occupation; divided into 35 classes and covering army, navy,
and marine service; the more important hazardous trades;
liquor dealing; and railway service.
5. Personal Disability; covering 32 classes, including past history
of diseases such as gout, blood-spitting, etc., unusual weights
and unusual heights.
6. Family history unsatisfactory; covering 2 classes, dealing re-
spectively with cancer and insanity.
7. Place of Residence; 22 classes, each relating to a different

county in the United States, principally in the South.

Care must be exercised in using the results for the following
reasons: All the lives investigated were accepted by companies and
therefore may not show average results in some of the specialized
classes. While those who were charged an extra solely on account
of occupation were included in the experience, no risks were in-
cluded if they had been treated as under average on account of
personal or family history. Accordingly all the classes in the
latter category may
be viewed as the better selected risks of each
class. Again, the standard of measurement (Farr’s Table Modi-
fied) has not been universally accepted as representing the normal
risk. If the standard mortality were too low for any group of
ages the result would be to give apparently unfavorable results for
those ages and vice versa.

Medico-Actuarial Mortality Investigation.

The Association of Life Insurance Medical Directors and the
Actuarial Society of America felt that the work of the Specialized
Mortality Investigation should be extended, and a joint commit-
tee was formed for the purpose, October, 1909; memorandum of
instructions issued May, 1910. Forty-three companies supplied
 ;

56 SOURCES AND CHARACTERISTICS OF

the basic information and the work of compiling, tabulating,

and recording the data was conducted at a central bureau in
New York City.
The
experience covered about 93 per cent, of the policies issued
in the United States and Canada by all legal reserve companies
during the years 1885-1909, traced to policy anniversaries in
1909. It dealt with the following:

a. 68 groups involving occupational hazard

b. 76 groups of medical impairments;
c. 4 groups of women;
d. 3 groups of colored risks;
e. 4 groups of joint life policies;
/. A study of the influence of build on longevity.
Policies which had been treated as sub-standard for medical
reasons were excluded; policies rated as sub-standard for family
history alone, or for occupation, were included. The experience
was based on policy years, and mean durations in case of death
;

the duration was curtate, thereby placing each death in the

proper policy year.
To investigate the influence of build on longevity, the com-
panies furnished records of their business on standard lives for
one month in each of the sixteen years, 1885-1900, January
being taken in the odd years and July in the even years, by this
means securing an average of summer and winter weight. The
mortality rates from this data were much lower than the stand-
ard table assumed in the Specialized Investigation. They were
however confirmed by the experience of two large companies,
and were therefore used for purposes of comparison. The rates
of mortality were low at the younger ages, the ultimate mortality
for the eleventh and succeeding policy years being less than 60
per cent, of the American Experience for attained ages below 40.
After the first year the mortality by policy years for entrants
under 50 showed the effects of selection to be relatively slight.
The committee asked the companies to furnish additional data
to examine further the improvement in mortality and a standard
table was thereafter formed. The following shows the extent of
statistics:
 — . ;

THE PRINCIPAL MORTALITY TABLES. 57

Total Number
Years of Issue. Number of Years’ Deaths. Expected Ratio.
of Entrants. Exposure. Deaths

1885-1892 80,976 781,852 7,180 6,850.03 105%

1893-1900 148,995 1,106,316 8,000 6,911.45 101%
1901-1908 270,404 926,108 5,042 5,441.91 93%
Totals 500,375 2,814,176 20,222 20,203.39 100.3%

The shows the mortality rates for the first four years
final table
of duration and thereafter is merged into a general table excluding
—
these years, now commonly mentioned as the M. A. Table.
Only the first two years showed a distinctly lower mortality than
the ultimate. The Committee was satisfied that the table might
with confidence be used for the particular purpose for which it
was constructed.
Subdivision of the data according to years of issue showed a
continuous improvement in mortality. The committee issued
a warning against the general use of this table for any purpose
other than that for which it was prepared. It is based upon
policies and should not be applied to the solution of financial
problems, since mortality rates are higher when based upon
amounts insured.
Five volumes of statistics were published from 1912 to 1914,
the first volume containing details of the investigation and basic
facts for the investigation of build, also the adjusted mortality
table. Tables of average height and weight were prepared and
in Volume II are published mortality ratios in groups of lives
according to the extent of departure from the average build.*
These tables should be used with caution, as the preponderance
of recent business has the effect of indicating a lower mortality
than normal in some cases, in others a higher. In addition to
showing the effect of build on mortality Volume II contains an
analysis of the causes of death amongst men at different ages;
also tables of mortality amongst womenf divided into four
classes

. Spinsters;
. Married women, beneficiary husband;
c. Married women, beneficiary other than husband
d. Widows and divorcees.
* T. A. S. A., Vol. XV., p. 315, and XVII., p. 17.
f See also T. A. S. A., XVIII., pp. 318-326.
58 SOURCES AND CHARACTERISTICS OF

Classification by plan shows that endowments are favored by

unmarried women, whereas life and limited payment forms are
more often taken by married women, including widows and di-
vorcees. The volume closes with statistics of mortality amongst
North American Indians and certain colored groups. The mor-
tality amongst negroes was shown to be about 40 per cent, in
excess of the expected in spite of the careful selection of such
risks.
Vol. III. deals with the “ Effect of Occupation on Mortality,”
the most important divisions being the Liquor Industry, Rail-
road, Metal Trades, and Mining. The causes of death are not
given.
Vol. IV contains statistics of cases showing medical impair-
ments, including the effects of alcohol, also diseases affecting
the various physical organs, the arteries, etc., including certain
surgical conditions. It must be remembered that cases ac-
cepted without rating, although coming within these classes must
have been unusually good in every respect except for the par-
ticular impairment. High mortality appears among those who
have suffered from syphilis, even after two years’ continuous
treatment and one year’s freedom from symptoms; also in cases
in which albumen or sugar were found, cases of alcoholic habits,
high pulse rate, abdominal girth greater than chest expanded, etc.
Questions of family history (especially history of tuberculosis),
habitat mostly in southern states, malaria, and joint life insur-
ance, are covered in Vol. V. was developed that under joint
It
policies to men and women, there was a high mortality among
women at the younger ages, but at the middle and older ages
they appeared better than men.
Students should read with close attention the warnings con-
tained in “An Interpretation of the Results of the M. A. In-
vestigation,” T. A. S. A., Vol. XV., pp. 62-76.

