Fertility of Marriage

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F.—FERTILITY OF MARRIAGE IN SCOTLAND.

THIS is the first Scottish census in which householders were required to give information relative to the fertilities of existing marriages. The- questions under this head in the Census Schedule were three in number; the first asked the duration of the existing marriage, the second the number of children born alive to the marriage., and the third the number of children of the marriage still living.

There are obviously four variables which must be taken into consideration in any calculation regarding the fertility of marriage—the duration of the marriage, the age of the wife at the time of marriage, the age of the husband at the time of marriage, and the number of children born to the marriage. Information regarding the first of these variables, the duration of the marriage, is provided by the answers to the first of the three scheduled questions; that regarding the second, the age of the wife at the time of marriage, is ascertainable by deducting the years of duration of the marriage from the reported present age of the wife; that regarding the third, the age of the husband at the time of marriage, is similarly deducible from the duration of marriage and the husband's present age; and that regarding the fourth, the number of children born to the marriage is provided by the answers to the second question.

The total number of married women enumerated in Scotland amounted to 762,835, and for each of these, with few exceptions, answers to the three fertility questions were given. All these cases were not, however, available for tabulation, because a considerable number of the married women were not returned on the same schedules as their husbands —no doubt in many instances due to the temporary absence of the husbands from home on Census Day—and such cases had to be excluded from the study because one of the variables, the age of the husband at marriage, was not ascertainable. Deductions from the total also fell to be made in respect of marriages in which the wives at the time of marriage were of such ages—over 45—that no fertility could reasonably be expected, such marriages obviously being useless for the purposes of a fertility enquiry. Age forty-five throughput this study has been taken as an arbitrary limit of the fertile period of a woman's life, and, although this limit may not be in strict accordance with physiological fact, it is defensible for working purposes, because the few and exceptional instances of fertility after age forty-five are quite insufficient to affect the general result. A further small number of cases were necessarily omitted on account of evident confusion and unreliability in the answers; these were mostly cases where there was clear evidence that children by previous marriages, or children born prior to wedlock, had been counted along with children born to the particular marriage under question. For instance, where a woman aged forty-three was returned as having been married for two years, and as being the mother of six children, such a marriage was excluded.

The effect of these deductions has been to reduce the total number available for tabulation from 762,835 to 680,684, the excluded marriages numbering 82,151." The reduced figure, however, is amply sufficient for the purposes of a biological study, and, as it amounts to nearly 90 per cent, of the total number of married women enumerated, it may be accepted as satisfactorily significant of the actual fertility of Scottish marriages.


The total number of children born alive to the 680,684 marriages included in the study was 2,728,235, or an average of 4.01 children per marriage. A statement such as this, however, is of little interest or value, because widely varying quantities are included in the average, and great elaboration of tabulation has been necessary to obtain figures on which reliable deductions may be founded for the purpose of illustrating the influence of any particular factor upon the size of the average family.

Doubtless the principal factor influencing the number of children born to a marriage is the length of the continuance or duration of the marriage during the fertile period of the wife's life. The longer that duration, the greater will be the probable size of the family, and as that duration varies inversely as the age of the woman at marriage, the younger she is at marriage, the longer will be the period of possible fertility, and consequently the greater the probable number of children.

But there are also secondary factors influencing fertility, and as it is as much with these as with the principal factor—the duration of the marriage—that this study is concerned, the scheme of tabulation has been devised accordingly in order to meet these. Among these secondary factors the following may be mentioned :—the fertile power of men and women at varying ages, and the influence of class or occupation.

To obtain homogeneous results from the particulars relating to the 680,684 marriages, a very elaborate and lengthy tabulation was required, and so bulky are the resulting tables—they would extend to some thousands of printed pages—that their publication has been rendered a practical impossibility, and resort has been had to publishing abstracts of them only. The original tables, though unpublished, will be preserved in the Registrar-General's Department, and will be available for purposes of statistical study to any interested in them.

As publication by abstract in place of publication in full has been adopted, a short explanation of the leading features of our scheme is necessary, as a guide to the reader. The original tabulation consisted in counting the number of marriages for each possible combination of the four factors or variables to which we have already alluded, viz., the duration of marriage, the age of the wife at the time of marriage, the age of the husband at the time of marriage, and the number of children born to the marriage. For this purpose, a series of approximately 1,500 tables was required, each showing for one given combination of the duration of marriage and the age of the wife at marriage, the number of children born to the marriage in correlation with the age of the husband at marriage. By transcription, this original tabulation was converted into a second series of tables, of about the same length as the original, in which each table shows, for one given combination of age of husband at marriage and duration of marriage, the number of children born, in correlation with the age of the wife at marriage.

The method adopted for the abstraction, or summarising, of these two lengthy series of tables, was that of the elimination firstly of one variable and afterwards of another. Thus, Table XXXIII is a summary of the original tabulation in which the variable of the age of the husband has been eliminated, and consequently the figures show the number of families of specified size in correlation with the age of the wife at marriage and the duration of marriage, but without taking into account the age of the husband at marriage. Table XXXIV is a summary of the original transcript, the figures in it showing the number of families of specified size in correlation with the age of the husband at marriage and the duration of marriage, but without taking into account the age of the wife at marriage. The variable eliminated from Table XXXII, which is the most comprehensive of these abstract tables, is that of the specified number of children resulting from the marriages—a statement of the average size of family resulting from marriages of specified durations between men and women of specified ages at the time of marriage being substituted.

These Tables, XXXII to XXXIV, are further summarised in Tables XXVI to XXXI by the elimination of a second variable. They consequently each deal with two variables only. Thus from Table XXVI the eliminated factors are the duration of marriage and the number of families of specified size, and the figures indicate the average size of family for each combination of age of husband and wife at time of marriage, and the numbers on which these averages are founded. Table XXVII gives similar information for each combination of duration of marriage and age of wife at marriage, and Table XXVIII for each combination of duration of marriage and age of husband at marriage, the variables eliminated from the former being the age of the husband at marriage and the specified number of children in each family, and from the latter the age of the wife at marriage and the specified number of children in the family.

Tables XXIX, XXX, and XXXI are general summaries giving the specified number of children in the families in correlation with one other variable only; in Table XXIX this other variable is the age of the wife at marriage, in Table XXX it is the age of the husband at marriage, and in Table XXXI it is the duration of marriage.

The variable of the duration of marriage has been eliminated from Tables XXXV, XXXVI, and XXXVII in a special manner, for these tables deal not with all recorded marriages, but only with those in which the fertile period of the wife's life has been completed, and in which, for any combination of age of wife and husband at marriage, duration is a matter of only secondary importance. These tables thus deal with the total families resulting from marriages between husbands and wives of specified ages at the time of marriage. Table XXXV gives the average size of family in correlation with the ages of the parents at the time of marriage; Table XXXVI the number of families of specified size in correlation with the age of the wife at the time of marriage; and Table XXXVII the same information in correlation with the age of the husband at the time of marriage.


No attempt is made in the text which follows to give a full, far less an exhaustive, description of all the information to be found in these abstract tables. Instead of attempting such a description, a few points of more special interest have been selected, and are dealt with seriatim.

