Some Unconsidered Factors Affecting the Birth-Rate

Some Unconsidered Factors Affecting the Birth-RateAuthor(s): Reginald DudfieldSource: Journal of the Royal Statistical Society, Vol. 71, No. 1 (Mar., 1908), pp. 1-64Published by: Wiley for the Royal Statistical SocietyStable URL: http://www.jstor.org/stable/2339243 .

Accessed: 25/06/2014 03:31

Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp

.JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range ofcontent in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact [email protected].

.

Wiley and Royal Statistical Society are collaborating with JSTOR to digitize, preserve and extend access toJournal of the Royal Statistical Society.

http://www.jstor.org

This content downloaded from 195.78.108.60 on Wed, 25 Jun 2014 03:31:53 AMAll use subject to JSTOR Terms and Conditions

http://www.jstor.org/action/showPublisher?publisherCode=black

http://www.jstor.org/action/showPublisher?publisherCode=rss

http://www.jstor.org/stable/2339243?origin=JSTOR-pdf

http://www.jstor.org/page/info/about/policies/terms.jsp


Vol. LXXI.] [Part I.

JOURNAL

OF THE ROYAL STATISTICAL SOCIETY.

MARCH, 1908.

Some UNCONSIDERED FACTORS affecting the BIRTH-RATE.

By REGINALD DUDFIELD, M.A., M.B.

[Read before the Royal Statistical Society, 21st January, 1908. The Right Hon. Sir CHARLES W. DILKE, President, in the Chair.]

IN December, 1905, two papers dealing with the decline in the birth- rate were read before this Society. In one, that by Drs. Newsholme and Stevenson,' standard rates were calculated and corrected rates derived therefrom for a series of years were compared. In the other, that by Mr. Udny Yule,2 the effect on the birth-rate of the postponement of marriage was discussed. So far as I am aware, no one has estimated the absolute values of the potential fertilities resulting from the alterations in the age-constitution of the married population or of the decrease in the number of legitimate births resulting from " moral restraint." It is with this object in view that I have examined the changes which have taken place in

(i.) the ages of married women; (ii.) the combined ages of married couples returned as living

together; and (iii.) the excess of married women.*

The examination was limited to the fecund ages. In selecting the standard fertility rates, I shall be obliged to

criticise the data used by Drs. Newsholme and Stevenson. Such criticism is intended, however, only to demonstrate the unsuitability of the Swedish rates for my present purpose, for which I deemed maximum fertility-rates to be necessary. Those authors have shown in their Paper that their results are not affected by changes in the standard rates.

* The meaning attached to this phrase will be apparent on perusal of the section headed " Surplus Wives."

VOL. LXXI. PART I. B



2 DUDFIELD-Some Unconsidered Factors [Mar.

I have to admit that I have not dealt exhaustively with the subject I have taken in hand, there being, I feel sure, possibilities of further research of considerable interest. Some of them I hope to deal with in the future, bu-t the remainder demand more mathematical knowledge and statistical experience than I possess.

Much labour has been saved by the adoption of " index numbers," the figures for a given year being taken as the standard (= ioo), and those of subsequent years expressed as percentages thereof. Moreover, that method, I think, shows more clearly, not only the direction, but also the extent of the changes to be discussed. Owing to the uncertainties attaching to all estimates of population, especially in sex-age groups, it appeared to be almost useless to calculate the numbers of births on age-group fertilities for years other than those in which a census was taken. The six census years 1851-1901 have been selected, and data for England and Wales, London, Scotland and Ireland have been taken out.

By reason of changes in the tabulation of the census results, all the required data are not available for the years mentioned. Thus in the reports for England and Wales the ages of married women are given in quinquennial groups up to 1871, and thereafter in decennial. In the Scotch returns quinquennial groups have been used on every occasion. In the Irish, decennial groups were used in 1851 and 1901, quinquennial in the intervening years. The ages of husbands and wives in combination have been extracted in a most irregular mainer, the table being included in the reports for 1851, 1861, 1871, and 1901 as regards England and Wales, in 1851, 1861, and 1871 as regards Scotland, and in 1861, 1871, 1881, and 1891 as regards Ireland. In all these tables quinquennial age-groups have been used.

Swedish Fecundity Rates. In addition to the data afforded by the census returns, informa-

tion was required as to the fertility of women. Drs. Newsholme and Stevenson employed certain Swedish rates. From the first I had doubts as to the suitability of those figures for studying the question of fertility, and the searches I have made to trace the origin of the rates have confirmed me in that view. Those authors quoted a paper by McLean3 as the source of their information, but an examination of that paper gave no clue to the publication from which the rates were obtained. Finally, by the courtesy of Herr Widen, Chief of the Swedish Statistical Office, I obtained the original reports4 from which the rates were doubtless obtained. In his covering letter, Herr Widen remarks

"Les chiffres que vous avez cit6s d'apres M. McLean sonts



1908.] affecting the Birth-Rate. 3

"corrects, mais il faut observer qu'ils portent sur la proportion "d'accouchements par I,ooo femmes mariees de chaque age et non, "comme on pourrait, peut-etre, le croire, sur la proportion des "enfants n6s." *

The rates given by McLean were, therefore, fecundity and not fertility rates. The distinction between fecundity and fertility is one of quality versus quantity. Fecundity is measured by the frequiency of pregnancy, fertility by the absolute number of the progeny. The present case is an illustration of the confusion between the two terms which occurs rather frequently.t

It appears from the annual report5 for 1891 that the accouchements in Sweden during that year numbered 123,145, yielding I2I,798 living and 3,o69 dead children. These figures imply some, probably considerable, differences between the fertility and fecundity rates, especially when age-group rates are taken out. Although the report gives the numbers of twins and triplets born, and distin- guishes between the live and still births, the data are insufficient to calculate the number of children born of mothers at different ages.

Two other objections may be urged against the use of the Swedish figures for my present purpose. In the first place there is reason to believe that there are racial differences in the fecundity of women; and in the second, the fecundity rates for 1891 did not represent the full capacity of the Swedish women to bear children.

Attention to the first point was first directed by the Registrar- General for Scotland in the Census Report for 1871, in a discussion of the results of the first year of birth registration in Scotland. In vol. ii of that report (p. lxv) be gives a table comparing the percentage of mothers at each age to total mothers, in the two countries. The comparison made there is between the figures for 1855 in Scotland and 1863-67 in Sweden. I have thought it desirable to take out the Swedish figures for 1855, and the new comparison will be found in Table 1. It should be noted that the Swedish figures are based on all confinements, that is, include legitimate and illegitimate, live and still births, while the Scotch figures refer to confinements with legitimate and illegitimate children registered as born alive.

* The headline from the table (loc. cit., H. 143, p. 175) from which the figuires were takenreads: "Frultsamhetstalen0100." Fruktsamhet=fecundity; fruktbarl&et = fertility.

t It is interesting to note that the French, Italian, and German languages make no distinction between fertility and fecundity, except such as may be gatbered from the text. Fecondite, fecondita, and Fruktsbarkeit are all used in the double sense.

B 2



DUDFIELD-SOme Unconsidered Factn's [Mar.

TABLE 1.-Confinements, 1855.

Nunubers Registered. Percentaige in eacht Age-Group. Age-Groups.

Scotland.* Sweden.t Scotland. Sweden.

-20 ...... 2,639 1,309 286 1-12 20-.. ..... 19,494 14,824 21-12 12-64 .25 ...... 26,043 30,122 28'22 25-69 30 - ...... 21,574 33,868 2337 28 88 :35 ...... 15,295 24,034 16'57 2049 40-. ...... 6,420 11,612 6-96 9-90 45 - ...... 797 1,479 0-86 1-26 50 - ...... 38 29 004 0-02

Totals .... 92,300 117,277 100 IOO

Legitimate and illegitimate living children only. t Legitimate and illegitimate children, including 3till births.

The above figures suggest that fecundity is, or used to be, later

in its commencement in Sweden than in Scotland, and that it

continues with considerable intensity to a later period of life.* As

complementary to the foregoing table, the percentage distribution

of married women has been calculated for the year (1855). The concentration of marriages between the ages 30 and 40 years in Sweden is noteworthy.

* Complete proof of this is not available, owing to the absence of certain of the necessary data for Sweden. The following incomplete figures do, however, lend support to the view enunciated:-

Fecundity Rates per I,ooo Married Women.

1855.

Scotland. Sweden.

Total accouchements to total married women i 290,4 287-2 15-45 years ................J

Accouchements at ages- -20 years 505 ?

20- ........................... 423 452 25 ............................ 366 371 30 ........................... 305 317 35- ............................ 243 248 40 .......................... 115 142 45-50 19 23



1908.] afecting the Birth-Rate. 5

TABLE 2 - arried Women, 1855.

Scotland Sweden.

Estimated Eteraentages. N'tinlbted Percentages. Numbers. Nunbers.

15 ............. 3,303 0 98 1,400 0-32 20- ......... 38,405 11-48 25,651 5-93 25- 6......... 66,070 19-75 71,594 16-55 30- ......... 68,264 20'41 99,749 23-06 35- ......... 61,454 18 37 92,219 21'32 40 ......... 55,090 16-47 78,714 18 20 45-50 ........ 41,908 12'53 63,254 14-62

Total .... 334,494 100 432,581 100

That the fecundity rates for 1891 did not represent the full capacity of the Swedish women is evidenced by the figures in Table 3, which show the percentage decreases in the quinquennia 1886-90 and 1891-95 when compared with the quinquennium 1871-75, in which period a maximum mean rate of 300 confinements per i,ooo married women was recorded.

TABLE 3.-Sweden.

Fecundity Rates.* Comparaitive Figures. Rates for 1871-7 5 = ioo.

Age-Groups.

1871-75. 1886-90. 1891-95. 1886-90. 1891-95.

20- ........ 482 447 456 9217 94 6 25- ....... 389 372 363 95-6 93-8 30 . ....... 333 318 307 95 5 92 2 35- . ........ 265 253 243 9534 91-7 40- . ....... 158 142 136 89-8 86 0 45-50 24 22 20 91-6 83-3

15-45 300 289 279 96-3 93 0

# Accouchements per l,ooo married women.

Scotch Fertility: Married Women. I think that sufficient evidence has been adduced to show that

it is desirable to adopt some other standards for the present purpose. After much consideration I decided to use the results of the registration of births in Scotland during the year 1855. As is well known, the late Matthews Duncail made use of the data for Edinburgh and Glasgow in the preparation of his book on fertility in woman.6 During 1906 a new analysis of the results obtained throughout the whole country was published, the Authors being the Messrs. Lewis.7 From that work I have extracted analyses of the legitimate births according to the ages of the mothers, and



6 DUDFIELD-S&ne Unconsidered Factors [Mar.

the joint ages of the fathers and mothers. The numbers obtained, after distribution of the children whose parents omitted to state their ages, are to be found in Table I, Appendix.

A few remarks of a preliminary nature as to the comparison between the results obtained by Lewis and those contained in the Reports of. the Registrar-General for Scotland appear to be necessary.

According to the tabulation of the Register Office, the total number of births in 1855 was 93,349 ;* Messrs. Lewis, using cards, obtained one of 93,369-a negligible difference. Dividing the births into legitimate and illegitimate, the numbers are :-Register Office, 85,992 and 7,357 respectively; Lewis, 85,964 and 7,405, with differences of - 28 and + 48 respectively. These variations may also be neglected. As no distinction is made in this communication between the births of males and females, nothing need be said of the discrepancies between the two sets of results. They can be seen in the appended table (Table 4).

TABLE 4.-Analysis of Births. SCOTLAND, 1855.

Lewis. Registrar-Generail.

Total Births ............ 93,369 93,349 Legitimate ............ 85,964 85,992 Illegitimate ............ 7,405 7,357

Males .............. 47,801 47,8oi Legitimate ............ 44,010 44,044 Illegitimate ............ 3,791 3,760

Females ... . ... 45,568 45,645 Legitimate . ........ 41,954 41,948 Illegitimate .......... 3,614 3,597

A more important consideration is the extent to which the number of births recorded represents the true total of births in the year.t The total birth-rate in 1855 is given bythe Registrar-General as 3I*49 per 1,000 persons, rising to 33-99 next year. The mean rate for the five years 1856-60 was 34-66. Assuming that the mean-rate more nearly represents the true birth-rate for 1855, and applying the former to the estimated population for 1855 (2978,o65), a "corrected" total of 103,208 births is obtained, a difference of 9,853. It will, I think, be admitted that illegitimate

* A corrected total (93,363) was published in 1874, but as no analysis of that figure can be traced, the first total has been used here.

t The question of the probable completeness of registration in 1855 was discussed in the "First Detailed Report for Scotland," p. x; the "Tenth" ditto, p. xiv; and " Report on Census (1861) of Scotland," p. xviii.




births are always more likely to remain unrecorded than legitimate. The recorded percentage of illegitimate to total births in 1855 was 7 8, which proportion rose to 8-5 next year, and continued to rise during the succeeding years. The .mean percentage for the five years 1856-60 was 8-8, and if that proportion be applied to the "corrected" total of births (103,208), the number of illegitimate births included in the amended total becomes 9,o82, as compared with the recorded number 7,357-a difference amounting to 1,725. By these means I have estimated that the " correct" total number of legitimate births in 1855 was probably 94,I26 or 8,I62 in excess of the recorded, showing an estimated deficiency of 8-7 per cent. Such a deficit in the actual number of children born cannot be ignored, but I have thought it better to correct the totals of my calculations rather than attempt to correct the numbers of births at the different maternal ages. A com- plicated system of rating up the births at the different ages of the parents would, I believe, lead to more serious error than the application of a correction to the final totals.