Experience of Canada Life Office.

Published 1895 covering

,
J+6 years 1847-93.
,

One of the principal objects of this investigation, made by Mr.

Frank Sanderson, was to find out the
the effects of selection in
northern half of North America. All lives rated-up, or charged
an extra, as well as female lives, were excluded. The investi-
 i

THE PRINCIPAL MORTALITY TABLES. 59

gation was made according to the lives assured, and particulars

were taken out on cards of somewhat similar form to those of the
Institute 1893 Experience.
The policy year method of investigation was adopted, but some
slight complication arose in regard to the ages on account of the
next-birthday age having been inserted in the cards. The expe-
rience was reduced from fractional to even ages by means of the
formula
lx — lx—

it having been found from actual experience that on the average

the assurances were taken one-third of a year prior to the attain-
ment of the age next birthday. But this assumption was ingeni-
ously avoided in graduating the aggregate tables, constants hav-
ing been determined from the facts at fractional ages.
In filling in the mode were used: (1)
of exit four subdivisions
Existing, (2) Matured,
(3) Withdrawn, and (4) Died. The
matured contained expired term assurances and endowments.
The existing were carried to the anniversaries in 1893, and the dura-
tion was found by subtracting the year of entry from 1893, thus
giving an integral number of years in all such cases. The nearest
integral duration of exposure was adopted for the Matured and
Withdrawn, while those who died were carefully located in the
policy year in which death took place and assumed to be under
exposure to the end of that year. Duplicate lives were eliminated,
it would appear, from the select experience as well as from the

aggregate.
The total number was 35,287 covering 296,481 years
of entrants
of life. 55% of the entrants were “Existing” in 1893; 37% had
“Withdrawn” and “Matured”; and 8% had “Died.” The
average age at entry was 32; the average duration nearly 8 %
years. Of the total years of exposure, more than one-half relate
to ages below 40 and four-fifths to ages below 50, a fact that prob-
ably accounts for the small percentage of deaths for so high an
average exposure, although for the “Died” alone the average
duration was 13.55 years.
The tables deduced include an Aggregate Table, a table excluding
experience of first five years, some Select Tables, as well as full
particulars under each age at entry of the exposed to risk and
deaths for each year of duration. Statistics are given of the
60 SOURCES AND CHARACTERISTICS OF

withdrawals, and shown that nearly half of these took place

it is

at the end of the year. Makeham’s formula for graduation

first

was used for the aggregate table, the method of determining the
constants being that introduced by King and Hardy; log c = .0425.
In forming select tables the experience after five years was first
investigated, and connecting mortality rates were formed during
the first five years between the ages of 20 and 50 in the following
manner: The first year’s mortality was investigated by itself in
three groups of ages, and then graduated for each age. The
third year’s mortality was found by combining the second, third
and fourth years, the resulting mortality rates being graduated
by Makeham’s formula; and lastly, the second, fourth and fifth
years’ mortality were got by interpolation.
In the published volume there were included comparative tables
showing the death rate as compared with that of the more im-
portant mortality tables in individual offices and groups of offices.
The mortality of the Canada Life appears to have been exceedingly
favorable, being practically the same as that of the Australian
Mutual Provident. Statistics deduced from census returns would
indicate that the conditions in Canada are peculiarly favorable to
longevity. The satisfactory experience of the Canada Life office
may be caused to a considerable extent by climatic influences,
combined with strict medical selection and a goodly proportion of
risks from rural communities.
Dand N commutation columns and annuity values at 4% in-
terest are given, and it is found that the reserves by this table are
high as compared with the standard tables.
The government of the Province of Ontario adopted the experi-
ence as the basis for the calculation of minimum rates for fraternal
societies.
A separate investigation was made into the mortality amongst
substandard but the paucity of data and combination of
lives,

various classes of risks renders any conclusions from this class of

doubtful practical value.

Mortality Experience of Gotha Life Office, 1829-1896.*

This investigation, made under the supervision of Dr. Johannes
Karup, embraces the experience of the Gotha Life Office on all
classes of life and endowment insurances from 1829 to 1895; the
observations ceasing on the policy anniversaries in 1896. The
* This account has been taken from T. F. A., Vol. V, p. 87 et seq.
 THE PRINCIPAL MORTALITY TABLES. 61

policy year method was used and there were 150,594 lives with
2,255,813 years of exposure, and 46,480 deaths. All joint life,