Before dealing with these points it is only right to draw attention to a matter which affects to a greater or less degree all the calculations, and which is an apparent confusion in the minds of the householders in answering the question as to the duration of marriage. That there has been confusion is evident when the recorded numbers of marriages of specified durations are compared. Thus, recorded marriages of which the duration is reported to be less than one year number 16,755, while those of which the duration is reported to be more than one but less than two years number 26,974; marriages of more than ten but less than eleven years' duration number 2,928 more than marriages of over nine but less than ten years, and 3,215 more than marriages of over eleven but less than twelve years, while a similar anomaly is found in marriages of a duration more than twenty but less than twenty-one years. In short, there is a crowding of figures round certain selected durations similar to the crowding found round certain ages in a single ages tabulation, and referred to in the second volume of this Report.

Another consideration that must not be lost sight of, and which has a bearing on the conclusions derivable from these tabulations, is that the tabulations deal exclusively with marriages which have continued up to the completion of stated periods, while in fact a certain proportion of marriages do not continue so long, but are discontinued by the death of one or other of the spouses, or by separation or divorce. For instance, it is ascertained by the tabulation that the average size of the total family resulting from the marriage of a man of thirty with a woman of twenty-six is slightly over five children, but this figure is no doubt greater than would be found were it possible to ascertain the size of all families resulting from the union of men and women of these ages, and is so because there is no doubt that in a proportion of them the death of one parent, or separation or divorce, limited the size of family. Were it possible to include these discontinued marriages, the general average would be found to be somewhat, if not considerably, less.


The Chance of a Marriage being Childless .—The tabulation deals with 239,943 marriages in which the wife was of child-bearing age at the time of marriage, and which continued till the end of the woman's child-bearing period of life, and of these marriages 27,478, or 11.5 per cent., are childless. This percentage varies with the age of the wife at the time of marriage, the younger the wife the smaller being the percentage. Among marriages in which the wife at the time of marriage was aged 22 or under, childless marriages constitute less than 4 per cent, of the total; and among those in which the wife is aged 17 to 19, less than 3 per cent. But as the age of the wife at marriage advances the rate increases; it is 7 per cent, for age 25; 10 per cent, for age 28; 13 per cent, for age 30; 25 per cent, for age 35; 57 per cent, for age 40; and over 80 per cent, in marriages where the wife was aged 43 at the time of marriage.

The figures collected in Table XXXIII enable estimates to be made of the proportions which childless marriages constitute in those groups of marriages in which all the wives were of similar age at the time of marriage, not only when the fertile period of marriage has been completed, but also after specified durations of marriage. These proportions were calculated for each year of the wife's age at marriage, but on account of the relatively small numbers available for the individual calculations, due to the large amount of subdivision, the resulting figures were found to be too variable, and for smoothness of result it was found desirable to combine the figures over a group of years of the wife's life. The group selected was that of all wives whose ages at marriage ranged from 20 to 25 inclusive. Of each thousand of these marriages 733 were found to be childless at the end of the first year of marriage; 367 at the end of the second year of marriage; 159 at the end of the third year; 106 at the end of the fourth year; 91 at the end of the fifth year; 84 at the end of the sixth year; 74 at the end of the seventh year; 67 at the end of the eighth year; 64 at the end of the ninth year; 60 at the end of the tenth year; and 53 at the end of the period of possible fertility.

TABLE K.—PROBABILITY OF FERTILITY AFTER VARYING STERILE PERIODS.
(WIVES AGED 20-25 AT MARRIAGE).

DURATION OF MARRIAGE. In 1,000 MARRIAGES In Marriages previously
Childless, Probability of Birth
of Child
At end of each Period stated
in Col. 1 there are
Number
having 1st
Child during
period stated
in Col. 1
Childless. Not Childless. During Year. During that
and subse-
quent Years.
Under 1 year 733 267 267 0.27 0.95
1 and under 2 years 367 633 366 0.50 0.93
2 "    " 3   " 159 841 208 0.57 0.86
3 "    " 4   " 106 894 53 0.33 0.67
4 "    " 5   " 91 909 15 0.14 0.50
5 "    " 6   " 84 916 7 0.08 0.42
                 
6 "    " 7   " 74 926 10 0.12 0.37
7 "    " 8   " 67 933 7 0.09 0.28
8 "    " 9   " 64 936 3 0.04 0.21
9 "    " 10   " 60 940 4 0.06 0.17
10 to end of fertile period 53 947 7 0.12

From the same group of figures it may be gathered that out of one thousand marriages of women of ages between 20 and 25, a first child is born during the first year of marriage in 267 instances; during the second year in 366; during the third year in 208; and during the fourth year in 53; the figures for the subsequent years being much smaller and approximately falling to zero after the tenth year.

The same series of figures also enables calculations of the chance of marriages that are childless at the end of any specified number of years of marriage remaining childless to the end of the fertile period, or at any stated period. Thus of each thousand marriages of women between 20 and 25 years of age at marriage, 733 are childless at the end of the first year; 367 at the end of the second; and 53 at the end of the period of possible fertility of the women's lives. These figures show that the chance of marriages that are childless at the end of the first year remaining childless at the end of the second year is 367 ÷ (367 + 366), or 0.50, and the chance of remaining childless to the end of the period of possible fertility 53& #247; (53 + 680), or 0.07. The complements of these chances represent the chances of fertility; thus 0.50 is the complement of the chance of marriages that are childless at the end of the first year of marriage remaining childless during the second year, and represents the chance of the birth of a first child among such marriages during that year; and 0.93 is the complement of the chance of such marriages remaining childless to the end of the period of possible fertility, and represents the chance of the birth of a child at some subsequent date among marriages that are childless at the end of the first year. Figures showing these chances are collected in Table K, and it may there be seen that the chance, or prospect, of a first child rises from. 0.27 in the first year of marriage to 0.57 in the third, and thereafter decreases, falling below 0.20 in the fifth year, and below 0.10 in the tenth year. The chance of a marriage childless at the end of the first year remaining childless throughout the entire period of possible fertility of the woman's married life is 0.07, while the chance of at least one child is 0.93; and the longer the duration of the childless period, the greater is the chance of complete sterility, or, conversely, the less the chance of a child being born thereto. The chance of a marriage that is childless at the end of the second year remaining sterile is 0.14; of one childless at the end of the third year, 0.33; at the end of the fourth year, 0.50; at the end of the fifth year, 0.58; at the end of the eighth year, 0 79; and at the end of the tenth year, 0.88. On the other hand, the chance of the birth of a child at some subsequent date among marriages that are childless at the end of the first year is 0.93; among those childless at the end of the second year, 0.86; at the end of the third year, 0.67; at the end of the fourth year, 0.50; at the end of the seventh year, 0.28; and at the end of the tenth year, 0.12.

TABLE L.—PROBABILITY OF FERTILITY IN MARRIAGES WHICH FOR THREE
YEARS HAVE BEEN STERILE.