In analysing the confinements according to ages of wives- mothers as entered in the registers, it was found that no fewer than 8i i were at 45 years and upwards, while in I,OI2 cases the ages were not recorded. Of mothers aged 45 years and upwards, 773 were between 45 and 49 years of age, 29 between 50 and 55, and 9 between 55 and 60, the highest recorded age beinig 58 years.

After distributing the confinements of women whose ages were not recorded at registration, the corrected numbers become, at ages 45-49 years, 784 confinements; 50-54, 32; and 50-59, 6: or 826 confinements in all at ages over 45 years, yielding 829 children, or o096 per cent. of the total births. At first it may be thought that so small a proportion of births can be ignored, but, having regard to the large numbers, and increasing proportion, of married women at ages over 45 years, it would, I think, be unwise to omit that proportion from the present calculations. It therefore becomes necessary to determine what shall be taken as the upper age-limit of fecundity. It is usual to assume 45 years as that limit, but I have been unable to find any evidence in support of that assumption except a very general statement in Duncan's "Sterility in Women."8

I have examined all the communications dealing with fecundity and fertility in our own and foreign journals, which I bave been able to trace, for evidence on this question. The best data I have found are contained in a series of papers by Beneduce, in this year's "Giornale degli Economisti,"9 from which I have extracted the following particulars:



8 DUDFIFLD-SOme Unconsidered Factors [Mar.

Percentage of Total Confinements at Ages of

Period. 45- 50-

Sweden . ................ .... 1899-1903 IP29 1 Not g Norway ................................ '99- '00 2-19 f ven. Denmark .'96- '00 0(73 0,02 Finland .1900- '02 1,35 0 05 France ......... .................... 1899- '03 0 70 l New South Wales .1901- '03 0*70 4Not given.

I have also addressed communications to a large number of hospitals (both general and lying-in) and to Poor-law institutions in the Metropolis and the provinces. The replies received from 29 institutions and one private practitioner have enabled me to collate information relating to 119,259 confinements of married women. Among those parturient women were 51i aged 45 years and over, equal to 0-43 per cent. of the whole. With regard to II3,60i of the confinements, those at ages of 45 years and upwards can be subdivided into two groups, viz., 45-49 years (470 confinements) and 50-54 years (21 confinements), equal to 0o4I and 0'02 per cent. respectively. The data kindly furnished to me afford material for conclusions of an interesting character, with which, however, I do not propose to trouble you. I will only say that they suggest that pregnancy at ages over 45 years was more common in the past than it is now.

Further evidence in support of that suggestion is furnished by the figures given in Beneduce's articles, already referred to, from which I have extracted the materials for Table 5.

TABLE 5.-Percentage Distribution of Legqitinmate Births. (Beneduce.)

Ages of Mothers. Counltry and Period. r

-20. 20- 26- 30- 35- 40- 45- 50-54.

Sweden- 1871-80 ............... 0 95 12 01 23S99 26 31 22 37 1250 1 85 0 02 '81-90 ............ 0,95 12,92 25-41 26-21 21-25 l11a2 1-65 0-02 '91-1900 ............ 1-14 13-17 24-46 26-74 21 861 11-23 1-39 0-01

Denmark- 1891-95 .......1.. 119 15-34 27-71 26 78 19-84 8-42 0-72 0 00 '96-1900 ........... ....1 1-44 17-51 28-53 25-16 18-42 8-20 074 000

Finland- 1881-90 ................ 2 01 16 36 25-21 24-61 19-58 10-70 1-47 0-06 '91-00 ................ 2-13 17-87 25-06 23-77 19-24 10-37 1P50 0-06

Norway- 1874-76 ................ 0 76 12-57 24-83 25-53 2049 12-84 2-88 0 10 '89-92 ................ 0-67 11-50 24-84 26-25 22-31 11-95 2,36 0-12

France- 1892-95 ................ 4 07 23 38 29-67 22-52 13-82 5-61 0-82 0 11 '96-1900 ............3.170 24 62 29821 22,12 14 21 5 33 0 73 0'07




I decided, after considering the data I had collected, that the upper age-limit of fecundity must be raised, and I have tentatively fixed it at 54 years. In consequence, I have adjusted the results obtained in 1855 in Scotland by transferring all the births, recorded as taking place at maternal ages exceeding 54, to the age-group 50-54.*

The next matter to be decided was that of the year the population of which should be selected for the calculation of fertility rates. On a priori grounds it appears more reasonable to regard the children born in 1855 as the progeny of parents living at the middle of 1854,t but the common practice is to calculate birth- rates on the population of the year in which the births occur. I find, too, that all workers on the subject have followed this practice, and I have, consequently, decided to use the estimates for 1855. These were obtained in the usual manner by assuming that the growth of the population between 1851 and 1861 was uniform, and that the proportions of married women at different age-groups to the total population remained unchanged. I have, however, included in Table 6 the estimated numbers of married women and the fertility rates for both years.

TABILE 6.-Distribution of Births and Fertility Rates. SCOTLAND, 1855.

1854. 1855.

Ayes of Lre timate Motlhers. Registeren. Estimiated Estimsited g e. M alrried Fertilitv-Rates.* Married Fertili: y-Rates *

Women. Womien.

15- .. 1,672 3,286 508-825 3,303 506a2o6 20 ........ 16,357 38,180 428-418 38,405 425'908 25- ........ 24,423 65,681 371-842 66,070 369-653 30- ........ 21,088 67,860 310-757 fi8,261 308-918 35 ........ 15,186 61,i695 248-563 61,454 247 11t 40 ........ 6,409 54,765 117-027 55,090 116 336 45- ........ 789 41,660 18-939 41,908 18-826 50-54 .... 40 37,086 1-078 37,310 1-072

15- ........ 18,029 41,466 4 34-789 41,708 432-267 25 ....... 45,511 133,541 340 801 134,334 3381789 35- ........ 21,595 115,860 186-388 116,544 185 294 45-54 .... 829 78,746 10-527 79,218 10-464

* Pet- x,ooo married women in each group.

* The common law of England allows no presumption that a woman (be she spinster, wife, or widow) has passed an age when she can procreate and bear children. Practice has adopted a limit of 54 years. (" Lancet," 1905, vol. ii, p. 250.)

t For statistical purposes all the children born during the year 1855 might be assumed to have been born on the central day of that year (say, 30th June), and to be the progeny of parents living nine months earlier (say, end of October, 1854).



10 DUDFIELD-SOme Unconsidered Factors [Mar.

The use of the rates for 1855 underestimate the possible numbers of births by about o6 per cent. In certain cases, for reasons already stated, it has been necessary to use decennial age-groups instead of quinquennial. The use of the former intro- duces a second underestimate amounting, in all cases, except Ireland, to something between 0o3 and 0o7 per cent. In the Irish estimates there is an overestimate ranging between I 4 and i 9 per cent.*

There are considerable differences between the fertility rates given in Table 6 and the figures used by Newsholme and Stevenson, as will be seen from the following comparisons.

A es of Scotland, 1855 Sweden, 1891 Ages of Scotland, 1855 Sweden, 1891 Vives. (Fertility). (fecundity), Wives. (Fertility). (Fecundity).

15 - ....... 506 518 35- ....... 247 250 20 ....... 426 451 40- ....... 116 142 25 .-...... 370 375 45- ....... 19 N 30- ..... 309 312 50-54 .... 1

The difference between the estimated numbers of births for any year (say, 1901) calculated on the two sets of factors, is illustrated below *

E8tinzated Births: Jarried Women. 1901.

Estimated Births derived from Estimated Births derived from

Ages. Ages. Scotch Rates, Swedish Rates, Scotchi Rates, Swedislh Rates,

1855. 1891. 1855. 1891.

15 . .-.... 12,853 13,153 40 - ........ 83,179 101,528 20- . ....... 190,758 201,996 45- . ...... 11,142 ? 25- . ..... 320,754 325,394 50 -54 . 504 30 - .... 282,136 284,931 35 .... 206,253 208,664 Totals I. , 107,5579 I,135,686

After correcting the estimate based on the Scotch factors by the addition of 8-7 per cent., the totals are I,203,938 and I.I35,686 respectively, showing a deficiency of 68,252 in the latter, the ratio of the two estimates being 100: 94.

Scotch Fertility: Husbands and Wives. For the purpose of determining the fertility rates of husbands

and wives in combination, use has been made of the tables issued in certain of the census reports. As, however, the table for the census of 1851 in Scotland contained little more than oI per cent. of the

* The years for which decennial age-groups were used are: England and Wales, and London ................ 1881, 1891 Ireland ............................................................ 1851, 1901



1908.] affecting the Birth-Bate. 11

enumerated married women, a correction was necessary to include the remaining 9 per cent. (or a portion of them, at least). The method by which the required correction was made will be described when dealing with the question of " surplus wives." The final figures which were used to calculate the rates are given in Table II in the Appendix. Applying the figures given in Table I to the numbers of married couples, the rough rates given in Table III were obtained.

The rates in the last mentioned table exhibit certain irregu- larities, which evidently require to be corrected. After several trials, I concluded that the best method of " smoothing " was to combine certain of the age-groups in vertical columns, and by this means the rates given in Table 7 were arrived at. Such combination also affords a certain amount of correction for the errors which may be expected from the use of registration returns of onle year only, and from the small numbers both of married couples and births found under some of the headings.

TABLE 7.-Birth- Rates per 1 OO Couples. Corrected Estimates. SCOTLAND, 1855.

Ages of Ages of Wives (Mothers). Husbanids- _ _ _ - _ _ _ - _ _ _ _-_ _ _ _ - _ _ _ _-_ _ _ _ -

<Fathers). 15 - 20-. 25- 30- 35- 40- 45- 50-54.

15- ...2 02SO24 52037 68 750 57-143 - - - 20- . 55,769 45-659 40766 30'123 16-071 14-25 1 25- . 53-041. 44-288 39-663 33-732 27-704 14-500 t3,187 1'550 S0- .... 42-777 39-030 36'328 32'796 26208 12'575 J 235 .. 46 154 47-829 37,888 31 170 27,377 12 525 2,272 1P639 40- .... 36,363 34-815 35-147 30 790 23-433 13'507 2'416 0-144 45- ] 28'571 33'037 28,660 23,607 11752 2-284 50- 25 000 27-451 32-586 27501 20'486 9 543 P543 0'088 55-- 21 212 23'529 19-366 19,856 7'415 1X312

Note.-Italie, figures indicate rates based on less than loo couples.

Even now there is one peculiarity to which attention should, I think, be drawn, namely, the higher rates for husbands aged 35-39 living with wives at certain ages. Such higher rates occur at ages (wives') of 15-, 20-, 25-, and 40-. I do not think the changes are due to the special fertility of married couples at those ages. The onlv explanation I can suggest, apart from errors in collection, is that the men of 35-39 being (more or less) business men in the prime of life, took a more intelligent notice of the new requirement, and hence that a larger proportion of the births of children of such men were registered.

I have in the course of my reading found three tables similar to Table 7, which I include here (Table 7A, 7B, and 7c) for the purpose of comparison. One reservation must be made in comparing the tables, and that is that the figures in the reprinted tables do not, in



12 DUDFIELD-Sonte Unconsidered Factors [Mar.

TABLE 7A.-Norway, 1875. (Kimer.)10

Ages of Mothers. Ages of Fathers.

16- 20- 25- 30- 85- 40- 45- 50-54.

15- 20- 53-4 48-9 25- .... 503 451 40-1 30- ... 52-6 42-4 37-2 32-8 19-2 35- ... 413 346 31-7 19-7 4-6 40- .... 39-2 33-1 29-4 19 9 49 0-29 45- 320 27-5 17-1 436 036 50- ..3-9 0'13 55- 2-6 0.09 60-64. 003

TABLE 7B.-Budapest, 1888-92. (Rbr6si.)"

Ages of Motlhers. A g e s o f _ _ _ _ _ _ _ _ _ _ - _ _ _ _ _ _ - _ _ _ _ _ _ _ _ _

Faithiers. -20ltlles

_ 20- 25- .30- 35- 40- 45 50-

15 - ._ . 20- .... 4SO 350 27-3 22 - _ 25- ... 442 407 33-9 258 22-1 i6-0 30- 40-4 33-2 30-8 22-7 18-4 71. i8* 35 - ... 35-6 31-1 26-0 22-3 17-5 87 0-8 40- .... - 25-0 21'4 17-3 15-7 8-0 1-3 45- .. 19-7 18-9 14-1 10'8 5-6 11 50- - 222 20-2 12-5 10-2 3-7 04 55-59.... - - 5-9 11-2 76 3.0 03

Note.-Italic figures inidicate rates based on less than loo couples.

TABLE 7c.-Norma*y, 1899-1900. (Beneduce.)

Ages of Motihers.

Fdtliersf 15- 20- 25- 30- 85- 40- 45- 50-54.