survivorship, and short term insurances were excluded. The

experience was analyzed by lives, and by amounts; also according
to sex and classes of insurance (life, endowment, etc.), all according
to the duration of policies, thus producing select tables.
The nearest age at entry was taken, and the nearest duration
method used. Duplicate lives were excluded whether of the same
class or not, except for ascertaining the rate of claim, i. e., mortality
by amounts. The treatment of withdrawals followed the British
Offices’ Experience, except that exact calculations were made for the
first year.
An investigation of the manner in which the mortality changed
during the period was made, by tracing the new business of different
periods separately, and dividing 1829-1896 into four parts,
namely: (1) 1829-1852, (2) 1852-1867, (3) 1867-1881, and (4)
1881-1896. The mortality of each period was compared with (1)
the whole experience 1829-1896, and (2) the partial experience
1852-1896 by convenient age groupings for ( a ) the first five years,
and (6) the sixth and subsequent years. The results showed that
the mortality diminished from period to period, especially during
the first five insurance years, indicating an improvement in
methods of selection.
The final graduated Select Tables are joined to the ultimate table
after 7 years. The first year’s mortality declines from age 15 to
age 28, and until age 40 continues less than for age 15; this char-
acteristic is observed in a less pronounced form in subsequent
durations.
The practice of the company had been to accept many risks
on endowment plans where the excess mortality might be expected
to fall mainly after maturity of the endowment; indeed this seems
to be the only method used for treatment of substandard lives.
Endowment were divided into three classes: (1) a Volun-
policies
taries, ” i. e., those who apply for such of their own accord, (2)
“ Involuntaries,” i. e., those upon whom such policies were imposed,
and (3) a class of policies issued as collateral for loans. These
three divisions taken together show a mortality lighter than that
for whole life policies, being 84% during the first five years and
96.3% thereafter. The voluntary endowment class shows an
unusually low mortality and each of the other classes a mortality
62 SOURCES AND CHARACTERISTICS OF

considerably in excess of the whole life, the involuntary class

being slightly the worst, the heavier mortality of this last named
class being also distinctly observed during the first five years
after entry.
The female experience was not
there being 2,735
extensive,
deaths. During the first year women
appear as favorably as men,
but during the second and subsequent years for ages under forty
there is a noticeably higher mortality amongst females. From
about age 40 onward the excess of male mortality over female is

quite appreciable.

Japanese Life Tables.*

These tables are the first to give the mortality of an Oriental
race, scientifically deduced from life insurance records. The
tables, formed by Mr. K. Ebihara, F. I. A., were published in
1912. The material, furnished by three Japanese life companies,
is of recent character, the oldest company having been founded

in 1881. The experience closed in 1905 and to avoid special

risks incurred during the Russo-Japanese war, all emigrants and
lives in military service effecting policies in 1903 or after, were
excluded.
The system of investigation followed closely that of the British
Offices
’
484,815 cards were sent in, of which 203,-
Life Tables.
143 related to endowments. Special features were:
1. Very heavy mortality at young ages and marked improve-
ment between ages 20 and 30 generally heavier mor-—
tality than British or American standard.

2. The method of handling selection. The actual deaths in

the year were 62 per cent, of the expected by the
first

Ultimate Japanese Table. This ratio of 62 per cent, was

used for all ages; similarly for the second, third, and
fourth years, the ratios were 87 per cent. 95 per cent, and
97 per cent.
3. The use of the function B [X ]+t, meaning “ Brought down”
or “net movement.”
* J. I. A., Vol. XLVII., pp. 100-105.
 THE PRINCIPAL MORTALITY TABLES. 63

MORTALITY OF ANNUITANTS.
Government Annuitants —N« f
I, 1829.

In 1808 the National Debt Commissioners of Great Britain

commenced to grant life annuities, and they applied to Mr. W.
Morgan, the Actuary Old Equitable, to compute tables for
of the
this purpose; these tableshe based on the Northampton Table.
In 1819 Mr. John Finlaison who had been appointed Government
Actuary pointed out that the prices charged for annuities were
too small, and that the Government was losing heavily. Specula-
tors had discovered the excellent values in such annuities, and had
been buying annuities on carefully selected lives, sometimes also
protecting themselves against loss by life insurance on the
same
lives. The loss to the government in the eleven years from 1808
amounted to nearly $10,000,000, yet a period of about ten more
years elapsed before the error was corrected. Mr. Finlaison had in
the meantime been taking steps to ascertain the rate of mortality
amongst annuitants. He took for his materials the nominees of*

1. Various English and Irish Tontines from 1693 to 1789;

2. Life annuities issued at the Exchequer from 1745 to 1779, and
3. Life annuities chargeable on Sinking Fund from 1808 (as
above).
In each case the facts were carefully tabulated, and in extracting
them duplicate lives were eliminated. The ages last birthday
were given in each case, and on an average the lives were assumed
to be half a year older. Those stated to be 30 were assumed on
the average to be 30|, the sum of the numbers at 29 and 30 were
assumed to give double the number exposed to risk at age 30.
Mr. Finlaison drew up twenty-one tables, two of which he ad-
justed by the formula:
Graduated p* = Mvl-i + 2 p1-s + 3pL_ + 4p*_, + 5p'
2

+ 4p*+ + 3p,+2 + 2p' +3 +

1 p'+J.
called Finlaison’s Method of Graduation.
There is reason to believe, however, that he subjected his data
to some modification before applying his method of adjustment.
One of the most important features of this investigation was the
marked superiority of female life over male. Values of annuities
were deduced from his results and employed by the government.
 : : —

64 SOURCES AND CHARACTERISTICS OF

Government Annuitants —No. II, 1860.

This table was formed by Mr. A. G. Finlaison (son of Mr.

John Finlaison), the Actuary of the National Debt, the materials
used being the nominees of
1. The Irish Tontines of 1773-1777 3,384 persons.
2. The English Tontines of 1789 8,171 persons.
3. The annuities granted by National Debt Commissioners
1808-1850 16,812 persons.
28,367

Of these 28,367 persons, 11,829 were males and 16,538 females;

19,434 had died during the period over which the observations
extended; while amongst the males were 675 carefully selected
lives nominated by speculators who had purchased the annuities.
This practice has been stopped by law. The Tables were never
extensively used, and are now of but little interest.

Government Annuitants —No. Ill, 1883.