AGE OF WIFE AT
MARRIAGE.
IN 100 MARRIAGES Probability of First
Child after 3
Years' Duration.
Childless after 2
and under 3 Years'
Duration of
Marriage.
Childless at end of
Period of Possible
Fertility.
First Child born
after 3 Years'
Duration.
15 14.29 1.95 12.34 0.86
16 22.64 3.82 18.82 0.83
17 10.92 2.63 8.29 0.76
18 11.47 2.34 9.13 0.80
19 9.07 2.97 6.10 0.67
15-19 10.34 2.77 7.57 0.73
         
20 11.33 3.58 7.75 0.68
21 12.85 3.62 9.23 0.72
22 14.58 4.38 10.20 0.70
23 16.36 5.06 11.30 0.69
24 19.88 5.74 14.14 0.71
20-24 15.05 4.49 10.56 0.7
         
25 20.86 6.75 14.11 0.68
26 22.95 7.47 15.48 0.67
27 26.60 8.71 17.89 0.67
28 25.96 9.76 16.20 0.62
29 28.57 11.63 16.94 0.59
25-29 24.44 8.52 15.92 0.65
         
30 30.52 12.82 17.70 0.58
31 34.63 13.39 21.24 0.61
32 35.45 16.86 18.59 0.52
33 36.27 18.72 17.55 0.48
34 39.21 21.04 18.17 0.46
30-34 34.46 15.87 18.59 0.54

Among the childless marriages included in this group—i.e., where the wife was aged 20 to 25 at the time of marriage—if the duration of marriage is less than five years, the chance of there being a child at some subsequent time is greater than that of the marriage remaining childless, while, if the duration is five years, the chances are nearly level, and in longer durations are reversed, the chance of remaining childless being greater than that of having a child.

Table L has been constructed to show how the chance of a first child being born after three years of marriage is affected by the age of the wife at marriage. It may there be seen that the older the wife at the time of marriage the less is the chance of a first child being born after that period of marriage has elapsed. Among wives whose ages at marriage were between 15 and 19, this chance averages 0.73, and varies between 0.67 and 0.86; among those whose ages at marriage were between 20 and 24, it averages 0.70, and varies between 0.68 and 0.72; among those whose ages at marriage were between 25 and 29, it averages 0.65, and varies between 0.59 and 0.68; among those whose ages at marriage were between 30 and 34, it averages 0.54, and varies between 0.46 and 0.61; and among those whose ages at marriage were between-35 and 39 the chance averages 0.32, and varies between 0.28 and 0.39. In marriages which are childless for three years, and in which the age of the wife at the time of marriage did not exceed 32, the chance of the marriage remaining childless after the expiration of three years, is less than the chance of a child being born at some subsequent date, but where the age of the wife at the time of marriage exceeded 32, the chance of the marriage remaining childless is greater than that of the birth of a child.


The Chance of there being One, Two, or more Children ,—These probabilities have been calculated from the figures in Table XXXVI, which represent the number of families of specified sizes resulting from the marriage of women of specified ages at the time of marriage. Only marriages in which the fertile period has been completed are dealt with in that table, and are here considered. These probabilities are collected in Table M, where they are expressed as the chance of the specified number of children or more being born. Thus, from Table XXXV it is ascertained that in 19,422 marriages of women of 23 years of age at the time of marriage—which marriages continued to the end of the fertile period—the family amounts to three or more children in 16,998 instances, and the chance of at least that number of children being born is thus found to be 16,99819,422, or 0.88.

The chance of there being at least one child is the complement of the chance of marriage being childless, and decreases as the other chance increases. The chance of marriage being childless is small when the wife is young at the time of marriage, and becomes greater as the age of the wife at marriage increases, and, conversely, the chance of there being at least one child is large when the wife is young at the time of marriage, and becomes less as the age of the wife at marriage increases. If the wife is aged less than 20 at the time of marriage this chance is found to be more than 0.97; at age 20 it falls to 0.96; at age 25 to 0.93; at age 30 to 0.87; at age 35 to 0.75; and at age 40 to 0.43. An even chance of there being at least one child occurs at an age between 39 and 40. A chance of two to one against the birth of any child occurs when the age of the wife at marriage is about 41; one of three to one against when that age is 42; and one of four to one against when that age is 43.

The chances of there being two, three, four, or more children all vary in the same manner—the younger the wife the greater the chance of at least a specified number of children. Thus, the chance of there being four or more children is at a maximum (0.90) when the wife is 17 or 18 at the time of marriage; falls to 075 for age of wife 25; to 0.50 for age of wife 31; and to less than 0.10 for ages of 38 and over; and the chance of there being eight or more children falls from a maximum of 0.70 at age of wife at marriage 17, to below 0.50 at age 22, below 0.25 at age 26, and below 0.10 at age 30.

The chance of there being at least ten children is found to be 0.51 in marriages in which the wife was 17 at the time of marriage, to fall below 0.25 for age 22, and below 010 at age 25. The chance of there being thirteen children—the largest family dealt with in Table M—is small; at age 17 it is only 016, and falls below 010 at age 19.

Looking at the probabilities collected in Table M, it may be seen that, provided the marriage continues to the end of the fertile period of the woman's life, there_ is a level chance of a young woman marrying at 17 being the mother of at least 10 children, and that as the age of the wife at marriage advances the level chance applies to a smaller sized family. Thus, this chance in the case of a woman marrying at 20 is that she will be the mother of at least 9 children; for age of wife 25, at least 6 children; for age of wife 30, at least 4 children; for age of wife 35, at least 2 children; and for age of wife 40, at least one child.

TABLE M.—OBSERVED PROBABILITY, FOR EACH AGE OF WIFE, OF COMPLETE
FAMILY EXCEEDING A SPECIFIED NUMBER OF CHILDREN.

AGE OF
WIFE AT
MARRIAGE
* PROBABILITY OF HAVING THE UNDER-MENTIONED NUMBER OF CHILDREN,
OR MORE:—
1 2 3 4 5 6 7 8 9 10 11 12 13
15 0.981 0.961 0.925 0.875 0.813 0.738 0.682 0.616 0.529 0.440 0.343 0.276 0.192
16 0.962 0.940 0.918 0.889 0.859 0.809 0.746 0.675 0.578 0.484 0.363 0.258 0.169
17 0.974 0.954 0.928 0.900 0.865 0.822 0.768 0.696 0.617 0.513 0.387 0.272 0.157
18 0.977 0.956 0.931 0.899 0.858 0.803 0.741 0.666 0.567 0.464 0.343 0.220 0.124
19 0.970 0.949 0.923 0.890 0.846 0.789 0.715 0.632 0.531 0.410 0.284 0.179 0.097
                           
20 0.964 0.942 0.914 0.876 0.825 0.760 0.678 0.586 0.477 0.355 0.232 0.137 0.067
21 0.964 0.938 0.904 0.860 0.799 0.724 0.633 0.532 0.414 0.291 0.178 0.094 0.044
22 0.956 0.930 0.893 0.840 0.771 0.684 0.584 0.476 0.356 0.236 0.136 0.069 0.029
23 0.949 0.920 0.875 0.814 0.733 0.640 0.531 0.416 0.286 0.179 0.097 0.047 0.019
24 0.943 0.909 0.862 0.790 0.699 0.591 0.473 0.347 0.228 0.125 0.062 0.028 0.011
                           
25 0.933 0.893 0.835 0.753 0.649 0.538 0.416 0.292 0.178 0.095 0.045 0.020 0.008
26 0.925 0.881 0.816 0.721 0.608 0.484 0.357 0.233 0.132 0.067 0.029 0.013 0.006
27 0.913 0.863 0.790 0.686 0.564 0.439 0.303 0.186 0.099 0.047 0.019 0.008
28 0.902 0.843 0.761 0.649 0.519 0.380 0.247 0.138 0.067 0.029 0.013 0.006
29 0.884 0.818 0.724 0.600 0.458 0.323 0.197 0.108 0.052 0.024 0.011 0.004
                           