15- .... 37i6 50-70 37-69 66-16 43-75 20- ** 45-98 4772 39'06 40-53 38-51 32'53 10'60 -

25- .... 4684 43-25 4029 37-66 32-25 22 40 4-89 1*28? 30- .... 3655 43-62 37-56 35'30 29-60 19-69 3-56 35- .... 44-35 41-69 3663 31-53 28-39 1878 479 0.39 40- .... 52-0S 4095 36-55 31-91 26-43 17'95 4'89 0O38 45- .. 22-22 4088 32-99 29-14 24-95 15-00 3*gE 013 50- .... 33-33 29-57 33'16 2651 22-33 13-22 3-07 0o06 55- .... 1666 24-35 2363 2289 19-00 10-33 190 1 0 03

Note.-Italic figures indicate rates based on less than IoO couples.




all probability, represent the full fertility of the nations to which such tables refer. Further, Kor6si's table is based on numbers which the author states require to be corrected by addition of 8 per cent. to allow for incomplete registration in the first year included in his statistics. The rates in Table 7 are higher (in general terms) than those in Tables 7B and 7c, but for the reasons which have been given before that is what I should expect. They are lower than those in Table 7A except in the last column. A comparison of 7A and 7c (both tables refer to Norway and relate to periods separated by a quarter of a century) shows how the fertility rates fell during the intervening years. Table 7B is based on much smaller numbers, and occupies a special position.

I trust that I shall not be thought unduly credulous if I assume that the results, as given in Table 7, are very close approximations of the true fertility, and of fertility very near its maximum, which is the standard sought for.

Changes in Population: Numbers of Married Women. The object of this communication being to examine the relation-

ship between the changes in the population and those in the annual number of births, it is requisite to know what changes have taken place in the population. In Table 8 will be found the numbers of inhabitants of the United Kingdom and Ireland as enumerated at each census since 1851, and also the numbers of married women at fecund ages (15-54). In England and Scotland the numbers in both cases have steadily increased, in Ireland, decreased. The total increase of the total population of England between 1851 and 1901 amounted to 8i per cent., in Scotland to 55 per cent., and (the decrease) in Ireland to 32 per cent. The rate of change in the numbers of married women has not been uniform with that of the total population in any of the countries. In England and Scotland the increase in number of fecund women has always been slightly, but not equally, higher than that of the total population, while in Ireland the decrease in the former began by being less than the decrease in the latter, but since 1881 has been greater. The proportion of fecund women to total population has undergone but slight change during the half-century, increasing in the two first countries, and decreasing in the third. As will be seen from column 6 of Table 8, the total change amounted to but + 5 per cent. in England, + 4 per cent. in Scotland, and - 7 per cent. in Ireland.

The figures for London are somewhat peculiar. There the changes (increase) in the total population, and fecund women have been approximately equal, and those in the proportion of fecund women to total population insignificant. (See Table 8.)




TABLE 8.-Changes in Population and Fecund Women.

Index Ntumbers. Percentage

Total Married Women of Married Percentaged Populatioii. (15-54). WPoen Total Married of Married

tol'Iotal Pplto.Women Women PpPopulatiooplaio. (15-54). to Tot-al

Population.

Col. 1 1 2 3 4 5 6

England and Wales.

1851 ...... 17,927,609 2,553,894 14'24 100 100 100 '61 ... 20,066,224 2,961,516 14'75 112 116 103 '71 ........ 22,704,108 3,342,473 14-72 127 131 103 '81 ...... 25,974,439 3,753,606 14'45 145 147 101 '91 ........ 29,002,525 4,164,849 14"36 162 163 101

1901 .... 32,527,843 4,865,880 14 95 181 190 105

London.

1851 ..... 2,362,236 367,673 15'56 100 100 100 '61 ..... 2,803,989 442,362 15-77 119 120 101 '71 ..... 3,254,260 508,546 15-62 138 138 100 '81 ..... 3,816,483 579,469 15-18 161 158 97 '91 ..... 4,232,118 631,742 14-92 179 172 96

1901 ..... 4,536,541 697,418 15-37 192 190 99

Scotland.'

1851 ........ 2,888,742 362,669 12'55 100 100 100 '61 ..... 3,062,294 391.416 12-78 106 108 102 '71 ..... 3,360,018 425,096 12-65 116 117 100 '81 ..... 3,735,573 474,711 12-70 129 131 101 '91 ..... 4,025,647 506,367 12-57 139 140 100

1901 ..... 4,472,103 584,425 13-06 155 161 104

Ireland.*

1851 ....... 6,552,385 743,736 11-35 100 100 100 '61 ... 5,798,967 704,476 12'14 88 95 107 '71 ........ 5,412,377 637,088 11-77 83 86 104 '81... 5,174,836 574,858 11-10 79 77 98 '91 ... 4,704,750 506,087 10-75 72 68 95

190l ....... 4,458,775 470,281 10-54 68 63 93

" The index numbers, taking as basis (= ioo) the first year for which the number of registered births is given in each case, are:-

Total Marred Per- Total Married Per- Popula- Woen centage. Popula. Women. centage. tion. tine.

Scotlnd- Ireland- 1851 . 94 93 98 1851 .. 121 117 96

'61 . 100 100 100 '61 .. 107 110 103 '71 . 110 109 99 '71 . 100 100 100 '81 . 122 121 99 1'81 ..... 96 90 94 '91 . 131 129 98 '91 .. 87 79 91

1901 . 146 149 102 1901 .. 82 74 89




If it be assumed that no changes took place, between 1851 and 1891, in

(a) the age-composition of married women, and (b) the fertility rates,

then the index-numbers (total population and married women) in Table 8 would lead one to expect that the birth-rates of England and Wales and Scotland in 1901 would exceed those recorded in 1851, by some 9 per cent. in the former country and 6 per cent. in the latter. In London the birth-rate for 1901 should have been some 2 per cent. below that of 1851, while in Ireland the decrease in the rate should have been 5 per cent., and in the number of births 37 per cent. of the number recorded in 1851; or, as registration was not commenced until 1864, a rate in 1901 8 per cent. below that of 1871, and a total number of births 26 per cent. that of the latter year (1871).

Changes in Ages of Married Women. A reference to Table IV Appendix will show at once that very

great changes took place during the half century in the proportions of married women enumerated in each age-group. The greatest proportional diminutions were at the younger ages, 15-19 and 20-24, just the periods with the highest fertility rates. Compen- satory increases (proportional) are found at all the higher ages, except in Scotland, ages 50-54. The index-numbers given in Table V Appendix shows the extent of the changes in each age-group.

Changes in Fertility Rates. There is no direct evidence, statistical or medical, in favour of

any suggestion that any decrease has taken place in the potential fecundity or fertility of the human race in general, or the English race in particular. One factor must be cited which undoubtedly has had some effect on actual fertility in the United Kingdom, that is the later age of marriage. Physiologically, the best age for marriage of girls lies between 23rd and 25th years. If married much later than the latter age there is a probability that the woman will prove to be sterile, though (very occasionally) they have had unduly large families. There is no data for arriving at any measure of the loss of fertility resulting from late marriages; the only observations on the poiInt known to me are those to be found in Duncan's work on Sterility.

Comparisons of Actual Births with Estimation of Births from Standard Fertilities of Married Women.

Applying to the age-group numbers of fecund women, the rates given in Table 6 (those for 1855 were used), the figures in




column 4 of Table 9 were obtained. As has been already indicated, an addition of 8-7 per cent. appears to be necessary to the total derived from the standard fertility-rates to allow for births not registered in Scotland during 1855. By that correction the figures in column 5 are obtained. The numbers of legitimate births given in column 1 are the averages of three years, the census year being in each case the central year.

TABLE 9.-Numbers of Births Registered and Esti2nated from Fecund Married Women.

By Registration. By Estimationi. Index NumTbers (on Corrected Totals).

Perceiitage1 From After Totail added tor Corrected Oroed addition of On Regis- On Esti-

as Recorded. Non-regis- Total. Oeries 8, percent. tration. mates. tratioii. tTotNil.

Col.... 1 2 3 4 5 6 7

England and Wales.

1851.... 569,504 5 597,979 590,105 641,4-44 100 100 '61.... 653,355 3i 676,222 682,707 742,102 113 116 '71 760,615 2j 779,630 769,393 836,330 130 130 '81 .... 841,827 1 850,245 865,382 940,670 142 147 '91.... 855,759 2 872,874 948,841 1,031,390 146 161

1901.... 895,897 2j 918,294 1,107,579 1,203,938 153 188

London.

1851.... 74,867 5 78,610 88,248 95,925 100 100 '61.... 91,944 3i 95,162 103,831 112,$64 121 118 '71.... 110,338 2j 113,101 121,893 132,498 144 138 '81.... 127,982 1 129,262 139,677 151,829 164 158 '91.... 126,775 2 132,110 149,338 162,330 167 169

1901.... 126,559 2j 129,722 163,392 177,607 165 185

Scotlnd.

1851.... 83,854 91,149 94 '61.... 96,555' Not r 96,555 89,372 97,147 lO 100 '71.... 105,724 deemed 1 105,724 96,485 104,879 109 108 '81.... 115,095 115,095 107,613 116,975 119 120 '91.... 114,673 neces 114,673 111,962 121,703 119 125

1901.... 123,549J _ y i 123,549 131,630 143,082 128 147

Ireland.

1851 ... - 159,953 173,869 - 118 '61.... - - 150,383 163,466 l- I '71.... 146,7101 Not r 146,710 135,019 146,766 100 100 '81i. 122,301 deemed J 122,304 118,268 128,557 83 87 '91.... 103,088 neces- 103,088 98,002 106,528 70 72

1901.... 98,772J sary. L 98,772 95,990 104,341 67 71



1908.] affecting the Birtth-PRate. 17

In the case of England alnd Wales, a further correction of the recorded numbers of births for non-registratioIn appears to be essential. Writing in 1877, Farr (39th Annual Report) estimated that 5 per cent. of the births were not accounted for durilng the thirty-nine and a-half years, 1838-76. Assuming that approximation to be correct, and recognising that registration was more incomplete during the earlier than the later years of that period, I have tentatively used the corrections (added percentages) given in the second column of Table 9. Even now I have reason to believe that a proportion of the births remain unregistered largely owing to the fear of the operation of the Vaccination Acts, and I doubt whether the factors suggested for the years 1881 and onwards are large enough. In the case of Scotland, the uniformity of the birth-rates suggests that registration in that country has been, subsequient to the first year, very complete, or the proportion remaining unregistered very uniform. The Registrar-General for Scotland in his Report on the Census for 1871 (vol. ii, pl. lxiii) observes "that experience has shown that in Scotland almost all the "facts relative to births . . . . are produced with extreme "regularity year atter year.'

I have been unable to form any idea as to the correction necessary in the Irish figures, and give them as recorded.

It appears to be desirable that the figures relating to Scotland should be the first to be considered. Taking the year 1861, the difference between the corrected number of births in that year (96,555) and the result of the estimation (97,147), is less than I (actually o-6) per cent., a difference so small as to justify a conclusion that a fair amount of reliance may be placed on the methods used to obtain the estimate quoted. Looking at the last two columns, it will be seen that in 1871 the recorded number of births showed an increase of 9 per cent., while according to the estimate it should have shown one of 8 per cent. In 1881, the increase, according to the estimation, should have been 20 per cent., while the recorded number was i per cent. less. The variation between the two sets of figures becomes greater in each of the two remaining years, and in 1901 was I9 per cent.

In England and Wales the difference between the estimated and the recorded (" corrected ") numbers of births in 1851 amounted to 7-2 per cent., part of that difference may be due to incomplete correction for non-registration. Whatever its cause, the difference is of no importance for my present purpose, which is to compare the potential fertilities of subsequent years with that of 1851. Turning to the two last columns, it will be seen that, while the increase in registered births recorded in 1861 (13 per cent.) was

VOL. LXXI. PART I. C



18 DUDFIELD-&One Unconsidered Factors [Mar.

less than that of the estimate (I6 per cent.), in 1871 the increase was identical in the two cases (30 per cent.). After that date the increase in the estimate has beeil greater on each occasion, being in 1901 as much as 35 per cent. higher.

In London, the increases in registered births were greater than those in the estimate up to 1881, while in 1901 the increase in the estimate was 20 per cent. greater than that of the registered births.

In Ireland, the differences between the rates of change in the registered and estimated numbers of births have always been but slight. In 1881, the diminution in the number of registered births was 4 per cent. greater than that in the estimate; in 1891, 2 per cent.; and in 1901, 4 per cent.

Changes in Ages of Husbands and Wives in Combination. For the purpose of the next estimation, the tables of age of

husbands and wives in combination were used, and the influence of

TABLE 10.-Husbands and Wi"ves in Combznation.

'Tota Nuniber Equivalent to -Calculaited Numbers of of uerried -per cent. mtirried Birtl_s. Index Cal_lNBrted Index Couples Npm- rirt s. Nh un.- on samie 1Frt bers. berns1Nun Schedtile. Men. Women. Crude. First Correction.

Col ... 1 2 3 4 5 6 7 8

England and Wales.

1851 2,796,800 94-53 92741 563,233 612.234 100 646,206 100 '61 3,242,422 94,57 92 93 652,781 709,573 116 749,360 116 '71 3,672,011 94 55 92-99 737,118 801,247 131 845,343 131

1901 5,317,520 9476 93i00 1,072,398 1,165,697 190 1,219,334 189

London.

1851 370,500 92-82 90'42 82,576 89,760 100 95,954 100 '61 449,928 93,46 90-89 99,765 108,444 121 115,228 120 '71 523,106 93-95 91-51 115,791 125,865 140 132,979 139

1901 730,062 93-91 92-05 157,429 171,125 191 179,6b5 187

Scotland.

1851 385,096 93-84 91 19 77,334 84,062 94 90,009 94 '61 419,866 93-77 91P09 82.447 89,620 100 95,929 100 '71 461,399 94-00 91-46 89,826 97,641 109 103,866 108

Ireland.