Formed by Mr. A. J. Finlaison (grandson of Mr. John Fin-

laison), Actuary to the National Debt Commission, exclusively

from the records of the annuities issued from the National Debt
Office during the period from 1808 to 1875.
The number included was 30,788, of whom 10,929 were males,
and 19,859 females. The 675 selected nominees previously
referred to were also included amongst the males. 22,998 had
died during the period and 7,790 were alive at the close of the
observations. The tables published give the following particulars
for each age
1. Number of entrants. 3. Deaths, and
2. Number alive at close of observations. 4. Exposed to risk.
In the case of those alive at the close of the observations 1875 —
they were each kept under observation until their birthdays that
year in order to avoid fractional years of age. The following is

an extract from the table of elementary facts, age at purchase 60:

Number op Entrants 475.

Age. Alive at Close of Deaths. Number Exposed

Observations. to Risk.

60 _ 4 316.7
61 4 16 467
62 6 11 445
63 7 14 427
etc. etc. etc. etc.
 : :

THE PRINCIPAL MORTALITY TABLES. 65

The ages at purchase of the annuities were stated as those last

birthday, and it was found that, on an average, the annuitants

were actually four months older. Accordingly, the true average

age of the 475 entrants above mentioned was 60J^; and up to
the age of 61 these were exposed to risk for two-thirds of a year.
Mr. Finlaison, to get the mortality for the first year, and for age
60 at entry, divided the four deaths above mentioned by two-
thirds of 475, i. e., 316.7, this being equivalent to an assumption
that the rate of mortality during the four months from the birth-
day to purchase was the same as for the eight months immediately
following. A similar assumption was of course made for other
ages. For the second year’s mortality at age 61, the four who
died, and the four alive at close of observations must be deducted
from the entrants, thus giving 467 exposed to risk at age 61, among
whom 16 deaths occurred, which showed a rate of mortality of
.0343; similarly for subsequent years. The formula for deducing
the exposed to risk would therefore be

Elx]+n = E[ x ]+n - 1 “ d[>] +n _ l — 6[a;] +n ;

or
= EX — [ ] ]Ci e — So
and for the general mortality table where the entrants at all ages
were combined

Ex — 2n x_i + \n — 2 e — 2d -i
x x x

= Ex- 1 + \n - + f n — e — dx-
x 1 x x 1,

where n x represents the new entrants.

An analysis of the facts was made to ascertain the effect of the
which the annuitants exercise, and it was found to be
selection
unimportant after four years. The entrants at each age were
accordingly traced separately for the first four years of their
existence (for ages 40 to 80) and thereafter combined with the
entrants at all previous ages, thus giving Select Mortality
Tables.
The treatment was equivalent to a “ life-year” method, the
annuitants being traced on the average from birthday to birthday.
It has been suggested that the method of graduation by Wool-
house’s formula distorted the table, and resulted in higher mor-
tality rates than the facts justified; but this is now only of academic
interest.
66 SOURCES AND CHARACTERISTICS OF

Government Annuitants —No. IV, 1910.*

The Actuaryto the National Debt Commissioners of Great
Britain, Mr. J. Blakey, submitted a report dated 12th October,
1910, in which he gave particulars of an investigation into the
mortality of government annuitants from 1st January, 1875, to
31st December, 1903, including new annuities issued during
that time and annuitants living on the anniversary of purch. se
date in 1875. Where two or more annuities were granted, only
the experience of the first was included. The following table
gives a summary of the data:

Government Annuity Experience, 1875-1904. Summary op Data.

Males. Females. Total.

Number of lives under observation 5,504 13,863 19,367

Number of years of risk 57,652 163,378 221,030
Number of deaths 4,168 9,333 13,501
Number of lives existing at the close of the
observation 1,336 4,530 5,866

The investigation proceeds on the policy year plan, tracing the

mortality from the date of admission to the next anniversary,
and so forth, from anniversary to anniversary of the purchase
of the annuity, following the method of the latest British Offices’
Experience. The ages at entry were taken as the nearest age
at date of purchase. An investigation as to the effect of using
this showed that the assumption had the effect of understating
the tabular ages by about 20 days in the case of male lives and
—
about 15 days in the case of female lives a trivial difference.
A considerable number of annuities are purchased at the Na-
tional Debt Office under wills, etc., where the nominees do not
exercise any option, but in most cases the nominees themselves
are the purchasers.
The new tables are based on the assumption that the effects
of selection are practically exhausted after the expiration of four
years and the rates of mortality were, therefore merged into
the aggregate table after that period. The tables were graduated
by Makeham’s method, satisfactorily in the case of aggregate
tables, but modified for select tables in a manner similar to that
employed in the graduation of the British Offices Annuitant

* J. I. A., XLVII, p. 66.

 THE PRINCIPAL MORTALITY TABLES. 67

Tables. The following table compares the new values with

other important tables of annuitant mortality.

Annuity Values —Three Per Cent.

Males.

Age. Government Annuitants. Select.

British Offices,
McClintock’s.
Select*
1808-1875. 1875-1904.

40 $16.37 $17.34 $17.60 $17.41

50 13.83 14.24 14.40 14.29
60 10.64 10.82 10.88 10.73
70 7.36 7.45 7.44 7.15
80 4.64 4.59 4.54 4.08

Females.

40 $18.17 $18.69 $18.26 $19.32

50 15.28 15.78 15.51 16.03
60 11.82 12.29 12.23 12.28
70 8.06 8.59 8.41 8.42
80 5.02 5.27 5.05 5.01