30 0.872 0.797 0.687 0.557 0.402 0.265 0.152 0.078 0.040 0.022 0.010 0.005
31 0.866 0.779 0.653 0.501 0.343 0.213 0.110 0.050 0.028 0.015 0.007
32 0.831 0.726 0.586 0.429 0.278 0.149 0.075 0.040 0.020 0.011 0.006
33 0.813 0.696 0.545 0.379 0.232 0.125 0.065 0.034 0.019 0.011 0.006
34 0.790 0.659 0.488 0.318 0.173 0.091 0.045 0.027 0.016 0.009 0.006
                           
35 0.753 0.595 0.415 0.254 0.127 0.063 0.033 0.020 0.013 0.007 0.005
36 0.705 0.526 0.333 0.175 0.087 0.044 0.025 0.015 0.010 0.007
37 0.660 0.450 0.256 0.121 0.058 0.033 0.022 0.016 0.011 0.006
38 0.586 0.372 0.190 0.097 0.054 0.033 0.022 0.015 0.009
39 0.545 0.314 0.145 0.070 0.042 0.025 0.016 0.010 0.006
                           
40 0.429 0.217 0.097 0.055 0.027 0.013 0.008 0.005
41 0.357 0.152 0.065 0.037 0.019 0.012 0.008 0.005
42 0.272 0.109 0.057 0.032 0.016 0.006
43 0.184 0.077 0.030 0.012 0.006
44 0.140 0.047 0.023 0.007

* By moving the decimal point two places to the right, the values in this and the following Table may be read as rates per cent. Thus, of wives aged 20 at marriage, 96.4 per cent, had 1 child or more, 94.2 per cent, had 2 children or more, and so on.

There is similarly found to be a two to one chance in favour of a woman marrying at 37 being the mother of at least one child; and there is the same chance of at least 2 children when the woman marries at 34; of at least 3 children when she marries at 31; of at least 4 children when she marries at 28; of at least 5 children when she marries at 25; of at least 6 children when she marries at 22; and of at least 7 children when she marries at 20.

Taking a chance of ten to one against as a limit beyond which an event may be described as very improbable, it is found that a family of 2 children is very improbable when a woman marries at over 42; of 3 children when that age is over 40; of 4 children when over 38; of 5 children when over 36; of 6 children when over 34; of 7 children when over 31; of 8 children when over 29; of 9 children when over 27; and of 10 children when over 25.


The Chance of a family being Limited to One, Two, or more Children .— These chances—which are collected in Table N— are the complements of the chances of there being at least one child more than any given number. Thus, the chance of a bride of 20 becoming the mother of at least 4 children, assuming that the marriage continues to the expiration of the child-hearing period of her life is 0.88 and the complement of this-figure, 0.12, is the chance of the family not exceeding 3 children. This being so, it follows that the chance of a family being limited to a specified number of children varies with the age of the wife at marriage, in the same manner as the chance of sterility.

TABLE N.—OBSERVED PROBABILITY FOR EACH AGE OF WIFE, OF FAMILY
BEING LIMITED TO A SPECIFIED NUMBER OF CHILDREN.

AGE OF
WIFE AT
MARRIAGE
* PROBABILITY OF HAVING NOT MORE THAN THE UNDER-MENTIONED NUMBER OF
CHILDREN:—
0 1 2 3 4 5 6 7 8 9 10 11 12
15 0.019 0.039 0.075 0.125 0.187 0.262 0.318 0.384 0.471 0.560 0.657 0.724 0.808
16 0.038 0.060 0.082 0.111 0.141 0.191 0.254 0.325 0.422 0.516 0.637 0.742 0.831
17 0.026 0.040 0.072 0.100 0.135 0.178 0.232 0.304 0.383 0.487 0.613 0.728 0.843
18 0.023 0.044 0.069 0.101 0.142 0.197 0.259 0.334 0.433 0.536 0.657 0.780 0.876
19 0.030 0.051 0.077 0.110 0.154 0.211 0.285 0.368 0.469 0.590 0.716 0.821 0.903
                           
20 0.036 0.058 0.086 0.124 0.175 0.240 0.322 0.414 0.523 0.645 0.768 0.863 0.933
21 0.036 0.062 0.096 0.140 0.201 0.276 0.367 0.468 0.586 0.709 0.822 0.906 0.956
22 0.044 0.070 0.107 0.160 0.229 0.316 0.416 0.524 0.644 0.764 0.864 0.931 0.971
23 0.051 0.080 0.125 0.186 0.267 0.360 0.469 0.584 0.714 0.821 0.903 0.953 0.981
24 0.057 0.091 0.138 0.210 0.301 0.409 0.527 0.653 0.772 0.875 0.938 0.972 0.989
                           
25 0.067 0.107 0.165 0.247 0.351 0.462 0.584 0.708 0.822 0.905 0.955 0.980 0.992
26 0.075 0.119 0.184 0.279 0.391 0.516 0.643 0.767 0.868 0.933 0.971 0.987 0.994
27 0.087 0.137 0.210 0.314 0.436 0.561 0.697 0.814 0.901 0.953 0.981 0.992
28 0.098 0.157 0.239 0.351 0.481 0.620 0.753 0.862 0.933 0.971 0.987 0.994
29 0.116 0.182 0.276 0.400 0.542 0.677 0.803 0.892 0.948 0.976 0.989 0.996
                           
30 0.128 0.203 0.313 0.443 0.598 0.735 0.848 0.922 0.960 0.978 0.990 0.995
31 0.134 0.221 0.347 0.499 0.657 0.787 0.890 0.950 0.972 0.985 0.993
32 0.169 0.274 0.414 0.571 0.722 0.851 0.925 0.960 0.980 0.989 0.994
33 0.187 0.304 0.455 0.621 0.768 0.875 0.935 0.966 0.981 0.989 0.994
34 0.210 0.341 0.512 0.682 0.827 0.909 0.955 0.973 0.984 0.991 0.994
                           
35 0.247 0.405 0.585 0.746 0.873 0.937 0.967 0.980 0.987 0.993 0.995
36 0.295 0.474 0.667 0.825 0.913 0.956 0.975 0.985 0.990 0.993
37 0.340 0.550 0.744 0.879 0.942 0.967 0.978 0.984 0.989 0.994
38 0.414 0.628 0.810 0.903 0.946 0.967 0.978 0.985 0.991
39 0.455 0.686 0.855 0.930 0.958 0.975 0.984 0.990 0.994
                           
40 0.571 0.783 0.903 0.945 0.973 0.987 0.992 0.995
41 0.643 0.848 0.935 0.963 0.981 0.988 0.992 0.995
42 0.728 0.891 0.943 0.968 0.984 0.994
43 0.816 0.923 0.970 0.988 0.994
44 0.860 0.953 0.977 0.993

There is found to be a level chance of 9 children being the limit when the wife at marriage is aged 17; of 8 children being the limit when that age is rather less than 20; of 7 children when that age is rather less than 22; of 6 children when that age is between 23 and 24; of 5 children when that age is between 25 and 26; of 4 children when that age is between 28 and 29; of 3 children when that age is about 31; of 2 children when that age is rather less than 34; and of one child when that age is between 36 and 37.

Similarly it is observed that the chance of the family exceeding 10 children is never more than one third, or two to one against, no matter how young the wife at marriage. The same chance, one-third, or two to one against, is found that the family will, not exceed 9 children when the wife is aged 20 at marriage; that it will not exceed 8 children when she is aged 22, not exceed 7 children when she is aged 24, not exceed 6 children when she is aged 26, not exceed 5 children when she is aged 29, not exceed 4 children when she is aged 31, not exceed 3 children when she is aged 34, not exceed 2 children when she is aged 36, and not exceed 1 child when she is aged 38.