1861 775,107 93-56 90-95 136,029 147,863 110 I 158,510 111 '71 728,538 94.35 91-93 123,077 133,785 100 142,668 100 '81 657,365 94-40 92-29 107,094 116,411 87 123,382 86 '91 579,183 94-42 92-55[ 89,297 97,066 72 102,829 72



1908.] aft%cting tte Birth-Rate. 19

the changes in the paternal ages thus brought under consideration. Before proceeding to the results of that estimation, it is desirable to inquire how far those tables may be regarded as fair samples of the married population. Inasmuch as the number of married women recorded at each census has been in excess of the number of married men, it is impossible to say what the real number of married couples has been on any occasion. It is a defect in our census schedule that no provision is made for distinguishing the divorced and separated. All such appear under " married," although for all questions relating to the legitimate birth-rate, such persons rank among the unmarried and widowed.

In Table 10 are given the numbers of married couples who were returned on the same schedules, and the percentages of married men and women so enumerated. It will be seen that the percentages have been fairly constant, and steadily increasing.

In Table VI, Appendix, the percentage of each age-group, males and females, to the total married population, at each census, is set out. The figures are very fairly uniform, but there is a somewhat reffarkably small percentage of married men aged 15-19 (and 20-24 in Ireland) included in the combined ages table. On the whole, I am inclined to the opinion that the tables afford very fair samples of the age distribution of the married population.

In the series of tables numbered VIIA-D, Appendix, will be found the age composition of i,ooo,ooo, married couples, as deduced from the numbers given in the " H. W. Tables" of the census reports.* Tables VIIIA-D give figures indicating the rate of change from the standard of the first year of each table.

The tables as presented are unfortunately not easy to grasp, but I have been unable to devise a graphic method of setting out the information contained in them. Attention may be called to two rather striking features. One is the increase which took place in 1861 and 1871, in England and Wales and London, in the numbers of married couples returned at the ages appearing in the first three columns. In 1901 there was a marked decrease at those ages. In Scotland and Ireland the numbers at those ages have decreased from the first. The other point, one which would be expected from evidence available from other sources, is the increase in numbers at, or concentration round, the central ages of the tables. The rate of changes have varied very considerably, and by no means uniformly, as may be seen from the second group of tables. (VIIIA-D.)

* This formula is more convenient t.han the full description as "Tables of Ages of. Husbands and Wives in Combination." KErosi's term " bigenous " is eauallv applicable, but not an easy word to pronounce.

c 2




Before making any estimates of the numbers of births derivable from the figures in these tables, it is necessary to deal with the question of " surplus " and "added wives," as certain corrections required for the estimates cannot be made until the data relating to such wives have been obtained.

Added and Suiplus Wives.

It has already been stated that the total number of married women* has always been in excess of the number of married men, also that only a percentage of the married of each sex is included in the " H. W. Table " for any year. To correct the latter defect the method about to be described has been employed. It must be premised that the method is based on the assumption that all married couples are available for the production of children, as well as being in every case fertile. Unfortunately the census schedule gives no information as to the dissolution of the marriage tie by divorce or separation. Further, no allowance has been, nor do I see how it can be, made for husbands away from their homes in the course of their avocations. In any case, only a small proportion of them would be away for more than a year, and it seems fair to assume that, taking one year with another, the numbers would be negligible.

The method adopted was as follows:-The husbands who were not entered on the same schedules as their wives (the numbers are included in the H. W. Tables) were distributed horizontally, in the same proportions as the original figures of the table. (A reference to Table IX, Appendix, will make this clear.) The age-group totals for the corresponding number of wives were obtained by adding the distributed numbers vertically. Adding the number of the distributed or " added " wives to the original numbers in the tables new totals were obtained, which, when deducted from the total number of married women for each age-group, gave the (theoretical) number of "surplus" wives in each age-group. The numbers of " added wives " for each age-group are given in Table I 1, and those for " surplus wives " in Table X, Appendix. In the latter case the percentage of married women in each age-group which the number of " surplus wives " represents is given. The total percentage has decreased from the beginning, but the different age-groups show

* In the preparation of this communication, some scepticism has been aroused in my mind, as to reality of marriage in a proportion of women enumerated as "married." There is nothing to prevent a woman assuming that status for any reason convenient to herself, such as the inclusion of ar illegitimate child in the schedule.



1908.] affiecting the Birth-Rate. 21

changes in different directions, which are occasionally somewhat irregular.

In Table 10 (p. 18) the results of the estimations of the numbers of births, based on the numbers of couples as originally entered in the H.W. Tables, are given (column 4). To those numbers two corrections have been applied, 1st, the addition of 8-7 per cent., as already explained to allow for incomplete registration in the standard year 1855 (Scotland) (see column 5), and 2nd, by adding the estimated number of births for the " added wives " (column 7). The rates of change for the two corrected numbers are given (columns 6 and 8).

TABLE 11.-"Added Wives," according to Ages.

Ages of Wives.

15- 20- 25- 30- 35-* 40- 45- 50.-54.1 Total.

England and Wales.

1851 1,839 16,340 23,307 22,934 20,723 19,120 16,017 15,608 135,888 '61 2,361 19,253 26,351 25,679 23,596 22,591 18,970 17,205 156,006 '71 2,583 21,057 30,215 29,781 26,730 24,861 21,541 20,118 176,886

1901 1,577 20,719 35,876 38,765 38,710 36,656 33,367 32,557 238,227

London.

1851 386 2,825 4,151 4,379 3,905 3,596 2,792 2,507 24,491 '61 458 3,141 4,507 4,632 4,207 4,060 3,183 2,471 26,659 '711 420 3,251 4,784 4,914 4,469 4,200 3,472 2,919 28,429

1901 278 3,177 5,529 6,287 6,390 6,097 5,498 4,286 37,542

Scotland.

1851 343 3,031 4,258 3,915 3,370 2,977 2,250 1,843 21,987 '61 348 3,155 4,445 4,181 3,682 3,330 2,688 2,419 24,248 '71 317 2,756 4,404 4,322 3,S68 3,581 2,949 2,764 24,961

Ireland.

1861 673 5,886 7,067 6,907 5,194 7,078 4,754 5,669 43,228 '71 467 3,951 6,252 6,842 4,700 5,136 3,441 4,435 35,224 '81 162 2,260 4,258 5,668 5,084 6,140 3,739 4,045 31,356 '91 116 1,753 3,591 4,660 4,322 5,036 3,833 4,184 27,495

The numbers of births estimated to correspond to the numbers of " surplus wives" are given in Table 12. These figures are useful for correcting the estimates based on the total numbers of



22 DUDFIELD-SoMe Unconsidered Factors [Mar.

married women (see Table 9) by allowing for the excess of married women over married men. The results of the corrections and the new rates of change are given in Table 12, columns 3 and 4.

TABLE 12.-" Surplus JVives," Correction for.

Estiniated Births. Birthbs Equivalent Estimated Births. Index F'irst Correction. to Surplus Wives. Final Correction. Numbers.

England and Wales.

1851 ... 641,444 15,572 625,872 100 '61. .. . 742,102 16,765 725,337 116 '71 . 836,330 17,527 818,803 131

1901 ...... 1,203,938 27,571 1,176,367 188

London.

1851 ... 95,925 2,633 93,292 100 '61 ... 112,864 3,053 109.811 118 '71 . 132,498 3,361 129,137 138

1901 ... 177,607 3,716 174,881 187

Scotland.

1851 ... 91,149 3,185 87,964 91 '61 ... 97,147 3,425 93,722 100 '71 ... 104,879 3,612 101,267 108

Ireland.

1861 ... 163,466 1 4,442 159,024 112 '71 ... 146,766 4,507 142,259 100 '81 ... 128,557 4,575 123,Q!82 87 '91 .. 106,528 3,209 103,319 72

Summary.

Collecting in one table (Table 13) the index numbers of the changes in numbers and estimates included in the preceding tables, the general uniformity of the changes exhibited by the estimates becomes rather striking. There are unfortunately far too many lacunae, but that is inevitable with the lack of uniformity in recording the results of the census. Comparing the movements of the recorded numbers with those of the estimates, the following conclusions may be drawn, the figures for 1901 being contrasted with those of the first year of registration in each case.



1908.] afficting the Birth-Rate. 23

TABLE 13.-Summary. (Index Number8.)

On Recorded Numbers. Estimates of Birtlhs.

On On Total ProportionFecund Ntumber IOn

Proportion Women of Fecunid Oil Hlusbands Total FridFed as Legitni- atume- Married Husbantds anidl Wives

tiopl.a Womel Maoried Birthe (calculated after Wives Correctiou

(15-54). to', Birth. fronm Correction in Con). for Population. Age-Group for bination. Added Populatioti.Fer- " Surplus Wives."

tilitien). Wives."

Col.... 32 3 4 5 6 7 8

England and Wales.

1851.... 100 100 100 100 100 100 100 100 '61.... 112 116 103 113 116 116 116 116 '71.... 127 131 103 130 130 131 131 131 '81.. 145 147 101 142 14.7 '91... 162 163 101 146 161

1901.... 181 190 105 153 188 188 190 189

London.

1851.... 100 100 100 100 100 100 100 100 '61.... 119 120 101 121 118 118 121 120 '71 138 138 100 144 138 138 140 139 '81.... 161 158 97 1 164 158 '91.... 179 172 96 1 167 169

1901.... 192 190 99 165 185 187 191 187

Scotland.

1851.... 94 93 98 94 94 94 9t '61.... 100 100 100 100 100 100 100 100 '71... 110 109 99 109 108 108 109 108 '81.. 122 121 99 119 120 '91.... 131 129 98 119 125

1901.... 146 149 102 128 147

Ireland.

1851.. 121 117 96 118 '61 .. 107 110 103 111 112 110 111 '71... 100 100 100 100 100 100 100 100 '81 .. 96 90 94 83 87 87 87 86 '91 .... 87 79 91 70 72 72 72 72

1901 .... 82 74 891 67 71

England and Wales. (a.) The growth in the number of legitimate births has not kept

up with the growth of the population, to the extent of 28 per cent.




(b.) There has been a similar, but greater, lagging behind the increase in the fecund women, to the extent of 37 per cent.

(c.) According to the estimate, the increase in the number of births should have been 88 per cent., as compared with increases of 81 per cenit. for the total population, and go per cent. for fecund married women.

(d.) Practically the same results are obtained whichever set of estimates (married women, or husbands and wives) be used.

London. (a.) The increase in the registered number of births was 27 per

cent. below the increase of the population; and (b.) 25 per cent. less than that of fecund married women. The estimates based on husbands and wives are somewhat

higher than those based on married women. Taking the " corrected" estimates.

(c.) the H.W. estimate shows an increase of 91 per cent., 26 per cent. higher than the registered number; and

(d.) the married women estimate, an increase of 87 per cent., or 22 per cent. higher than the registered nuLmber.

Scotland. (a.) The increase in the number of recorded births was I8 per

cent. less than the increase in the population; and (b.) 2I per cent. less than the increase of fecund women. As regards estimates, there is only one available, that based on

married women. (c.) The estimate of births is slightly higher than the increase

of the population; (d.) and I9 per cent. above the recorded number of births.

Ireland. The period covered is shorter here than in the other countries,

as birth registration was not introduced until 1864. (a.) While the population has shrunk since 1871 by I8 per cent.,

the number of births registered has fallen by 33 per cent. (b.) The decrease in the number of fecund married women has

been 7 per cent. less than that of the births. (c.) The decrease in the estimated number of births (married

women) amounted to 29 per cent., or 4 per cent. less than the decrease in the registered number.

From the index-numbers given in Table 13, estimates of the loss of fertility due to "moral restraint" can be obtained, based on the differences between the index-numbers for legitimate births



1908.] affecting the BirthRate. 25

(column 4) and any one, of the index-numbers in columns 5-8. Having regard to the gaps in those latter columns, it is preferable to use the numbers in column 5. Limiting the comparison to the year 1901, the following results haye been (provisionally) arrived at:-

Estinmated loss by " moral restraint "-

{ 35 per cent. of the number of births recorded In England and Wales * 1..in 1851, say, 209,295. f 9g per cent. of the births recorded in 1861, say, In Scotland ........ 18,345.

In Ireland................. 4 per cent. of the number of births recorded in nIreland-- . l.1871, say, 5,870.

A second method of arriving at an estimate of such loss has to be described.

TABLE 14.-Ratios of 2lstinzates of Births.

All Married Women All Married Women, H. W. Table after (15-~54).* less Surplus Wives Final Correction.$ (15-54).t

Col ..... 1 2 3

England and Wales.

1851 .. . 641,444 625,872 646,206 100 97 5 100o7

100 103'2 1861 .......... 742,102 725,337 749,360

100 977 100t9 100 103,3

1871 .......... 836,330 818,803 845,343 100 97 9 IO01O

100 10392 1901 .......... 1,203,938 1,176,367 1,219,334

100 977 101,2 100 i03-6

London.

1851 .......... 95,925 93,292 95,954 100 97-2 '100

too 402,8 1861 .......... 112,864 109,811 115,228

100 9792 102,0 100 104.9

1871 .......... 132,498 129,137 132,979 100 97'4 10013

100 102,9 1901 .......... 177,607 174,881 179,685

100 99?4 lO11 100 102 7

* Col. 5, Table 9. t Col. 5, Table 12. 4 Col. 8, Table 10.




TABLE 14 Contd.-Ratios of Estimates of Births.

All Married Women All Married Women, H. W. Table after (15-.54).* less Surplus Wives Final Correction.:

Col ..... 1 2 3

Scotland.