British Offices’ Life Annuity Tables, 1893.*

This investigation relates entirely to the experience of annuitants
under contracts purchased from 43 life assurance and annuity
institutions, including the British annuity experience of three
American companies. Particulars of each annuity current at the
commencement of the observations in 1863 and of those subse-
quently granted up to 1893 were supplied upon cards, a separate
card being written for each annuity. The total of such cards
was 9,700 for male and 24,300 for female lives, reduced by elim-
ination of duplicates, etc., to 8,641 and 23,056, respectively.
In the select male section 4,214 were existing; there had been
4,427 deaths; and 67,250 years of exposure. The corresponding
figures in the female section were 11,956, 11,100, and 207,324.
The tables are published in the form of select tables, the entrants
at each age having been traced separately during the first five

years, the rates of mortality thereafter being those of a modified

ultimate experience formed by omitting the observations of the
select period.
It had long been felt that the government tables were not
applicable to the annuitants’ experience of life assurance com-
* See “An Account of the Principles and Methods adopted in the Compi-
lation of the Data, etc.,” C. & E. Layton, London, 1903.
68 SOURCES AND CHARACTERISTICS OF

panies, the rates of mortality in the latter being lighter than the
rates in the government tables. The fact that the observations
for the government experience extended from 1808 to 1875 was
in itself a deterrent influence, since it was believed that mortality
had continued to improve. Moreover, the selection exercised
against insurance companies is probably more intelligent, because
government annuities are often bought for small amounts under
the provisions of a will to pension old servants. Still further,
Life Office annuitants are doubtless of a better social class than
the government nominees. In the case of females, forming the
great proportion of the annuitants, the British Offices annuity
values approximate to those of the government at an age one year
younger. In the case of the males at the older ages the difference
is about half a year. The difference in reserves in case of a
“ model office” is roughly 3J^%.

Notation.
Male Annuitants Table aggregate O m* Female O af
“ “ “ select OM “

The graduation was performed by Mr. George F. Hardy. A

preliminary graduation of the Aggregate Table excluding the
first five years, showed that the male mortality from 40 upward
could be well represented by Makeham’s formula. The female
mortality could only be thus represented at ages above 65, and a sup-
plementary curve had to be introduced below that age. The con-
stants for these curves were obtained by equating to zero the sum
of the deviations of the adjusted and unadjusted deaths, also the
sum of the accumulated deviations.
Three trial graduations of the male table were made, for assumed
values of log c equal to .040, .038, and .036; and the final value
adopted was .038 as giving on the whole the most practical results,
while following closely the ungraduated facts. An arbitrary ad j
ust-
ment was made in one of the constants, so as to make the male annu-
same as the mortality
itants’ mortality at the younger ages nearly the
amongst assured lives. The facts at these ages were meagre; and,
but for this adjustment the annuity values of the annuitants
would have been appreciably smaller (i. e., higher mortality) than
those of assured lives.

The graduation of the Select Tables for the first ^ve years was
made by introducing into Makeham’s formula a function dependent
upon duration after entry.
 THE PRINCIPAL MORTALITY TABLES. 69

McClintock Annuity Tables.

In 1896 a paper appeared in the Transactions of the Actuarial
Society of America* giving particulars of the annuity experience
of fifteen American companies collected by Mr. Rufus W. Weeks,
Actuary of the New York Life. At first all the annuities issued
prior to 1890 were used and this material was afterwards carried
forward to 1892 with additional new issues in the meantime.
A feature of the experience was the preponderance of foreign
business; about three fourths of the lives were European and one
fourth American. The experience was based on lives; duplicates
were eliminated. The age was taken at the birthday nearest to
the date of first exposure; observation began on entry into any
one of the companies and continued until death or the anniver-
sary in 1892 when the experience closed. The exposure of a few
deferred annuities in the experience was taken from the date at
which the first annuity payment became due at which date —
there is usually an option to take a cash settlement. Men and
women were investigated separately, and complete select data
is given for each age at entry. The number of lives included in
the experience was 4,365 men, and 4,821 women.
Mr. McClintock took this data and derived two aggregate
mortality tablesf for male and female annuitants respectively.
They were graduated by Makeham’s Formula and have a com-
mon —
value for the constant c namely: log c = .04. Mr.
McClintock stated that the tables differ somewhat from those
1
which might be formed from a mere adjustment of Mr. Weeks
data but that he had endeavored to admit only such diversions
as seem reasonable. His female table, for example, shows a
somewhat higher mortality at ages under 70, because he con-
sidered that the experience at those ages had been materially
affected by the large proportion of recent entries. With reference
to the male table Mr. McClintock stated that he thought it best,
if any departure from Mr. Weeks’ experience should be permitted,

that such departure should be on the safe side. That is to say,

the mortality in Mr. McClintock’s adjustment would be lighter
than that actually shown by a direct application of the experience.
This table has been adopted by the State of New York and
several other states as the standard for annuity valuations. The
* T. A. S. A., Vol., IV, .p. 275.
t T. A. S. A., Vol. VI., pp. 13 and 137.
 :

70 SOURCES AND CHARACTERISTICS OF

following table illustrates the manner in which McClintock

figures vary from those of other standard tables

Complete Expectation op Life I*.

Males. Females.

Government Oam McClintock Government Oaf McClintock

Age. 1883 Select. Select. Aggregate. Age. 1883 Select. Select. Aggregate.

40 26.04 28.31 28.08 40 29.84 30.16 32.47

50 20.26 21.23 21.11 50 22.92 23.49 24.53
60 14.38 14.82 14.64 60 16.26 17.01 17.22
70 9.33 9.54 9.18 70 10.30 10.88 11.00

Annuitants Resident in the United States and Canada.