The Average Number of Children in Family .—Tables XXXII and XXXV (3) contain statements of the average number of children found to have resulted from the marriages recorded in the census schedules, the former dealing with all marriages in which the wife at the time of marriage was of child-bearing age, and the latter with those marriages only in which the wife, being of child-bearing age at the time of marriage, had attained the age of 45—the arbitrary limit of child-bearing here adopted—before the taking of the census. In Table XXXII the averages are stated for every combination of age of wife and husband at marriage, and are given separately for each year of duration of marriage. The averages given in Table XXXV (3) represent the number of children, or complete family, resulting from marriages of spouses of specified ages.

The marriages included in the three parts of Table XXXV—i.e., marriages in which the wife had reached the end of her fertile period—number 239,943, and as the children born to them number 1,316,995, the average number of children to each marriage is 5.49. This average represents, as has been said above, the mean or average size of the total or complete family resulting from all marriages in which the wife was of child-bearing age at the time of marriage, and had reached the age of 45 during the continuance of the marriage.

The same table shows how this average is affected by the age of the wife at marriage. The total or complete family resulting from marriages in which the wife at the time of marriage was aged 17 is found to be 9.02, and this average is found to be a diminishing quantity as the age of the wife at marriage increases. It falls below 9 when the age of the wife at marriage was 19; below 8 when the age was 20; below 7 when the age was 22; below 6 when the age was 25; below 5 when the age was 27; below 4 when the age was 30; below 3 when the age was 33; below 2 when the age was 36; and below 1 when the age was 40.

TABLE O.—INFLUENCE OF ONE YEAR'S DELAY OF MARRIAGE
ON AVERAGE NUMBER OF CHILDREN.

MARRIAGE
DELAYED FROM
AGE:—
Decrease in Average Family
dependent on 1 year's delay of
Marriage on part of:—
MARRIAGE
DELAYED FROM
AGE:—
Decrease in Average Family
dependent on 1 year's delay of
Marriage on part of:—
Husbands Wives Husbands Wives
Crude
Differences.
Crude
Differences.
Graduated
Differences.
Crude
Differences.
Crude
Differences.
Graduated
Differences.
19 to 20 0.21 0.44 0.45 32 to 33 0.18 0.23 0.32
20  "  21 0.35 0.45 0.43 33  "  34 0.24 0.30 0.31
21  "  22 0.25 0.43 0.42 34  "  35 0.25 0.34 0.30
22  "  23 0.43 0.46 0.42 35  "  36 0.18 0.36 0.29
23  "  24 0.38 0.45 0.41 36  "  37 0.22 0.29 0.28
24  "  25 0.32 0.41 0.39 37  "  38 0.32 0.26 0.27
25  "  26 0.29 0.38 0.39 38  "  39 0.11 0.20 0.26
26  "  27 0.27 0.36 0.37 39  "  40 0.10 0.32 0.25
27  "  28 0.30 0.36 0.37 40  "  41 0.21 0.20 0.25
28  "  29 0.20 0.35 0.36 41  "  42 0.23 0.16 0.23
29  "  30 0.34 0.32 0.35 42  "  43 0.06 0.19 0.22
30  "  31 0.18 0.31 0.33 43  "  44 0.17 0.09 0.21
31  "  32 0.21 0.42 0.33        

The average number of children in these completed families resulting from the marriage of men of specified ages is found to vary in a similar manner, a result no doubt largely attributable to the well-known fact that the ages of husbands and wives are highly correlated. The maximum average complete family for any age of husband at marriage is found to be 8.25, and to occur when the age of the husband at marriage was 18. This average falls below 8 when the age rises to 20; below 7 when the age rises to 23; below 6 when the age rises to 26; below 5 when the age rises to 30; below 4 when the age rises to 34; below 3 when the age rises to 38; below 2 when the age rises to 46; and below 1 when the age rises to 54.

The effect of postponement of marriage for one year may be estimated by comparing the average complete family of any age of the wife or husband at the time of marriage with that of one year younger. The figures dealing with this calculation are collected in Table 0. It may there be seen that the effect of each year's delay of marriage in the case of both men and women is a diminishing quantity as the age advances. In the case of women aged 20 to 24 the effect of one year's delay averages 0.45 of a child in the complete family, or, in other words, 45 fewer children are born to each 100 marriages; and, in the case of men, 0.32 of a child per marriage, or 32 children to each 100 marriages. When the number of the average total family is calculated in connection with the age of the woman at marriage, this figure falls to 0.37 for ages 25 to 29; to 0.32 for ages 30 to 34; to 0.29 for ages 35 to 39; and to 0.19 for ages 40 to 44. When the average total families are calculated in relation to the age of the men at marriage this figure falls to 0.28 for ages 25 to 29; to 0.23 for ages 30 to 34; to 0.22 for ages 35 to 39; to 0.15 for ages 40 to 44; to 0.12 for ages 45 to 49; to 0.09 for ages 50 to 54; and to 0.04 for ages 55 to 59.

Marriage Fertility since 1861

The observed differences, as shown in Table O, are too rough to be satisfactory indications of the true effects of the postponement of marriage at each age of the marrying woman, and for this purpose a series of graduated figures have been prepared. These graduated figures, which are also shown in Table O have been prepared by fitting a parabolic regression curve to the observed means. As was found when comparing the quinquennial average effect of a year's delay of marriage, these graduated figures show the effect of postponement to be a diminishing quantity as the wife's age advances. If a woman's marriage be delayed from age 19 to age 20 the result is a reduction of 0.45 in the most probable number of children, and this figure falls below 0.40 when the delay is from age 24 to age 25; below 0.35 when the delay is from age 30 to age 31; and below 0.30 when the delay is from age 35 to age 36.

When the average number of children in the family is calculated in connection with the years of duration of marriage, and independently of the age of the wives and husbands at the time of marriage, it is found, as might be expected, that the number increases as the duration increases. Thus, an average of one child is found in the third year of the duration of marriage; an average of two children in the sixth year of marriage; one of three in the tenth year of marriage; one of four in the fourteenth year of marriage; one of five in the twentieth year of marriage; and one of six in the twenty- eighth year of marriage. These periods vary with the ages of the wives at marriage. When the wives are aged less than 25 an average family of one child is found in the third year of marriage, but when aged from 26 to 34 this is not found until the fourth year, and when aged 35 or 36 until the fifth year, and when aged 37 or 38 until the seventh year. An average family of two children is found in the fifth year when the women at marriage were 16 to 21; in the sixth year when they were aged 22 to 24; in the seventh year when they were aged 25 to 29; in the eighth year when they were aged 30 to 32; and not until the thirteenth year when they were aged 35. An average family of four children is found in the tenth year when the wives were aged 16 at the time of marriage; in the eleventh year when they were aged 20; in the twelfth year when they were aged 21; in the thirteenth year when they were aged 23; and in the fourteenth year when they were aged 24.


Decline of Fertility of Marriage during Recent Years .—To study this subject, all marriages in which the fertile period of the woman's life was completed during the continuance of marriage, and consequently in which the families are complete, have been tabulated in relation to the year of marriage and the age of the wife at marriage, and this tabulation will be found in Tables XLVI (1), (2), and (3). Some of the figures of this tabulation have been produced in graphic form, and will be seen in the accompanying chart.