1851 . ... 91,149 87,964 90,009 100 965d 98 7

100 102-3 1861 ........ 97,147 93,722 95,929

100 96.4 95*7 100 102-3

1871 ........ 104,879 101,267 103,866 100 96-5 99

100 102.5

Ireland.

1861 . .. . 163,466 159,024 158,510 100 97-2 96 9

100 99 6 1871 ........ 146,766 142,259 142,668

100 96 9 97-2 100 100 2

1881 ........ 128,557 123,982 123,382 100 96.4 95.9

100 99 5 1891 .... . 106,528 103,319 102,829

100 96 9 96 5 100 99 5

* Col. 5, Table 9. t Coi. 5, Table 12. : Col. 5, Table 12.

On comparing the results of the different estimates of numbers of births given in Tables 9, 10, and 12-see Table 14-the ratios of the estimates derived from all married women to those derived from married women less "surplus wives" are sufficiently uniform to suggest the reasonableness of adopting a correction figure for " surplus wives," which may be used to fill up the gaps in column 6 of Table 13. The arithmetical means of the figures in column 2 of Table 14 give the following as the percentage deductions which (may be taken to) represent the corrections to be made (deductions) for the " surplus wives " included in " all married women, aged 15-54 years ":-

Englaiid and Wales ........ 2 3 London ......... 2-5 Scotland .............. 3-5 Ireland ......... 3'2

Applying those corrections to the estimated numbers of births given in column 5 of Table 9, the totals set out in column 1 of Table 15



1908.] affecting the BirthRate. 27

TABLE 15.

Estinmated Dilferences. Nunmber of Birtlhs on Estimated Mar ried Number of Recorded Women Births Number of (15-54), by Constanit Birthis. A . c Ddafteolfr Birth-Rlate. Bits. A. B. C. Deduction) for Brhlse " Surplus Wives."

Col ... 1 X 3 4 5 6

England and Wales.

1851.... 626,691 626,691 597,979 i 0 - 28,712 - 28,712 '61 .... 725,034 701,894 676,222 + 23,140 - 25,672 - 48,812 '71.... 817,095 795,897 779,630 + 21,198 - 16,267 - 37,345 '81 .... 919,035 908,702 850,245 + 10,333 - 58,457 - 68,790 ;91.... 1,007,668 1,015,239 872,874 - 7,571 -142,365 -134,794

1901 .... 1,176,248 1,134,311 918,294 + 41,937 -216,017 -257,954

London.

18a 1.... 93,527 93,527 78,610 - 0 - 14,917 - 14,917 '61 ... 110,042 111,297 95,162 - 1,257 - 16,135 - 14,880 '71... 129,186 129,067 113,101 + 119 - 15,966 - 16,085 '81... 148,033 150,578 129,262 - 2,545 - 21,316 - 18,771 '91 .... 158,272 167,413 132,110 - 9,141 - 35,303 - 26,162

1901 ... 173,157 179,571 129,722 - 6,404 - 49,849 - 43,445

Scotlan,d.

1851 ... 87,959 88,122 .... - 163 .... .... '61 ! 93,747 93,747 96,555 i 0 + 2,808 + 2,808 '71 :::: 101,208 103,122 105,724 - 1,914 + 2,602 + 4,516 '81.... 112,881 114,371 115,095 - 1,490 + 724 - 2,214 '91 117,413 122,808 114,673 - 5,395 - 8,135 - 2,740

1901.4. 138,074 136,871 123,549 + 1,203 - 13,322 - 14,525

Ireland.

1851.... 168,305 171,905 ... - 3,600 .... .... '61 .... 158,235 152,015 .... + 6,220 .... .... '71 .... 142,070 142,070 146,710 i 0 + 4,640 + 4,640 '81.... 124,443 136,387 122,304 - 11,944 - 14,083 - 2,139 '91.... 103,119 123,601 103,088 - 20,482 - 19,973 - 31

1901 .... 101,002 116,497 98,772 - 15,495 - 17,725 - 2,230

NOTE .-Difference: A = column 1-2. B = column 3-2. C = coluimn 3-I.

are obtained. It may be assumed that the estimate for one year .(for England and Wales and London, 1851 has been taken; for Scotland, 1861; and for Ireland, 1871) represents the full fertility of the women of the country. On the further assumption of a constant birth-rate, the estimates given in column 2 of Table 15 have been



28 DUDFIELD-So2ne Unconsidered Factors '[Mar.

obtained. The differences between the two estimates are set out in columns 4 (Difference A). In columns 5 and 6 of the same table will be found the differences between the recorded numb3-rs of births and the foregoing estimates. Difference B, algebraic difference of recorded number and estimate based on constant birth-rate. Difference C, the algebraic difference of recorded number and estimate based on married women less " surplus wives." The last difference is the one to be considered. Comparing 1901 with the standard year, and allowing for the difference of that year, the following estimates of the deficiency from "restraint" are obtained:-

229,242=36 per cent. of the estimated number England and Wales ........ of births (England and Wales, 1851) based

on all married women less " surplus wives." r28,528 = 30 per cent. of the same (London)

Lo'ndn . l,I estimate.

S 17,333 = i8 per cent. of the same (Scotland, Scotland . 1 1861) estiwate.

r 6,870 = 5 per cent. of the same (Ireland, 1871) r estimate.

These latter results approximate sufficiently closely to the estimates already given.

One reflection may, perhaps, be permitted at this point. "M Moral "restraint " is, to a considerable extent, the outcome of Malthus' teaching, the basis of which was the supposed danger of the population growing faster than the means of sustenance. During the past autumn I was much impressed with the figures given in " The Times"' Annual Report on the cereal crops, and with a report issued by the Board of Agriculture.

The former12 shows the increase in the amount of wheat raised at the present time from each acre under cultivation. In 1807, whern the yield was regarded as a. large one, the estimate was 20 bushels to the acre. In 1897, when the yield was described as under the average, it amounted to 29 bushels. For 1907, the official return is 33 97 bushels to the acre, an amount which is, at present, described as " decidedly over the average." It may fairly be anticipated that that description will not remain as a true statement of the case.

In the Report of the Board of Agriculture'3 is a table showing the increase in the total population of the principal wheat-consuming countries and the increase in the area taken up for the production of that crop. It appears that between 1881 and 1906 (the dates are approximate only) the inhabitants increased by 33 per cent., and the area under wheat by 42 per cent.

Much land suitable for the cultivation of wheat still remains to be



1908.] affecting thte Birtht-Rate. 29

utilised, and the scientific improvement of the plants is as yet in its infancy. Hence it appears to me that the principal argument used by Alalthus lacks solid foundation. There are, however, causes for "moral restraint" other than those founded on Malthusian doctrines. Such causes will probably remain permanently effective.

Bibliography. I Newsholme, A., and Stevenson, T. H. C.-Human fertility in the United

Kingdom and other countries as shown by corrected birth-rates. " Journal of the Royal Statistical Society" (1905), lxix, p. 34. Also: An improved method of calculating birth-rates. " Journal of Hygiene," v, p. 175.

2 Yule, G. Udny-Cbanges in the marriage- and birth-rates in England and Wales during the past half century; with an inquiry as to their probable causes. " Journal of the Royal Statistical Society" (1905), lxix, p. 88.

3 McLean, W.-The declining birth-rate in Australia. "Intercolonial Medical Journal of Australasia," March 20, 1894.

4 Statistik Tidskrift Atgiven af Kungl. Statistika Centralbyr&n [H. 139 and 143].

s Bidrag till Sveriges Officiela Statistisk: A) Befolkningstatistisk. Ny f6ljd xxiii. Statistiska Centralbyr'ans underdaniga beraittelse f6r Ar 1891. Tables 11 anid 12, pp. 32 and 34.

6 Duncan, J. M.-" Fecundity, Fertility, Sterility, and Allied Topics." 2nid Edition. Edinburgh, 1871.

7 Lewis, C. J. and J. N.-" Natality and Fecundity." 1906. 8' Duncan, J. M.-" Sterility in Woman." 1884, p. 27. i Beneduce.-" Giornale degli Economisti." 1907.

Ei Kier, A. N.-" Bulletin du xxvieme Anniversaire de la Societe de Statistique de Paris" (1885).

" Kor6si, J.-An estimate of the degree of Legitimate Natality, &c.-" Philo- sophical Transactions," 1895, p. 781. (An abstract of the paper is to be found in the "Journal of the Royal Statistical Society," vol. lvii, p. 690.)

12 Article, " The Cereal Year," " The Times," 7th December, 1907. 13 " Agricultural Statistics," vol. xli, part iv, p. 345.

Note.-An alternative method of estimating "surplus wives " is to be found in " Studies in Statistics " (Longstaff), p. 384 et seq (ed. 1891).




APPEND IX.

TABLE I.-Legitimate Bir-ths.

Scotland, 1855.

Ages Ages of Mothers. Totals. Fathers. 15- 20- 25- 30- 35- 40- 45- 50-54. Fathers.

15 ........ 167 136 22 4 - _ - - 329 20- ......... 1,015 6,486 1,916 244 27 6 2 - 9,696 25- ..... 375 6,673 10,702 2,395 356 39 1 1 20,542 30 . ........ 77 2,030 7,221 8,640 1,784 186 10 1 19,949 35 ........ 24 705 2,975 5,712 6,255 733 29 5 16,438 40- ........ 8 227 975 2,636 4,010 2,748 121 2 10,727 45- .. ... 5 58 372 877 1,734 1,605 339 4 4,994 s0- ........ 28 160 415 632 746 178 11 2,170 55 ........ 1 10 50 108 261 236 83 11 760 60- ........ 4 30 57 127 110 26 5 359

Totls } 1,672 16,357 24,423 21,088 15,186 6,409 789 40 85,964

TABLE II.-Estimated Numbers of .3farried Couples.*

Scotland, 1855.

Ages of Wives. Ages of

Husbands. 15- 20- 25- 3 35- 40- 45- 50-54.

15- .... 321 260 32 7 4 -

20- .... 1,820 14,205 4,700 810 168 42 13 6 25- .... 707 15,067 26,982 7,100 1,285 269 54 22 30- ... 180 5,201 19,877 26,344 6,578 1,479 341 101 35- .... 52 1,474 7,852 18,325 22,847 5,852 1,276 305 40- .... 22 652 2,774 8,561 17,112 20,345 5,007 1,384 45- .... 11 203 1,126 3,060 7,345 13,657 14,836 4,211 50- 11 102 491 1,509 3,085 7,817 11,535 13,672 55- 1 33 209 432 1,135 2,538 4,757 8,636 60- . 1 36 131 420 819 2,128 3,549 8,476

* See also Table IX.




TABLE 1II.-Fertility-Rates per ioo Married Couples.

Scotland, 1855.

Ages of Wives.

Ages of Jusbands.

15- 20- 25- 30- 35- 40- 45- 50-54.

15- .... 52{024 52,037 69-750 57-143 - -

20- .... 55-769 45659 40-766 30 123 16 071 14-295 153394 -

25- .... 53 041 44-288 39-663 33-732 27-704 14-500 18P51 4-545

30- 42-777 39 030 36-328 32-796 26-208 12-575 2-932 0,990

35- 46,154 47-829 37-888 31-170 27-377 12-525 2,272 1-639

40- .... 36363 34-815 35 147 30-790 23-433 13a507 2 416 0-144

45- 45 454 28 571 33-037 28&660 23-607 11-752 2-284 0 094

50- .... - 27,451 32-58?6 27-501 20A486 9,543 1-543 0,080

55- .00 ,000 30-303 23-923 25-000 22-995 9-298 11744 1-273

60- .... 11111 22-900 13-571 15506 5-169 0-732 0-589

Note.-Figures in italics represent rates calculated on less than soo couples

For adjusted rates see Table 7 in text.



32 DIJDFIELD-SoMe Unconsidered Factars [Mar.

TABLE IV.-Married Women. Proportional Figures.

[Total (15-54) for each year = ioo,ooo.]

Census of Ages. .

185i. 1861. 1871. 1881. 1891. 19(1.

England and Wales.

15- .... 871 1,003 1,034 863 693 522 20- .... 10,497 10,846 10,810 10,710 9,949 9,205 25- .... 17,629 17,273 17,494 1 35,800 35,864 1 17,833 30- .... 18337 17,853 17,901 18,769 35- .... 16,508 16,379 16,054 31036 31)373 r 17,153 40- *--- 14,632 14,973 14,516 I ' 14,694 45- *-- 11,754 11,990 12,093 21,591 22,121 12,163 50-54.. 9,772 9,683 10,098 r 2 { 9,661

London.

15- .... 942 1,071 1,068 979 735 553 20- .... 10,780 10,968 11,375 11,399 10,720 9,922 25- .... 18,429 18,269 18,624 137960 37584 r 18,545 30- .... 19,685 19,078 18,816 j ' 19,204 35- .--- 16,794 i6,658 16,241 30,692 31 087 17,161 40- ... 14,476 14,920 14,269 f ' 14,339 45- *-- 10,460 10,771 10,827 l18)970 19874 f 11,501 50-54... 8,434 8,265 8,780 J l 8,775

Scotland.

15- .... 889 848 855 723 507 635 20- *. 10,330 9,949 9,335 9,756 8,733 8,912 25- .... 17,770 17,468 17,543 17,633 16,892 17,401 30- .... 18,360 18,381 18,468 17,732 18,343 18,462 35- ... 16,529 16,412 16,648 16,766 17,165 17,279 40- .... 14,817 14,999 15,015 15,214 14,853 15,095 45 - .... 11,271 11,975 12,066 12,135 12,921 12,443 50-54.... 10,034 9,968 10,070 10,041 10,586 9,773

Ireland.