An unusually low rate of mortality amongst annuitants resident
in the United States and Canada was indicated by the investigation
into the experience of American and Canadian companies by
Arthur Hunter in 1904. As the number of lives observed at that
time was relatively small, the Council of the Actuarial Society
recommended to the companies that additional data be furnished
when the then available statistics should be doubled. This con-
dition was fulfilled in 1910; and the companies supplied their data
up to the year of issue 1909, the exposures being carried to the
anniversaries in 1910. All the companies represented in the
Actuarial Society granting annuities furnished their figures. Only
immediate annuities were included, issued on single lives for the
whole of life, under which the consideration had been paid in cash.
Accordingly all temporary, deferred, joint, and survivorship
annuities were excluded, as were also annuities issued in exchange
for dividends.
In the experience to the anniversaries of the annuities in 1910
thirty companies contributed 12,174 cards, 6,620 relating towomen,
and 5,554 relating to men; more than three-quarters of the expe-
rience was supplied by six companies. After eliminating simul-
taneous contracts, there were 5,510 annuities on women, with 1,585
deaths; and 4,042 (42 per cent, of the total) on men with 1,295
deaths. The average ages at purchase were 63 for women and
61^4 for men. The nearest integral age was taken, and the duration
of the existing was obtained by deducting the year of purchase from
1910. Duplicates were brought together by sorting, (1) according
to year of birth, and (2) according to name.
 ;

THE PRINCIPAL MORTALITY TABLES. 71

As compared with the British Offices’ Annuity Tables (Select),

the mortality among women was 84 per cent, by lives and 87 per
cent, by amounts of annuity. While among men the corresponding
percentages were 85 per cent, and 95 per cent, respectively, both
sexes indicating a lower mortality in the United States and Canada
than in Great Britain. There was no evidence that the mortality
differed widely by ages at entry in its relation to the British
Offices’ Annuity Table.
A comparison of the experience to the anniversaries of 1904 with
that to the anniversaries of 1910 showed that there had been very
little change in the experience for the 6th and succeeding annuity
years, the ratio of the 1910 table being for all ages and years of
issue 85 per cent, of the British Select Annuity experience for men
and 88 per women. During the first five annuity years,
cent, for
however, the experience on the issues of 1904 to 1910 showed a
marked increase over the experience for the same annuity years to
the anniversaries in 1904. Two hypotheses have been advanced
as explaining this change: (a) that there has been greater care in
obtaining proof of the ages of the annuitants at the date of purchase
and (b ) that the proportion of people seeking annuities was lower
than formerly, and the proportion of those actively canvassed was
higher, —
hence less selection by the annuitants.

Danish Survivorship Annuity Table.*

This table formed by Christian Jensen is based upon data de-
rived from the experiences of voluntary survivorship annuities,
granted by “ Statsanstalten for Livsforsikring,” the Danish
State’s Life Insurance Institution. The investigation deals with
female beneficiaries —
Danish women only. No tables were com-
puted showing death rates of the insured lives. Obligatory
annuities on Civil Servants were not included.
The period of observation is 1842 to 1900 and the experience is
by lives, carried forward until the last policy for any particular
beneficiary terminated. Exact ages from birthday to birthday
were used, and the observations ceased on the birthday of the
beneficiary in 1900, or with the first birthday after death prior
to 1900. The graduation was by Makeham’s Formula. The
constant log c = .04579609 is the same as that used in Hunter’s
Makehamized American experience, thus facilitating the use of
* T. A. S. A., Vol. X., p. 253. Survivorship Annuity Tables. Dawson, p. vi.
72 SOURCES AND CHARACTERISTICS OF

the two tables for joint lives. The other constants were derived
by the “ Method of Least Squares” from the table at age 40 up-
wards, involving 4,041 deaths.
The experience showed an improvement in the death rate
towards the end of the period. The mortality of the Danish
population is said to be as good as that in the healthier parts of

the United States, so that the tables may be used until American
Tables for Survivorship Annuities are available. In the absence
of other authoritative tables showing the rates of mortality of
annuitants under Survivorship Annuity Contracts, this table has
been adopted as the standard for workmen's compensation allow-
ances in the State ofNew York.
 THE PRINCIPAL MORTALITY TABLES. 73

MISCELLANEOUS MORTALITY INVESTIGATIONS.

In addition to the tables herein described there have been many
other investigations, some of which are of great interestbut space ;

will not permit that they be discussed in although references

detail,
to the more important of these experiences may with advantage be
given. Those who may have occasion to study any particular
phase of mortality may thus have some knowledge of the lines of
research and may be guided in the way towards which their further
inquiries can profitably be directed.
These special investigations may be placed in general divisions
as follows:
1. Investigation of death rates of different races;
2. Mortality rates in various countries and localities;
3. Observations according to class or occupation;
4.The experience of individual insurance companies.
The mortality of different races has not been scientifically
analysed with any completeness. Of course, it is necessary that
the various peoples should be under similar conditions in order that
proper comparisons may be made. At various times investigations
into the mortality of the colored race in the United States have
been undertaken, as in the Specialized Investigation of the Actu-
arial Society and the U. S. Life Tables, 1910. The experience of
individual companies on the same subject has also been dealt with,
but the results have seldom been made public, although they have
frequently been stated incidentally.
The mortality rates in different countries may be viewed either
as affecting Caucasians resident in foreign lands, or as affecting
the native population. Conditions as affecting whites resident
have changed greatly in recent years through
in tropical countries
a better knowledge of malaria and other tropical diseases which
are frequently transmitted by causes formerly unsuspected, often
by mosquito bites.Yellow fever has disappeared from certain
countries, while notable changes have been observed in such regions
as Cuba and the Panama Canal Zone, making the older investi-
gations of mortality in such regions of doubtful value. Some of
the less progressive countries do not seem to have taken advantage
of this growth of scientific knowledge.
The Journal of the Institute of Actuaries contains many refer-
74 SOURCES AND CHARACTERISTICS OF

ences to mortality in different countries, as for example mortality in

certain parts of Africa;* the mortality in certain parts of Australia;!
the mortality among the natives of In<Jia;t assured lives in the
West Indies, § etc. Much valuable information with reference to
the mortality in semi-tropical and tropical countries is .given in
the Transactions of the Actuarial Society, Vol. X, p. 395; and by
James Chatham in Trans. 3rd International Congress, p. 338.
Under the division of mortality according to class or occupation
one most important publication is the Supplement to the Report
of the Registrar General in England and Wales, Part II, published
in 1908, dealing with the death rates in different occupations in
,
England during the years 1900- 01-’02. This report succeeded
another of the same nature, less complete, published ten years
earlier. The question of mortality amongst dealers in alcoholic
liquors was investigated by the Associated Scottish Life Offices, ||