A scrutiny of these tables and a glance at the chart afford ample evidence of a continuous drop in the fertility of marriage. In Table XLVI (3) it may be seen that marriages of women aged twenty, and taking place in 1864 or previous years, resulted in complete families averaging 8.48 children, and that this average has steadily declined. It- is 8.42 for marriages of the years 1865 to 1869; 8.04 for those of the years 1870 to 1874; 7.88 for those of the years 1875 to 1879; 7.59 for the years 1880 to 1884; and 7.39 for the years 1885 and 1886—no corresponding figures being available for marriages of subsequent years because the completion of the fertile period had not been reached at the date of the census. Similar quinquennial averages for each alternate year of the wife's age from 21 to 39 are collected in Table P, those of the other alternate years from age 20 to 30 being given in the chart. These figures show the uniformity of the drop. The total fertility of marriage for age of wife 21 has fallen from 818 children per hundred marriages to 700; for age of wife 23, from 740 to 597; for age 25, from 673 to 503; for age 27, from 580 to 437; for age 29, from 574 to 353; for age 31, from 483 to 304; and generally similar though less steady declines are found in the older ages. The oscillations iii the decline of the average at the older ages may he attributable to the smallness of the numbers dealt with, marriages at these ages being much less numerous than at the younger ages. For ages 20 to 24 of wife at marriage, the decline averages 128 children per hundred marriages; for ages 25 to 29, 168 children; for ages 30 to 34, 156 children; and for ages 35 to 39, 164 children.

Although this test demonstrates that the actual fertility of marriage is now less than formerly—that a woman marrying at any specified age will probably be the mother of fewer children than was the case formerly—it must not be assumed that this is the only, or even the most important, factor accountable for the well-known drop of the national birth-rate during recent years. Other factors may be at work, but no attempt is here made to discriminate or to estimate how much of the decline of the birth-rate is due to decreased fertility, and how much to other factors. It is almost needless to state that any dissertation regarding the causation of the decreased fertility of marriage, a subject on which census information throws no real light, would be quite out of place in this Report.

TABLE P.—NUMBER OF CHILDREN PER 100 MARRIAGES, BY DATE OF MARRIAGES
AND AGES OF WIVES.

CALENDAR
YEARS OF
MARRIAGE.
AGES OF WIVES AT MARRIAGE.
21 23 25 27 29 31 33 35 37 39
1861 and before 818 740 673 580 574 483 400 382 388 175
1865-1869 800 738 651 565 500 439 322 310 200 217
1870-1874 782 704 624 5823 498 433 338 287 193 216
1875-1879 738 659 594 539 464 429 368 287 211 144
1880-1884 710 639 568 505 437 371 326 277 202 162
1885-1889 700 597 523 460 419 359 315 252 192 148
1890-1894 503 437 375 330 277 230 159 127
1895-1899 353 304 251 198 142 112
1899-1904 174 146 97
1905 84

Occupational Fertilities .—This term has been coined, and is used, to indicate the comparative fertility of marriage in relationship to the occupations of the husbands.

Occupational fertilities, as ascertained by the returns of the present census, are dealt with in Tables XLVII and XLVIII. The figures in these tables show not only the number of families included in each occupational group, the mean number of children in each group, and the number of families of specified sizes in each, but also the standard variations of the means, and the probable errors of the differences between the occupational means and the general mean of all families included in this study. In the construction of Table XLVIII the occupational fertilities are not taken as significantly greater or less than the general mean unless the differences between them are at least three times as large as the probable errors of those differences.

The simplest method of studying the fertility in occupational groups would be to estimate the average number of children in all families of which the husbands were returned as having a particular occupation, but such a method would not be satisfactory, because the resulting figures might not be fairly comparable, and might be too much influenced by factors other than those peculiar to the occupation. For instance, were an average family of five children found by this method in one occupational group, and one of four in another group, the difference could not reasonably be ascribed to occupational influence; it might be due to the wives in the one occupational group being younger at the time of marriage than in the other, or it might be due to the marriages of the one group being of longer duration than those of the other. To obviate such fallacy—the fallacy of comparing dissimilar quantities—only a selection of all marriages has been included in this study, an endeavour being made to get groups which, within reasonable limits, are fairly comparable.

In selecting from, the census records those marriages which can legitimately be used for this purpose, attention was paid to the two principal causes of variation of the number of children in a family, namely, the duration of marriage and the age of the wife at marriage. It was found impracticable to carry out this scheme of selection to its logical limit, i.e., the use of those marriages only in which all the wives were of one age at the time of marriage, and which were all of the same duration, or all of which had continued beyond the fertile period—for such excessive or refined selection would have resulted in reducing the number of marriages in the occupational groups so far that they would have been too small to establish reliable averages for the majority of the occupations; and a freer, if not so perfect a selection, has been made. Accordingly the limits of selection for inclusion in this study were (l) that the wife should be over 22 but under 27 years of age at the time of marriage, and (2) that the marriage should have continued for at least 15 years. No doubt five different ages of wife at marriage may be a rather wide limit for the purpose, but this was necessary in order to secure even moderate figures for many of the occupational groups. The same may be said of the inclusion of some marriages in which the wives had not attained the completion of their fertile periods at the date of the census. The selection is not perfect, but may be accepted as the best in the circumstances, and as sufficient for our purpose. While it limits the probable error arising from paucity of observations, it also diminishes the chance of fallacy arising from comparison of dissimilar quantities, and may therefore be accepted as capable of giving results which are reasonably reliable.

Table XLVII contains a statement of the number of these selected marriages in each occupational group, of the number of these having specified numbers of children, and of the mean or average number of children per marriage, the occupational groups being arranged in order of magnitude of the mean number of children. Table XLVIII supplies a more accurate comparison between the mean number of children in the occupational groups, and the mean found in all the marriages included in this study, the method of making the comparison being indicated by the formula given at the head of the table. In it the occupational groups are arranged in three classes; (1) those in which the mean or average number of children per marriage is significantly greater than that of the marriages of all occupations taken collectively; (2) those in which that mean is not significantly either greater or less than that general mean; and (3) those in which it is significantly less, the test of significance being whether the observed difference between the mean of a group and the general mean is at least three times as large as the probable error of that difference. In the text which follows no reference will be made to the actual differences of the means, but merely to this classification, occupations included in Class 1 being accepted as of high fertility, and those in Class 3 as of low fertility. Should further and finer classification be desired, the figures given in these tables will enable it to be made,

Professional and Allied Occupations. —These without exception are found to be occupations of low fertility. Among them may be mentioned the clerical, legal, medical, and teaching professions, officers of the army and navy, artists, men with literary and scientific pursuits, land surveyors, civil engineers, dentists, veterinary surgeons, and pharmaceutical and dispensing chemists. Of the twelve occupations named at the end of Table XLVIII, where the arrangement is in order of the crude means, eleven are occupations more or less professional in character, while the twelfth, consisting of civil service, law, and other clerks, is closely akin thereto.

Labouring Occupations. —These are in marked contrast to the foregoing, for the majority are found to be of high fertility. Coal heavers, navvies, builders' labourers, dock labourers, and general labourers are all found to be in Class I. This indicates that the average size of family is with them significantly greater than the general average.