15- .... 7,894! 1,067 815 582 484 376 201 *- J ' 10,474 8,234 7,514 6,599 6,432 25-.... 3803 14,903 15,402 13,734 13,159 .32585 30- } 33, { 16,604 19,520 17,992 16,871 . , -5 . 32598 13,324 14,506 16,017 15,569 33171

40-- .... I 3,58 18,166 16,357 19,362 18,145 45 . 23,428 { 11,744 10,861 11,646 13,716 1 50 -54... .f 13,818 14,305 13,153 15,457 J 27,436



1908.] afteting thte Birth-Rate. 33

TABLE V.-Married Women Jndex-.Yumbers.

[Proportionis (0?) in 1851 = 1oo.]

Ages. 1851. 1861. 1871. 1881. 1891. 1901.

England and Wales.

15- 100 115 119 99 79 60 20- 100 103 103 102 95 88 25- 10011 981 98 99 98 199 100 101ho10 35-

.... 1001 9971 981 1 1042

4- .1001100 1901101 979 98 1100 101 1001102 40-5 ....... 1001

10 99 100 10 Olo

.5 . } 1001100 102 } 101 103 103 } 100 103 10 101

London.

15- 100 114 113 104 78 59 20- 100 102 105 106 99 92

30- 1001100 99 98 951 } 9 99 99 101} 99 35. .... 1001 100 '9 103 98 9 98 99 1021101 43- .100 . lo 3 97 } 9 } 99 45- . } 100' 103 } 100 103 }104 } 1105 11011 ,50-54 .... 100 J'O 100 1010 104 10

Scotland.

15- 100 95 96 81 57 71 20 - 100 96 90 94 84 86 25- . . 100 98 99 99 95 98 30- 100 100 100 96 100 100 35- 100 99 100 101 103 104 40 100 101 101 103 100 102 45- 100 106 107 108 115 110 50-54 .... 100 99 100 100 105 97

Ireland.

15- 100 146 115 102 90 86 25- 100 94 105 95 90 98 35 -- 100 96 95 108 103 102 45-54 .... 100 109 107 106 124 117

VOL. LXXI. PART I. D




TABLE VI.-Percentage of Married Persons included in the Combinedc Age ("H. W.") Tables.

1851. 1861. 1871. 1881. 1891. 1901.

Englad and Wales. MALES.

15- ... 7205 7520 79A46 82-38 20- ... 9250 92-85 93-27 9840 25- ... 94-67 94-62 94-69 9588 30- ... 9504 95,09 94*95 95 91 35- ... 95,27 95,32 9509 95.55 40- ... 94-83 94-92 94*90 95-03 45- ... 94-85 94 77 94-85 9451 50- ... 94,16 94-25 94,25 93,89 55- ... 9400 94 04 9406 92-95

Total .... 94-53 94-57 94-55 94'76

FEMALES.

15- ... 8703 8762 89-42 9172 20-- ... 91-04 91-42 91P74 92-61 25- ... 92,01 9234 92-48 93-14 30- ... 92-77 92-96 92-98 93-51 35- .... 93.35 93-39 93A42 93-69 40- ... 9318 93-42 93-43 93.43 45- ... 9330 9348 93848 9303 50- .1 9270 91,00 93,06 92-53 55 - 93-35 93A40 93,33 91P74

Total.... 9 274 9Z 93 92.99 93 CO

London. M ALES.

15- ... 6160 65 09 73 07 77 00 20- .... 9109 9201 93.43 94.79 25- 93,85 94,38 95,00 96,00 30- 94-01 94-61 94,97 95.59 35 - 93.99 94*55 94171 95-02 40- 9325 93,99 94.45 94-26 45- 93,21 93(60 93-96 93.47 50- 9225 92,73 93-16 9270 55- 89-88 90 92 9161 90-12

Total.... 9 z8 2 93 46 93'95 93'91

FEMALES.

15- 85-91 8668 1 88-91 89,60 20- 90'23 9076 91-91 93.37 26- 90'66 91-56 92-33 93-12 30- 91,19 91-98 92,30 93-13 35- * 91-60 91-93 92-32 9302 40- 90,82 91-38 91-85 92 56 45- 90,63 9082 91-50 91 67 50- 89,32 89 70 90 28 9073 55- 87,64 87,38 88&49 87-63

Total .... 90?4z go'89 91-51 92 o5




TABLE VI Contd.-Percentage of Married Persons int Combined Age Tables.

1851. 1861. 1871. 1881. 1891. 1901.

Scotland. MALES.

15- ... 7097 69-76 76-85 20- ... 8944 1 93-68 91P26 25- ... 9269 92,82 93,68 30- ... 93,88 9400 94,30 35- ... 9433 1 94-32 94-60 40- ... 94-23 1 94,17 94,32 45- ... 9P51 92,23 94,19 50- 93*95 93.93 93.97 55- ... 94.77 93*37 94100

Total .... 93'84 93-77 94O00

FEMALES.

15- ... 83-03 83,33 84-52 1 20- ... 87,92 88-22 89l16 25-.... 89,59 89,55 9041 30- ... 9070 91P19 91,12 35- ... 91-69 91,55 91,70 40- ... 91,76 91-61 91-78 45- ... 92-25 92,21 92-07 50- ... 9227 92,03 92,18 55 ... 93.54 92,90 93-02

Total .... 91l99 91-O9 9 I46

Irelaud. MALES.

15- .. 76-35 74,87 72,25 67,92 20- .... 8871 88-92 88-68 89 07 25- .... 9178 92,11 91-47 92,54 30- - 93-77 93.73 93-58 93,58 835- 94,13 94.55 94-23 94,15 40 . 94-79 95,21 95-13 9471 405 . 94*49 94-91 95,06 94,81 50- 94,51 94,90 95.53 95-41 55 - 93.04 94-88 94 77 94.79

Total.... 93.56 94'35 94'4? 94'42

FEMALES.

15- 83,31 85,03 81-49 81,52 20- .... 88,79 88-27 87-78 88,74 25-- 90 55 9029 90,50 91-26 30- 91-89 9197 91-94 92-32 35- 9282 92-73 92-67 92-84 40- 91-83 92 58 92-56 92-81 45- 92-67 9305 9373 93.44 50- 91-41 92-82 93-68 93.47 55- 90-28 92 59 93 47 9319

Total... 9O095 91-93 9ZZ29 9Xz55

D 2




.~~ I00u 1 c0ic lo0a I'OoC loo+Ic\c

X @ 0 &a an lu CtC 00 L_t 0 P-

; -

60: _00 *n toL -8 t M m

?( D I a 00

t tI Q-

k ?

M I + I00

to

_ __ _ _I4 t 00

U 00 O m X

m X

I i . I lo - 4 p.4 0 r -4 _ _ _ o_ _-4 cz c f-q r4 a __ _

I~~~~~~~ I >S o0ntCC CQ0t

r~~~~ 0 I HOQ:I 00b~00 1 mZIQ0C Pcz

--1 '0o1I I IX~1^@1^^

. ~ 11>0 1 0.. w &

l P4 C

I Ct 0

fC

0

C?

0

01t

0

C_ i:o

It 1>CQ _-'h0 _0 t _1 0 w- I o

C to

oeq-

I ____

_k_m_- ____

,? O $ > Q 4 ? I ̂ ̂^N > 0 + O ~~~~~~~~~~~~~~~~-4 1* km4-

coy4w O 0

p

.

I-4..d

1

_P4 P Y -444

%v 1 t- w 0 00ovc

T_4 - TT T I I I II S~~~~~~~~~~~~~~~~~~~~~~~~- P-s I- 1- ka ul C> C* M co ? 4*tO?

0.4 * 0 0 M GC co GD 00 c W Mt M S Deo

O I- .:, I . "

l l~~~~~~~~~~~ la c co I I | zo X I~~~~ ODF8 to 0;w I a o N; 1oc I 0" teNI * bSHXHoe:o A I A A e q I Q o X e~~~k I 0 t^ Z t t - I laN 10 llb M o

1?s 3 ii 0 'N *CZt-' cz 1>Xt 0- - 148> 1< Y

~~~~~~~~~~~k II _1, P- 00 I - CO I- ot * I oOr0 ecoo~~~o L- oo U>Q

I eq,O oeo

4~~~~~~~~~~~c c

I~~~~~~~~~~~~ Mg Oo U) 0 00 10 |~~~~~~~0 000c k- 0 cq cw a



1908.] aj?ectin.g the Betil-Rate. 37

| Ot>G O u IfO Cn P ~OOO | > 4 | QO OQ 0| I C o km 0

&t iO,-u- 0 C' cq el

t - 7--4t 0 m -*

'-4 0 .X i c'oo k$a&c Or-O L-fc e o W

C, q,-.I- Iq i 4a m m I Ik- _- 8 & aOIIoil.ice Q O - -OCC O- - -

I bO O]_ O 0~ _,i C;lQ C;l-4C r- _ o ^ I __ O 3 0 w0 q0t - mo ~ sss s<Dr ! c m owco oo8

I I -I c - OD tz to I . o o km I I-

| t 0 q 0 C

Io to o

caj Cao

C 00

cqc 'c

m

'

_I I O r ,* cq M *4 t- 1- x- _ cq 0 -X M. a> cs; . *o_ M P- co

I mjaoo~ ao :I c

ID p --I r-U C- 7-4 C J -4 cq cI ____I __ __ __

~~~~ I__~~~~~~~~~~~__ __.___ I neNs lseaz m cqc 0 1q Um -1 t- C km Itf 000c cqvk-

- - ~ ~~~~~~~~~~~~~ 0 0 m m ma 4c q 0 -M

qcq IN I 0

oo .!f p COQC tCb1s U*qO ;UgCZ _ l c o km o W 0co l8f

K c okm cq oo,- I oo 0 r-4 , (4 c v, c c I U* t- _ _ _ - I f CO_l _ _- _

Ic Xo It- to t i I co I co 1 4e I t oo 00 co co I o cnW.I co cso t- I t- t-oo

I Io r- r- r- r- c ÎN tO tIe ? I~ o .e

}D e0 Co 44 1 r- <D O .at ao I co co4 csi j cq C, ca UZ I0 co c k-

S~~~~~~~~~- rI _{ 00 U* I Du c:c 5 U.) > co co IU :v k- 1 I co 0 0C l I ~~~~~~~): P oo co I Co ..I C00 _I I O P05 blC 4 Cr: Oq : - CO I~~~~~~~~~~~~~U *q aq cq >0U I C_+O e- 0>0H 1- 00q > 1c 0Fm >

o~~~~~~~~~ aa c)i 00 Io to I I0 XoJ-k o ri a qmrI t

b e o - I Ct:> Ct:>^Ct:>^C;I I t0e{ t0e Ct:> H^H^co - u- co t- vzco t-

, O

<? 2 I I X I | I~~U



38 DUDFIELD-SoMne Unconsidereed Factors [Mar.

Q OD O J 000000 00 0 0t 00 0 00 0 O U 000 k- Kb I I00 100 0 00 N UZ C

-fl-4 cJ 010 I0^^- 0^ ^00 0C0 4- U: 4 to r- Ilk+O b DC D :eq e XXXC

I I

I I H _ XI ~ I000~IcOlO 0 I O n I W wI I U:k m 1 a - I I I I I H H H X Nri m c I 00 m t- m k C: o I t- oo C5 m

A I I I I

I- "i1 01010 I N N cc

tC

o 5___ ____ - _N;___ o_e_oo __to^

I caI x: Ioco la>q MM CZX In oco o

CO-I t q N 00 I CD

. O I 0 00

I 00ti 00 co-H 0 00 0 _1_

I) ____-____ ___ I CqJc0cotoco I t- - I ., . oooo 00 10!a- I M 0 - = I o c

t o l I~~~~~~~~~~~~~~0 to IZ m aq t- k-

ob^n I Xcn I +

te 06CC4 0 06 0001 f: ,1l000ai t: x ~ ~ ~ __ _ _ I_ __ _ I_ __ _ I_ _ I _______ ________

0000I0I I00000~ i00 1 I

00010 00~0 Z - t . 000001l m -4j0C010k or l0t~~~~~m 001Or-I 0 00 00 0 -?- qx I U Q I ~I I I_ _ I__ _ _ i-