also in the Specializedand Mediqo-Actuarial Investigations. The

question of comparative mortality among abstainers and non-
abstainers from the use of alcohol has been a subject of much
controversy.** Those who use alcohol freely are unquestionably
on the average poor risks for insurance purposes. The low
mortality amongst the clergy generally was long ago indicated by
investigations made by the late James Meikle into the Church
of Scotland Minister Widows Fund, and this experience has been
confirmed again and again, the most recent investigation of this
type being that into the Presbyterian Ministers’ Fund by L. G.
Fouse, details of which have not been published.
Several interesting tables have also been prepared showing the
mortality of British Peerage Families, the statistics being taken
from books published from time to time giving information regard-
ing the individualmembers of the Peerage. These publications
also afforded a means of investigating the numbers of marriages
and and thus computing premiums for insurance against
of births,
the birth of issue. ft Peerage and clergy statistics have also been
used for determining the mortality in infancy and in childhood
* Vol. XXXIII, p. 285, XLVI, 308. J Vol. XXV, p. 217, XLIII, 365.
t Vol. XXXVI, p. 151. § Vol. XXVII, p. 161.

||
See J. I. A., Vol. XXXIII, p. 245.
** See paper and discussion, J. I. A., Vol. XXXVIII, p. 213; correspondence,
same Vol., p. 273; and Transactions 5th International Congress, Vol. I, pp.
517-545.
ft See especially J. I. A., Vol. XXVIII, p. 350.
 THE PRINCIPAL MORTALITY TABLES. 75

which has depended in the past very greatly upon the class of the

parents, so that the ordinary census tables of mortality in infancy are

not applicable for calculations relating to children’s endowments.*
There have been many important investigations conducted by
individual companies which have furnished information on par-
ticular points. For example, the Mutual Benefit Life Insurance
Company investigated especially the mortality on policies con-
tinued under Extended Insurance.! Several companies, following
the Mutual Life investigation of 1857, have taken up the causes of
death of insured lives. These have not been discussed much by
actuaries though they prove of great interest to medical men.
The experience of the Connecticut Mutual Life Insurance Co.
from its commencement to 1878 was published in 1884, and
amongst other features showed that the mortality under term
insurance had been excessive as compared with other classes, but
it is explained that this might partly be accounted for by term

policies taken out by the early Californian miners. Tables of

discontinuance were also given, but under present day conditions
these are not now of much value. More recent rates of discon-
tinuance were given by the New York Life,J but even these rates
have been greatly improved upon since 1907.
The information contained in the Medico-Actuarial publication
with reference to height and weight was recently supplemented
by the publication of “ Standard Mortality Ratios incident to
Variations in Height and Weight among men” compiled by a
joint committee of the Actuarial Society and the Association of
Medical Directors. This publication deals not only with devi-
ations from standard weight as affected by age, but treats of (1)
Medium sized, (2) Tall, and (3) Short men; also (4) Abdominal
girth of stout men. A Practical Rating for Overweights Was
submitted by A. A. Welch in T. A. S. A., XVII, p. 17.
The Washington Life Insurance Company published mortality
results in1889 containing amongst other interesting data an
investigation into the rates of mortality amongst policy holders
taking their dividends as reversionary additions as compared with
those taking cash. The latter were found to be very much the
better lives confirming the results of a previous investigation by
Mr .G. F. Hardy. § The mortality experience of the Provident
* See J. I. A., Vol. XVII, p. 26.
t T. A. S. A., Vol. X, p. 597. § J. I. A., Vol. XXIII, p. 1.
t T. A. S. A., Vol. IX, p. 103.
76 SOURCES AND CHARACTERISTICS OF

Life & Trust Company from 1866 to 1875 showed unusually low
mortality rates, apparently due in part to the large proportion of
endowment policies issued by the company. Further investiga-
tions of the same company up to .1911 (T. A. S. A., XIV, p. 277)
show low mortality in Endowment policies as compared with
Life, and unexpectedly low rates in Term policies. An interest-
ing investigation of mortality by plan of insurance, as experienced
by the Aetna Life Insurance Company, appears in Vol. XVII, p.
246. The mortality rates applicable to policy issues from 1885
to 1905 are relatively high in relation to the entire experience;
while all issues indicate a low mortality during the years from

1905 to 1913.
The experience on deferred dividend policies after the dividend
period expires, policies being continued, was submitted by Arthur
Hunter, Vol. XIV, p. 38. The results show a clear condition of
by policyholders adverse to the company. On more
selection
than one occasion it has been shown that when an automatic
provision for extended insurance or even for paid-up insurance
goes into effect, there is a tendency towards high mortality in
the first year or two after lapse. Probably the policyholders
“ allowed their policies to lapse as a direct result of serious im-
pairment in health and without regard to consequence.”*
These and many other phases of the mortality question have
been ably discussed, yet the conditions of life have been changing
so rapidly that results obtained some years ago while possibly
indicating the trend of events or showing that certain causes may
lead to good or evil effects, are not necessarily applicable to
present day conditions. Accordingly there is almost unlimited
scope for further research, and we may expect to see a still closer
scientificstudy leading especially towards the improvement of
conditions in unhealthy regions or occupations.

*T. A S. A., XV, p, 303.

 THE PRINCIPAL MORTALITY TABLES. 77

Table Showing the Rate of Mortality (qx ) According

to Certain Tables.

Thirty
Age. American
Experience.
Actuaries
Table.
American
Offices.
hm O* 0*( 5 ) Age.
(Males).