Agricultural and Fishing Occupations. —These may generally be described as of high fertility, for the majority of them are found to be in Class I, and to have an average size of family significantly greater than the general mean. Of all occupations, that of crofter is found to have the highest fertility, heading the list given in Table XLVII. Fishermen-crofters, agricultural labourers, fishermen, shepherds, farmers and graziers, farm grieves and foremen, " others with agricultural occupations,. are all in Class I, while cattle-dealers, foresters, nurserymen, and dairymen are found to be in Class II. None of those occupations are in Class III. and thus none are found to have fertilities significantly less than the general average.

Workers in Mines and Quarries. —These are found to be of high fertility. The families of coal and shale miners, and stone and slate miners, dressers, and quarriers are found to average a number which is significantly greater than the general mean, and the same is found in the case of owners, agents, and managers of coal and shale mines. Owners, agents and managers of stone and slate quarries are found to have an average fertility hot significantly different from the general mean:

Transport Workers.— Tables XLVII and XLVIII include three groups of men with these occupations—carters and others concerned with transport by road, seamen and others concerned with transport by water, and men with occupations on railways. The first of these groups, carters and others with allied occupations, is found to be of high fertility; the third, railway servants, is found to be of low fertility; while the second, men of the merchant service, is found to be of a fertility not significantly different from the general mean.

Commercial and Clerking Occupations. —These are found to be of low fertility, insurance agents, commercial occupations, and clerks (civil service, law, commercial, and banks and insurance), all being found in Class III. No similar occupations are found in either Class I or Class II.

Trades. —A scrutiny of Table XLVIII shows that tradesmen are found in all three classes, some being of high fertility, some of low, and some of fertility not significantly different from the general mean. Among those of high fertility are glaziers, plasterers, masons and builders, ironfounders, blacksmiths, and engine-drivers and stokers (not railway or marine). Among those of low fertility are tailors, carpenters, painters, engineers, patternmakers, plumbers, coppersmiths, hairdressers, electricians, instrument makers, and printers. Among those with a fertility not significantly different from the mean are chimney sweeps, tanners and curriers, boilermakers, shipwrights, type cutters, coachbuilders, brassfinishers, cycle and motor car makers, brassfounders, saddlers, cutlers, millwrights, and bleachers and dyers.

Makers and Dealers. —This group of occupations includes the shopkeeping classes, and along with them some occupations, such as bootmakers and bakers, which may or may not belong to the shopkeeping class, but which, from the description given, cannot be separated from them. This group is generally found to be one of low fertility, the majority of the occupations in it being found in Class III, with fertilities significantly less than the general mean. Among those in Class III are butchers and fish dealers, furniture dealers, hardware dealers, grocers, watchmakers, booksellers, drapers, tobacconists, and greengrocers. Occupations of this group with fertilities not significantly different from the general mean include bootmakers, bread and biscuit makers, and general shopkeepers. No occupation in this group is found to have a high fertility.

Manufacturing Occupations. —These include a mixed and ill-defined group of occupations ranging from stalled tradesmen to labourers, and these are found to be in all three classes. Among those in Class I (high fertility), are workers in iron shipbuilding, workers in iron and steel manufacture, and manufacturing chemists; and among those in Class III (low fertility), are workers in flax and linen manufacture, engine arid machine makers, workers in stationery manufacture, in wool and worsted manufacture, and in indiarubber manufacture. The list of those with fertility not significantly different from the general mean is fairly long, and includes workers in brick and pottery manufacture, in floorcloth manufacture, in silk manufacture, in sugar manufacture, in paper manufacture, in hemp and jute manufacture, and in cotton manufacture.

Domestic and Allied Services. —Occupations of this nature are found to be of low fertility, and are all included in Class III, having average fertilities significantly less than the general mean. These occupations include both indoor and outdoor domestic servants, waiters, barmen, innkeepers, and publicans, and keepers of boarding, lodging, and eating houses.

Public Services. —Occupations connected with these services, with the exception of scavengers, are found to be in Class II or Class III. Scavengers alone, of the occupations in the group, are found to have an average fertility significantly greater than the general mean. Those in Class III, having fertilities significantly less than the general mean, include police, postmen, municipal and parish officers, soldiers, and men of the Royal Navy. Occupations connected with the service of gasworks and waterworks, of baths and washhouses, of harbours and docks, of drainage and sanitation, and of churches and cemeteries, are found to have fertilities not significantly different from the general mean.


Child Mortality and Occupation of Mothers .—A scrutiny of the fertility figures of the census, and a separation of the children of the married women into surviving and deceased children, throws some light on the relative child moralities in families in which the mothers are not occupied, as distinguished from those in which the mothers are occupied.

All returns were not included in this study, because the fact that there has been a considerable loss by death among the children of a marriage does not imply that they have died young, or at a period when the guardianship of the mother was in any way responsible for their health. Many of the marriages reported in the census are of long duration, and as the families are frequently grown up, and may even have reached old age, the deaths occurring in them are not of necessity indicative of child mortality. Consequently, for the study of child mortality, an arbitrary limit of fifteen years' duration has been taken, marriages in which the duration is less than that being included, and those in which the duration is of that amount or more being excluded.

In all 5,458 marriages were collected from the census returns in which the husbands and the wives were living together, and in which the wives were described as having remunerative occupation, and which had durations of less than fifteen years; and for purposes of comparison a sample of 5,458 marriages with unoccupied mothers was carefully selected. The mode of selection of the latter was as follows :—The tabulation cards of all marriages had been arranged for other purposes by duration of marriage, and by ages of husband and of wife; these were examined for the cards of those mothers who were returned as " occupied," and as each one of these was found and separated the card next to it in the bundle was picked out and laid aside. The cards so collected formed the sample. Having obtained these strictly comparable samples, the numbers of living and deceased children recorded in each were tabulated and compared. The resulting figures are given in Table Q.

TABLE Q.—MORTALITY IN FAMILIES OF WORKING MOTHERS.

Note.— Only marriages of less than fifteen years' duration are included in this Table. See explanatory reference in text.

REFER-
ENCE
Nos.*
OCCUPATIONS. MARRI-
AGES.
CHILDREN. PERCENTAGE.
Total. Living. Deceased. Living. Deceased.
  Mothers not working 5458 13970 11908 2062 85.2 14.8
               
  Mothers working 5458 12881 9790 3091 76 24
               
42,43 Domestic Servants 102 128 92 36 71.9 28.1
52 Charwomen 193 468 333 135 71.2 28.8
53 Laundry Workers 138 298 221 77 74.2 25.8
103-105 Farm Servants 152 293 245 48 83.6 16.4
283-287 Cotton Manufacture 149 364 254 110 69.8 30.2
288-292 Wool and Worsted Manfactr. 271 748 619 129 82.8 17.2
296 Flax, Linen Manufacture 190 383 318 65 83.0 17.0
297 Hemp, Jute Manufacture 1,554 4,618 3,268 1,350 70.8 29.2
317 Tailors 51 90 67 23 74.4 25.6
319 Dressmakers 156 274 232 42 87.4 15.3
321 Seamstresses 55 121 99 22 81.8 18.2
390 Hawkers 205 560 405 155 72.3 27.7
Others 2,242 4,536 3,637 899 80.2 19.8

* See pp. 101 and 102.

The total number of children found to have been born to the 5,458 marriages in which the mothers were at census time without remunerative occupation was 13,970, and the number of children born to the 5,458 marriages in which the mothers had at that time remunerative occupation was 12,881, the average number of the family among the former being 2.56, and among the latter, 2.36.