7 [. I I I I04 I I CO 10C0f. O I I , I CD 1 Ci N I b 0> CQ0 I 10c0tr 0 1C0. OI10_4C0 J-

t 00X . I X>H I 00 .00 00 O 0 0H0X^ 0 0

10 l ti ( 4) 01 01 t- - o o0 o: I c I r mO

~~~~~~~~~~~~~~k m I, 1q 0 b 1 "It* Iq CO bO t0 1 0 > ~ ~~~~~~ O 4 I q c I m -I k o 4000C x Cw 00 m 1 000D m I cq U"

H ~~~~~~~~~~~~~~~~~'l X- N m I-l X I -XIf -r. 1 I~~~~~~~~~0 _{ Cb C6 O U- 01- CO I -Os 6C 00 1C t :; 0f: ? e e; xf: 00 I I Uz ?s Ci m 1 0: ~ + b I O X-0 0C QC UD CC~ I T- T- "

UA~~~~~~~~~~~~~~ m I m Ci :; 1t |b :; D cq U di Ot 0 o It 0tb 0

Gt l I _{ _{ ~~~'Z O 0 , -i _ tC 5 0 fCq| I oZt c :u>t

ulco (D I'l X* m oD m I 0 In oo wfS (D tl rC5 D I q @ Co I oo oo

CO I U0 D 0) 0: (D eq I0 CO CO CQ -' I X*ss IX0 OtC

X6 lo 0:0X0 16 ::0 1~ 4~

e I Ct3CD ? I ocôtqcq ooooÎU aHH



1908.] affiecting the Birth-RaSte. 39

t- =

,cc c 4I C.c e oo I a _4 r

Cf. o

= o*H c :c

Z3 oo o ooo O 0 u:I uzu 00 00 m 00 xo km la -3 C g rI I.-

"- 7 H

I N m m IN m m di c a x q o oI om o o t- uz I oo m c:zI cz I - U" m 0: e 4 t_ Ci aq m C= X0 C 0o q 00 1i >D t- 0: 00 aa o c

(D o- 00 oo m km e b oo co .- c , 1b aa, cq i m m 00 di oo D t- .n

co- eo- r-- cq oq oq oq 0q N o:

C o m co uzV o' m co

-

~~ ~~~ ~~~ ca m ~~~~~~ m m CS CQ Cit CO 0:C 0H

I .- cesooocI N CN m so rI r- r.- 00 4 k- L-bt o t t<: e ct q

I~~~~~~~~~c ca cq c : o+H ta m m s Dr D

s ~~ ~ ~~ X 00 00 H 0: e CD b s 0 N 0 0 0-. k- = Oo0 Cl.

mm - i.- ec CO O0 on "-I r DOCt0 D DC C I 00O ". C ] d ua je CD ~- s 4 cq U HaUc i" ?q 0^t OO a q~X0 + | uaboo I nôzuro ! oosss I oo: I mcqcaH I c Dctt o

M M _ - ~I I Cq dq Cq 4 ' 0e cq 00 0 I~~Io~bc

m~~~~ ~~ ~~ - 0 I xo = -I = .I I. -90 N .- m II o m m m q rir- .Ir- -4r- - 0-1

U~~~~~~~~~~~~~~~~~~ N I M M M I M 0+l- Ho" k-e10Q bO t I I~~~~~~~U X 0o: UZ CI C s Cq I-- t 0 : I 0 00 0O u 0zC

~~~~~~~~~~~~10 o 00 I0 00 CM ul CO i0 M r- aq U D i oq ~ ̂o00o du ^:- O~~~~~~~~~~~~~~~~~~~~~ tn cUIbtby\ P DU :> In i_ 1_ _ Dee e~~~~~~~~~~~~~~~~~~~~~~~~r bD I III

r- -4r4r4 r4r4rIri r qr q rqr - - - - - - - - -

oo. 00 MOCC| I0 M^^^^ 00 m 00 0 0

Iq Iq Iq Iq r - "I 1> r4 '>r-

I o: t

b~~mIo I oOo 1 0 I O Iou o



40 DL-DFIELD-Some Unconsidered Factors [Mar.

r- ~ OCqC e aq-4 ,-4 10 COCW a 1

rn . |

O _ 1 1 Sit

ee | - 4i 0.1

| f of

_ t- to t-

| =t t-

+ QL

ac en- I oo k 00 X I t- k- 1- u CC>XÎO 0: \ X- m *~ I l-4 ' ' I-c a o:o

I I I 1OO I 'HOC I wc j.to

I4 C1e 1iIC:

1 I I I ~~~~- \?O COCQCC COCOQ

____ t ___ r- jr,4r" m -4

I~~~~~~~~~- P- aq.o I a., oo I cAu 0 0m1C+

4 1 r-4r-4 ?.-I

K W

O ? I CO 1 _C _1 G O It: 0 u XC NO

cq r-4 0 o !4 N~~~~~~~~~~~~~~~~~~~C . COCfC o aC

g^co c^ I c c I a

__________I~o a ___ m - kf~Xkl -4 r-Ix 6 1 1, 1 I I

r4r4 ~~O~~I'~4 C~Ci~~ CO'- r-4

w r 0 3 I c I cq I N I NX I N0 1 00 C . I _ _ I _ _ _ _ _ __ _ _ _

OC C e I I l ?eX I Q4C61 1

v r-4 eo o-4 kfl cXOOC *CD r-

PC CCd c 1eM U Cci cCt'r- 1 t- o I -

C^

oo P-1j CD I CC] C^ I CO - X IC 4OU I It~CO~ ~OC~It~ 1OI 1 I Itq t INt

I ~0 0 - I - 006 00-x

rq -q '-4 0) .0~~~~~~~~~~"O"

<~ ~ I I I I

= Eo CO X- xflqi CO C C k

1:XO0 1 sQ_i _e {~k CO<D5 m oi'.4ci c6 c6> a I 1> C Oc P||O N. 4 sP CO I r-4 or ; o if Q

"4 1 0P- 1 *? w t- I CD C O r IQ t- 1q 0 XI CQ

t -,di Cl*oo o o 0e k- c N oo 00N cCO ae o I :UO eD I 1- w cc 'e CO CO r- r e H I0 q I C

m I I *-l zS; S;^ It:>^siFg X I C;x^~ ; I comcm X, uI ^ -

oo 00 00 ceIo ou o qIc :0 u q

r-- 1" 1.~ CO 1




. t t-o 10!4c X>-s r-l mco ok lcaz tlo - D I I O eO I a I ,4o co I *:u^:I c o o oo m

cooo

m

c

0 nt o oacq

X-

_O ooo

~~ I I _ _ _ _ _ _ _~ _ z _ _ _

,

Io ORDCo I ECO:@ I acoo rI I ao I ca I -t __ __ - ,-.I ,-.I -

XOu; 00O COCD XiX HOO N CD

o o0o I o oI x cq oo I x_ _ o1 I c _ U: I oo o

cq c oq cq I to.oo Ho oH I o co I coao oD + io

Iuc I I%DIO 1O1b 1e g -4

C

q r- =M r-

N i U X O+C 0t

Q AU

iK;oKo~3c0, 00 Otac OOO 8O

I0c q c - ot 0 X MM I

m Co C4 C5 io C CQ c C c X0 X

Ca --- ee I -~klcc

-4r4 mc t0Cj otl.. COOr4 1 0cO tco C0

00 CD _14 cO " m CQ mo U: t- 00 Ct 004 ao t- a o u D CO U: GO eD t- IQ VI\ ^s = 1*I- t_ oo o c;,

I r-I I 4 I I

a~~~~0 I iooc I IO~L.~'~~I,4~ I IOC

t I I co i | c co I cc I-- C- 4 Ic oc o

A ~ ~ ~~~ I- I I I I I H I

- t Ihi 0tm.t~.Kt~0L04 oIQo I I I

I ?i - ocq U o i m 0D u 00 0 I X. ooo

.D U S j CO + b I b ~~* Cq I 00 U= X- I O I 00 0 DI O k-U

F I I I d4?eD I NOCO 1-oAD I OO^^ I Xt_ O I COD

't cq o r- r- 1-IN I oeeI oo o X- o0-+

l~~~~~~~~~~~~~~. e ee 0: ce 0: 0 l l v~~~~~~~~~~~~~~~~~~~~~~~~a GI I l I

.C4) r.-4 co 04 ur O I X CO 0

C Icqall 101 01o ~~ I e o u: I u: ce ~~~~~~~~co ca r e I

x o xo r- xo 4 sP X- csm

H I I N ca o | u: c e 0 m o I ONao I Q :u Iz co co mm co ca o aP oo' ooof' a& oo - CO co Ci C

m I I I I i I

I 00 I Df k-I-4v O I kO 0 I m 0 I X 0

I10:U AC O Io~b IA CO sU CO CO

d N I m" -I o4 I I 00 Ô

I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~1t I14 I I 1 1 1

~ ~~1 1 1~~~~~~X- x 110 1 '

<t I I I I I~~~~~~~~~~~0 I 0 . I-e

: o e o ut > c:~~~xo s u; uX X cO t~~~~co




w I I I I

I;r I I -4 q O jU I km OO C1O <D O4 I m = ~~bL~ ~ IkOC'~~C~ kf~~Q~O~- - -- - - - -Q -O

e$aqcq $&

X c~o irq -'

mooo'at 114m 1

um i I Iqc--t 0 I1 O IO I cok uf? ",:: I I I I c 1 k

I1 1 I ~~ oI o00 I 21e 0I CqO Io ktoCto I I ,,, I ioH eococom I co o'Ii

I t C,oIt

_____ ____ 00LD c - 00c Z 0o $'tl co t- l

II I CC__ l~~~~~~~~~~~~~~- r- I _IC0 1 1 t- CO CQ I q C;1 r-i 1

a~~~~~~~~~~~~~~~I 1q c )c 101 I IqmC om N -x -c K I C 0oIco I qoeo od4 X= I =o-CO

co- Q i I I . I I

j1~~~~~~I ~~~~~ ~~~~IC~~~:o6'?00 6 e6cfm0OO m 00 C~~1~~~4 ~~~0~IC0 t-~~~~OO

~c0Oc c ck CODO

8-4 b~~~~~~c _ _ _ _ _- OD 1 .. 1 .tf 4 ~ 0 m t - __, ____m O I C5 00I e In I 4O-cO c -I +- I n oaO I0 Ux D -- "It -I 400 A1 X I,, IH~,ooo,Qn I oscoo

co "tcOzcOI c co cODoq ot I co ao ^.I , 0 m (L I - - I _ C) __ 0 co 0 __ _ 00

H I IO0x1 c0 - t <n cs i to 0 I O C00t t to C* I I c0 o

k~~~~~~~~~~~~~~~~., o0 to co 0, 00 m eD I uz m CQ X- co m 0 0 t- O \

OIII oD OD I COC0 2 C0 I C 0 C O

r- t 0 0 r- t r4 00 tom 0000to cC0 0 00 C), C)

I C - 45 00 I o m to 00 to I4- 4 00 Ct D O , 00 Cq I 0 _- Ci I cot.000 I000 C to 0 4 I C o I 00 0 1 C C I C0JQc.000c

oo I 0 C) 0 u I C O 0 0 C Q I kQ Cq O GD D 0 to 0 0 0oo

I I Ii~ 1 OQ~IC~ Iq 1q

00 to U. 04

1 N

OO ut co

I aO r-4 O-

o Xa >-4I

H | C] Ci _I Ci I i C 00 D to t- 00C m Cto t- d0 I to X- C0 0 (L X- 00

0 00~~~~~~~~~~~~~~~~0 I tCOCLl~~~~_ilqCq~1-




. t- cs t ooooc t- 000 0 o 0co P4 Icroq t- icqo 0 8 8 XS It_ 00 llU:CU:O x00 CO t-1 O O m tO D to OM= O c It- 00 0 CQ m 0 O u:> Cil 1- O- 0 xo _I O 19 0 o0 _I4 O O O

O O 0 co I t 00 L- I o o_I O M cqol I Co O OO

o w o m x wo - N I -o t N t - c o N oir X r co OOf I~ C~I oo -h u I~ O0 t u0 r I Co 'ft ?O I P- - O C C1 I . , x- t 00 uZ I O 00 Cq

e, CId CD km ? O CO r e C Oe O l a

I I o Ci^'l00 1CCr 00 C U 0 0, C c -4Q CO - 4t xC 0

0 0 !f

0 00000 I 0ICC La-4r-4- 0 c a

ICC4 E

I Ho,-~cq cq cq iN c o- oV r o X ao

o so+oo -Po M M : M o coo u oc r00' 00# II u ooo

cJ oo oq 0 s oo 0 M " o M ,q XO '1 M N l II xo M o = M M 1. ,

2 C^C^<D I Ou1 0 00 H - H-^.I4.e, 6 6 I ts^ 4ôo,- I >ô 06 Xs I 0-4

m t - 00 t - I o o0 q -I _ _ _ 00, CiOU:ees O o - M M o D C q M: M M OC r a ^q M?? r-I r-I xo M xm n^cs X^ o^^^^

V

I

C000 rI

00 000000 I0 0 M c

_ _ _ _ M

_M _ _l_II _ _ _ _ _-I _ _ _ _ 1

a~~ ~ ~~~~~~~~~~~~~~~~~~ _ '- l l

_ ; i - 0 _ __I 0 _ _ _ M -I i 1 0 ls M I o M - -I

00 ?-. xo M 05 &O t-LOa C I q M I C,-40 : IM ? 0 0 UZ X~~~~~~~~~a o * co 't DOI ?-- XI -4 M V- M M I -X I X e t- L- M w M

a~~~~~~~~~l w ooa o I xooo 1- 0 ~ ~ k- m 1 Ul -M M)t-k

e I I I I t~

;) M I I I I I 0 0 X U $ I Ci V: ~~~ co i- 00 x 0 co - 00 q <D co w 00 cq t- M Cq 0 M M X- M CZ f~~~~~~~~~~ I II co to o 0 I to M - cn M I0 co 0 km c I to o co = If k- X -H