20 .0078 .0073 .0068 .0063 .0040 .0065 20

25 .0081 .0078 .0070 .0066 .0048 .0069 25
30 .0084 .0084 .0075 .0077 .0060 .0075 30
35 .0090 .0093 .0082 .0088 .0074 ,0084 35
40 .0098 .0104 .0094 .0103 .0092 .0098 40
45 .0112 .0122 .0112 .0122 .0115 .0120 45
50 .0138 .0159 .0142 .0160 .0150 .0154 50
55 .0186 .0217 .0189 .0210 .0204 .0208 55
60 .0267 .0303 .0265 .0297 .0289 .0292 60
65 .0401 .0441 .0386 .0434 .0420 .0422 65
70 .0620 .0649 .0578 .0622 .0621 .0622 70
75 .0944 .0956 .0878 .0984 .0926 .0927 75
80 .1445 .1404 .1341 .1447 .1384 .1385 80

Gotha Healthy English English North-

Age. 1852-95 English Life No. 3 Life No. 6 Carlisle ampton Age.
Whole Life No. 1 (Males). (Males) Table. Table.
—Males. (Males).

20 .0053 .0070 .0083 .0046 .0071 .0140 20

25 .0047 .0078 .0092 .0057 .0073 .0158 25
30 .0045 .0082 .0101 .0067 .0101 .0171 30
35 .0058 .0086 .0113 .0090 .0103 .0187 35
40 .0078 .0094 .0130 .0119 .0130 .0209 40
45 .0104 .0108 .0154 .0148 .0148 .0240 45
50 .0144 .0130 .0188 .0194 .0134 .0284 50
55 .0213 .0166 .0246 .0257 .0179 .0335 55
60 .0320 .0237 .0325 .0360 .0335 .0402 60
65 .0467 .0368 .0459 .0497 .0411 .0490 65
70 .0709 .0556 .0673 .0721 .0516 .0649 70
75 .1061 .0840 .0988 .1054 .0955 .0962 75
80 .1619 .1249 .1418 .1520 .1217 .1343 80
78 SOURCES AND CHARACTERISTICS OP

Table Showing the Complete Expectation op Life (e*)

According to Certain Tables.

Thirty
Age.
American
Experience.
Actuaries’
Table.
American
Offices. ll M oW 0m 0 3f(5) Age-
(Males.)

20 42.2 41.5 43.1 42.1 42.9 43.7 42.4 20

25 38.8 38.0 39.5 38.4 39.2 39.6 38.7 25
30 35.3 34.4 35.8 34.7 35.6 35.6 35.1 30
35 31.8 30.9 32.2 31.0 31.9 31.7 31.4 35
40 28.2 27.3 28.5 27.4 28.2 27.9 27.7 40
45 24.5 23.7 24.8 23.8 24.7 24.2 24.0 45
50 20.9 20.2 21.2 20.3 21.2 20.6 20.5 50
55 17.4 16.9 17.8 17.0 17.9 17.2 17.2 55
60 14.1 13.8 14.6 13.8 14.9 14.1 14.0 60
65 11.1 11.0 11.6 11.0 12.1 11.2 11.2 65
70 8.5 8.5 9.0 8.5 9.7 8.7 8.7 70
75 6.3 6.5 6.7 6.4 7.6 6.6 6.6 75
80 4.4 4.8 4.9 4.7 4.8 4.8 80

Gotha Healthy
English English English Carlisle North-
Age. No 1 Life No. 3 Life No. 6 Table. ampton Age.
Select. Aggre- (Males). (Males). Table.
gate. (Males).

20 43.0 43.6 43.4 39.5 41.0 41.5 33.4 20

25 39.2 39.7 39.9 36.1 37.0 37.9 30.8 25
30 35.3 35.6 36.4 32.8 33.1 34.3 28.3 30
35 31.3 31.4 32.9 29.4 29.2 31.0 25.7 35
40 27.4 27.4 29.3 26.1 25.6 27.6 23.1 40
45 23.6 23.5 25.6 22.8 22.2 24.5 20.5 45
50 20.0 19.8 22.0 19.5 18.9 21.1 18.0 50
55 16.8 16.3 18.5 16.4 15.8 17.6 15.6 55
60 13.9 13.1 15.1 13.5 12.9 14.3 13.2 60
65 11.4 10.4 12.0 10.8 10.3 11.8 10.9 65
70 7.9 9.4 8.4 8.0 9.2 8.6 70
75 5.9 7.2 6.5 6.2 7.0 6.5 75
80 4.3 5.4 4.9 4.6 5.5 4.8 80
 THE PRINCIPAL MORTALITY TABLES, 79

Table Showing Percentages which the Rates op Mortality According

to Certain Tables, Bear to the Rates According to
the American Experience.

Thirty Ameri-
Age. Actuaries
Table. can Offices.
hm o" 0*( 5 ) Age.

20 93 -87 81 52 84 20
25 96 -87 82 60 85 25
30 100 89 92 71 89 30
35 104 92 98 82 94 35
40 106 96 105 93 100 40
45 109 100 109 103 108 45
50 116 103 116 109 112 50
55 117 102 113 110 112 55
60 114 99 111 108 109 60
65 110 96 108 105 105 65
70 105 93 100 100 100 70
75 101 93 104 98 98 75
80 97 93 100 96 96 80

Gotha Healthy English English North-

Age. 1854-95, English Life No. 3 Life No. 6 Carlisle ampton Age.
Whole No. 1 (Males). (Males). Table. Table.
Life, Males. (Males).

20 68 89 106 59 91 180 20
25 58 96 114 70 91 196 25
30 53 97 119 80 120 203 30
35 65 97 126 100 115 209 35
40 80 96 132 122 133 214 40
45 93 96 138 133 133 215 45
50 104 94 137 140 97 206 50
55 115 89 132 138 97 180 55
60 120 89 122 135 125 151 60
65 116 92 114 124 102 122 65
70 114 90 109 116 83 105 70
75 112 89 105 112 101 102 75
80 112 86 98 105 84 93 80
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