Of the 13,970 children born to the marriages in which the mothers were unoccupied, 11,908, or 85.2 per cent., were ascertained to be living at the time of the census, and 2,062, or 14.8 per cent., to be then deceased. Of the 12,881 children born to the marriages in which the wives were returned as having remunerative occupation, 9,790, or 76.0 per cent., were alive at census date, and 3,091, or 24.0 per cent., were then deceased. This comparison shows a distinct difference, and seems to support the inference that the fact of the, mother having remunerative occupation decreases the chance of survival of the children, and increases the chance of the death of the children at the younger age period. The chance of survival through the younger age period when the mother is unoccupied is 0.85, or fully 5½ to 1, but when the mother is occupied this chance falls to 0.76, or 3 to 1.

The tabulation further shows that the chance of the early death of children in all marriages with occupied mothers is 0.24, but this ratio is not the same for all occupations. It is found to vary from 0.30 when the occupation of the mother is in cotton manufacture, 0.29 when it is in hemp and jute manufacture, 0.29 when it is charing, 0.28 when it is domestic service, and 0.28 when it is hawking, to 0.15 when it is dressmaking, 0.16 when it is farm service, and 0.17 when it is in either wool and worsted, or flax and linen manufacture. When the wife's occupation is that of a tailor the chance is 0.26, when that of a laundry worker, 0.26, and when that of a seamstress, 0.18. Some of these ratios are based on figures too small to give altogether satisfactory results, but the general result—the fact of a higher mortality among children of working mothers than among those of non-working mothers—may be accepted as well established.


A Fertility Table .—Among those advocating the inclusion in the census of a study of the fertility of marriage there were some who claimed that by the use of the ascertained figures tables might be constructed to show the probable fertilility of marriage, in the manner that a life table shows the probable duration of life; and to meet these expressed views an endeavour has been made to construct such a table. The difficulties, however, have been unexpectedly great.

Tables XXXII and XXXV (3) may, in a way, be accepted as fertility tables, for these tables show the average number of children found by observation to result from the marriages of men and women of specified ages after the marriages have continued for stated periods, or continued until the wives have attained the age of 45. In short, these tables contain the essential information wanted in a fertility table. But these tables are not satisfactory for use as a general fertility table, because the figures in them, being based on crude observations, are inevitably rough and subject to oscillations, the roughness and oscillation being due to the nature of random sampling and to paucity of data for certain combinations of the independent variables.

For the purposes of this study, partly to ease the work and partly to get two independent series of observations, the recorded fertilities were divided into two groups, the one including all marriages in which the wife had attained age 45 before the census, and therefore in which the fertilities were complete, and the other including all marriages in which the wife had not attained that age and in which the fertilities were quantities subject to increase. Marriages in the first group, those of completed fertility, numbered 239,943; and those in the second group, those of continuing fertility, 440,741. The fertilities in the second group are influenced by all three independent variables, the age of the wife at marriage., the age of the husband at marriage, and the duration of the marriage; but those in the first group are influenced by only two of the variables, the influence of duration being eliminated.

The only published method of determining the most probable value of one character from two or more other characters, known to he correlated to each other and to be first character, is that of multiple linear regression. But the essential condition attached to the application of this method is that the regressions dealt with must be linear. An examination of the data, however, showed that this condition was not fulfilled.

When it became apparent that the regressions were not linear, Dr Tocher, Lecturer on Statistics, University of Aberdeen, stated that while non-linear multiple regression formulas had not yet been published, suitable formulae could probably be found to fit the data. On his recommendation the data were submitted to Mr George Rae, B.Sc., Aberdeen University. This course having been sanctioned by the Treasury, the work of construction of tables was proceeded with, and the results of Mr Rae's work are embodied in a Memorandum prepared by him and published as an Appendix to this Report. (See Appendix II, and also Tables XXXVIII and XLV).

Mr Rae, in his Memorandum, fully explains the method of construction of his Tables, and has indicated where there might be divergences and a possible explanation of them.

It might be of interest to give here the multiple linear regression formulae and the formulę used by Mr Rae in the construction of his Tables. In them C = the average number of children per marriage, W = the age of the wife at the time of marriage, H = the age of the husband at the time of marriage, and D = the years of duration of marriage. The first equation in each case applies to the linear regression, and the lower to the non-linear regression.

Marriages of Completed Fertility.

C = 14.889 - 0.332 W - 0.028 H
C = 20.149493 - 0.555812 W - 0.173804 H - 0.002846 W2 - 0.003494 H2 + 0.012675 WH

Marriages of Continuing Fertility.

C = 3.299 - 0.076 W - 0.024 H + 0.267 D
C = 6.571791 - 0.297399 W - 0.087090 H + 0.314894 D + 0.004307 W2 + 0.000955 H2 - 0.002118 D2

The complete list of the ordinary and partial correlation coefficients and the ordinary and multiple linear equations is printed in Appendix I, and, though strictly accurate only when the regressions are linear, the values may still be useful for the purpose of drawing general conclusions.

If we consider, for instance, the following equation,

(1) C = 14.89 - 0.33 W - 0.028 H,

we can see roughly the effects of the age of husband and of wife at marriage. As is to be expected, the age of the wife at marriage exercises a preponderating effect on the size of the family. A difference of three years in the age of wife at marriage., for a constant age of husband at marriage, means on the average about one child less at the end of the fertile period, while it would take a difference of about forty years in the age of husband at marriage, for a constant age of wife, to bring about the same result. On account of the small effect of the age of husband at marriage on the mean size of family at the end of the fertile period, this mean size of family could, in most cases, be got approximately either from equation (1) or from the ordinary linear regression equation between C and W, namely

(2) C = 14.72 - 0.36 W

For example, if W = 25 and H = 30, equation (1) gives G = 14.89 - 0.33x25 - 0.028x30 = 5.80; while equation (2) gives C = 1472 - 0.36 x 25 = 5.72, using W = 25 alone. The result from Mr Rae's Table is 5.62.

Again, from equation (1) we have seen that it would take a difference of about three years in the age of wife at marriage to bring about, on an average, a reduction of one child at the end of the fertility period, while the age of husband at marriage has a much smaller effect than that of the wife on the size of the family. This latter statement apparently contradicts the result given in the linear regression equation—

(3) C = 11.86 - 0.23 H.

Owing, however, to the high correlation (.709) between W and H, the result is not contradictory, and is really clue to the influence of the age of the wife at marriage, because the correlation, .709, shows that there is a strong bias in men and women towards securing mates of the same age as themselves.

On examining the linear multiple regression equations for the group of marriages, where the fertilities are continuing, we see the predominating effect of the duration of marriage.

Further, from the following equation,

(4) C = 3.299 - 0.076 W - 0.024 H + 0.267 D,

it is clear that the influence of the wife at marriage is greater than that of the husband. It is also evident that, for constant ages of parents at marriage, there is added on to the size of the family on an average one child every three or four years. As the combined influence of the ages at marriage of the parents is considerably less than the duration of marriage, we get a similar result by taking the linear regression equation between the mean size of family and the duration of marriage. Finally, from equation (4) we note that, for a constant duration of marriage and a constant age of husband at marriage, it takes a difference of about 13 years in the age of the wife at marriage, in order to reduce the average size of the family by one child; and a difference of about forty years in the age of husband at marriage for a constant age of wife at marriage and a constant duration of marriage to effect the same reduction. Each of these numbers is, from the nature of the assumption made, only roughly approximate. They are probably both rather large. It must be remembered that the results here discussed are results based on the assumption of linearity of regression—an assumption which is shown not to hold for the characters under discussion.

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