CA III I I I I H ~ I I I i i

~~~~~~^ ~ ~ ~ 1 I1 coC DS DI0 C tIXc tI~oOv t e: D C

c00 =kmt '-d I4 M l o b0 I k0C00kI It I000 I ' O CZ tO

-o COI 0 I C "00^ 4 ' P -4 00 ^q4 *C

a: I ~ ~~I I I I ~~

< ~ ~ ~~ ~~ ~ ~~~~~~~~~~~~~~~~~~~~~~~~~~ r- l I b

< ~~~~~~~~~~~~~oo M'4 IoC: iOe :OC

co I . 00 N > , o o,0 Q , o M M x, 00 0 t00 M 0 , 0CO11

Co -, c n co -H - - oo - -- 00" --00"

I IOt .0 0P COt.0 CD :CItO U) CO~0 00 UZCOt~00 C Ot'-000 00" 00"" 00""" 00"" 00"" 00"I I I~

I . I ' I (UN I I ?

cO oO



44 DITDFIELD-Sonle Unconsidered Factors [Mar.

X;O~~~~~~~~ 1 00? 10 ?I k- CD ?b8 1C CDX 1 8s? 1 - ?

O< Hes 0 0H00O 1 I OCt1 o Oo 04o o

I 11 IHooolg~lnrc

I II I 0"-H0N IOCDCN I3NHX

Ii

I

,t~

II? O C) C co I- OC 0 c11 cq a C + r- CDO O 00 cr; ca o O C) t . co jq HO 00 C-lfi O C Ct LO aoCD m 4R 0D- s C)C

ao co o 0 C) 0 I I4- I I t

_ _ _ _ - ot _ _ _ _ _ _ _ _ _

LJ OO~~~~~~~~~m O- M I: Cmcqk t - e

I~~~~c I, :Bmx ! mcor-l mm o1 o elsomt t ~ ~~~~~~~~~~~ , I I I I 0 ,,I8OAAX=I0

S~~~~~~~~~~~~~~~~~U 0 co "- l I

u I 1 1 A I I IQO I0

k~~~~~ ~ -___ i___1--

oo o I oooI o0 o oo0 o 0

A ali I0 ~ 1 I I I I C I

HH . _____

> I I I | 'I 4~~~~~~~~~~~~~~~~C




000 00. 0 0 0I I 000 00I a _ __ __ __ O_ __ __ __ ___ __ __IO_____ c 0 10 q~ u: IO

O0 0000 OOmO- 0000 000 - 000o

0000 k 00100MCqIoc00o FEms= A -h-~~~~~0r- 000 00 0 00 00

0~~~~~~~~~~~~~~~~~~~~~0

0 00 o om co W 0 r 0 000 0o

Al o00 0 0000 0 0000 0 0 00c

I oDoo-u oI o ooo.e 1 ooo O or 8

I F _ _ _ _ _ _ _ _ _ _ _ _- t- _ _ _ _ _ _ _ _ _ f- _ _ _ _ If o ; m 800k4 4 0 Mc

aIsX~~~!88oHl8soooloooolonno~srl= Oms A~ ,

q~~~~~~~~~~~~~~~~~~~~~~~~~~qc

a~~~~~~0 .n

oocb ooo

00 Io tto co t0 c qo

00 000Cti01 000~H H I ~H I I CHQo 0 00

v3 2' I IOCO 000~O 0C~i0IIO 0~COC 000I I

> ~ ~ ~ ~ __ _ _ _ I_ _ _ _ _ _ _ _ _ _ _ - I_ _ __ _ I I I__ I I _ _ _ _ _

_ _ _ _ _ _ _II I _ _

N g o 0e I ooo0 1 00~o I 0 00~~0 00oooxIHoHxI o

a ~ X "--- l I I I - I Ma n X}

.. , . _ .-~b |e I I . I I I I~~~~~~~~~~~~A S S I I I I I I~~~~~~~~~~~~~C




Ieo I gao~ 1 Ia sloDD oa>o?o+Xo

iz ~~ X ~? 1 ~ ~ om a o la 0 00 lq > m t- OD > o 1 0?>

r,4 4 tE-4 ' -4 '- -4 r-

I _ _ _

co

I - 0

c

1 0-e O_ _0_

1 0 __

l 41 IIO t. O1O I Ot~OQO114 ??+S ?0sm I!

11-1llll1~Q~1~~>X! <1>"1?> 10m0 o,*0t 00

4i I X I [ Z Ic 10 Io0

b! o cQli I I ~0COOo I -4 c c=n

e I I 0 00 H a ~~~~~~~r I O- H 0- 0 OIN0

0 1~~~ ~ ~~~ ~~-4 r4 I r- I '-I '-4 l'-4'- '- 4

tot I - m 0 .I a- _ _ _ _ _ _ _

H I i I __ _ _ 1 __ ______ _____ _______

I I~~~~~~~~~~~~~~~~~~~~~~~~~~~ m q 0 ri 0 OOO -MD 0 o k

'- -4 ~ r -4 ,4 -4 r- -4 '-4 '-4 r'-I I- - - -

-i3 00 J cr oo^^ cJo^ ^ cJ C^ a v ̂oja)^ ^

I 0 0 o co '-

O " O O e O

* 1Dt k CO*. to co t-0 uiOCO - 0 ko wt~-0 k0 Co t- 0 '-

bLm o M o ( 0 O M 0

l0 . "4 ri - - r4, 4, ri IV C



1908.] affectig Ow B&rtkPRate. 47

W 0000 j 00 00_1_I 0000 t-00

_ _ _ _ I IC, 111 C,0 0 o I< I I

o Ocq 0 Im1000 o coo k 40 cot, rU 0 8c oooso o'o ooocq 0ob0- o00-

_ ,_ _ I _ _ _ _ _ _ _ _ _ _ _ o O O o0 O N 0 mm _I O OO tO 0ao 0o

_ i_ __ _ _ __ _ _ _ _ _ _ _ _ K I_ _ i I I

o m OmObt-. 00000 OO)- 000'. OmOb

a n I 0be 0-4s I 000003'-. 0'X400t'-. i 0X>HLO 0 km OOO 0 0 H 0 I O . H 0 0 0 H0 10 N0 00 10 0 -00- ) O O ObbO

0 < OC~0~10~. 0~LO 0 I

A~~~~~ I ?-- 10 8 cOm o - 0?- Rtx oclH ooe oon

o ____ ____o ____ ____ K___ ____

-m IO I I I I I

km co . x 8 8 8 I . ' oo to 1- - l 0 t 0 k to t- _ _ __ _ t-

oo - - oio Q00 00 0 00 0 M~t 00O

l 0~0O eI??IH?I??H??;D000r'CIOObOO

H~~~~~ _- ~ ~ l l l l,-4,4,I

H1~i000 1- 0r-4-I000l I~0 0-I0' I

cxI IH _ _H 1 _ _ Hr_ _ _ _ _ __IH

0000I0 I 0 00 100~O0 10000 ? OOIC t-1:1

OOOCQ 0 0 )OCDO | ???? ] 80-?

I 4~H 4~HH H H ~ ~ H HH I -100



48 DUDFIELD-SoMe Unconsidered Factors [Mar

Is _ _o

_ _o

_ _DO I _ _ _

_co _ _ _

71 II1OX 7 1 1

a ~ ~ ~ ~~ I 0 I* 0zX 0.H O4 1 00e

0~~~~~~~~~ Om 9 8 I 005 8 00 0X 0O Q"

)~~~ K o_ _ > e0b10s00__ ___

___ j.Io -

Q | | | N _I | O 3 0 ~050 0 | - OCD8 H0 H

tOCD I $ s ~ 0 10H0 00F

-I _I I_ I _I

<1TH IIO =?H0I Z ? H ~ -"H "~H "~ H H

_ _ _ _._ _ _ _ _ _ _ _ __a b : X b u D tc

0 K V K ^_ ̂_ _ _^ -_ _ O ^ X^ ̂ -d l i




0-44cq l ooorlo0lg c1ooJ 8=i

000 OM= co (Z)Tqo M l loco l+n oco foulzull lOMk_ coo

o ooo~ oH8 ocIm oC0 OM=

I I IH HH H - H ~ H HIH

?~~~~~~~~~X. lon 0oc tg,c hooc 1? loogo o ? O O O O? O O O O r-i o m o 0

e 1 1 gs~~~ ! gn~~ 1 oso Wgos 1 1 0> to o

$ _ r ~ ~ I .____ I____ I__I___

I ID O 0 m 0 0 1 00 00 o O

O O t- oO a

0c O aO O

O .-

0 C Om O

iw~~~~~0001c f o -*~1 imH o~ em up 1 t

I I

>~ H > s 0 ~ > I 0?XX 0000

o oo 0o O o z ooO o Q Q

VLLXI. 1PART 1.?>~-~t1>1>

_11 _. _ _

_n I _ _ o I_ _ _ _

14 S 4I VOL. LXXI. PART I. E




4Z I x o1tot.i lOxCe loX QgOO ItH5

00,0U Otrc0to Ito-qt l b I OI i G__o_

I ' 000 I I I OO OOOm 0OCulz I-I 01--c I O

II ooolo[roooaklo0 I ! -____4 =gct 2~~I I0O~ I0O-O !0~~Q IorEonlls Cq ZO3-c

t ~I _ _ _ _ _ I I

a~~~~~~ I,oooc,~X,~,s+o OftI o OOI o I o -- I o I o H08 e S I o I o to CO =, to t- x 0 r-- o o 0 CO N Ho 0 m o o C j cq aH

0 I I !ooIlc>!oNm acolc oco o IoXo >I

7 1 I l~~~~~~ADc~~~ 1~~?o~1? I?<o ~~~ lc~ ~oc

Hn l~ ~ co I q r-I ! k- IZ Il IO t rl o oarq- 0 Om If N 0c t, cn i w 0 x 0 I 8 D 0 t- t- 8 0b t- 088SO 0 r8 C > km

k~~~~ I I l m WX- 9 I f 0 to..c 8 ooc It co 0 o> I,1 mQt

I 00q I X- I III cl c o 1

0

00 co

0

{ i vi _I

H1.-I _ *I _ _ 8 QbXsQb 0 0 X0bt

s? Y ~~~~~~~~~~~~c



1908.] aftecting the Birth-Rate. 5I

0. 1 1 II I So ,.0 ~ o a ococ oOXc I o o I oa w On

aq aLo a q 0 o H o ax V- o .. o

,. Hoa co . km

I0-0 I0 I 0 ~0 1 I- m14I

a0 oo o H o r Ho 0 O

t? 00 b X o o OOOIO I N 0 co e

O ooooomo oa oo0 0 oxooo oc 8o B t I _ _ _ _ _ _ _ _ _ I_ _ _ _ _ _ __~H I H

m~ ~~~~00 0O0 IC~ I I I

r-4 tD ) > I O>,? I g,e V I ? 1r 18~c

I 0kO~~~~ 0~~0~~ ~~0~O I . k 0 0 100

_ _ _ - _ _ 1~~r- 1qu W X w i - x w

,~~~~~~~ - o o km co H o m , co c o c ,o cfbIXXo,o w 4 O n ~~~rI H rHH r-H I ~ H I r- I H HH I H

H 00 1 8 co oto 18 oo 1 8 oo00 8 o o r18 o -1 8 o

> ? 1 8 a)~~~t cI' m 0 1.1 m (D 8- ci xo xo 1 c q 8 cr1 xooo

, - 4 K i_ __I_ __I_ I _ _ _ _ _ _ _ _ _ I I

o I - U I - I C I 00- - - C - OU-0 0

CO co

E&2



52 DUDFIELD-Somne Unconsidered Factors [Mar.

,0 -I o R cq La t_o ? ;: ~ 11 | |10 c i 10

13 c eq to m cO1-Hot cos

0I '1 10 0310 1

0) C

oi co co La .0m X > > > e 4 Q e bs e

to lHnu:bo 42~~~~~~~~~~~~~4 4 H

o * 00. ,o a0 to 00 oC _1 __ PC

O e I + S Q Q Nt~00O 10'tO o4'o1 *F~~~~~~~~1 10 10 I0 IC I0 10 ?>

.? S > > KiCi I0~~ 000 iG \ :t0H iO

O 0) q) _ C \ CI C o

X b b CO2>10 10 '01 1 H5O- 101 >e I -0

H ~I . 01 1 e 0 I O oNI 00

0111' I: l b o COXO 'C I1 Co _I ce

I ICct co I Oso Co 1 io t o c OC I o to0 t

CO ,, -I , 1 10 s i\ t IU ?X IC S > I I ^ + I CO CC>- I <: zS 'r Cl^ 0

* -I'~~~..Q(3 0~~~~0 0~~00~~ a4)0 1001

o 10 I 10 1 I o C 1 1 o I. coI

10 j I0 1 9 1 01t? | O%X I 0-0 1 0 I

l 1 1~~ H 17-4 I0I&I

~ I O> H GO O 100 CGO 1r I \0 0 ,I0F 0100I 1 C

X o>NIe? t DX?|0 0 1co iq J > -'co I4 Cto

0) 1c - - - _ _

I O01~ 10 ~ 100 01 -010

La 0 co 0 :) o

co 00 001 ~ 'x t- t-0C Z 01 mto10

01 0 a4 r-(

Co Co " i V00 ;To km 0\tt 00IN010 X 0 -00 0 10 w . 00 .0) "di O 1 0 0010 t- .x

0) - - - - -~~ ~ ~ ~ ~~~~~~ I_ _ t - _ _ _ _ _ _ _ _

10 Co 00010 t, 00 1~0 10 01 0\1 'xC o 0 - 0~ 10 O\M ,- '-4 x N00 w t

'0~~~~~~~~~q 0

.0 . .~~~~~~~~o r -)x

' -4 01 4 01 Co C-O




' 13 co

b I

x * + I X I e~~~~~0 o I *

> X=. e I e O ?^ I ~^MM

I e lt: lo- O -4 "I- cq k-: 00 CQ t- ,

O 1r 0 < um O o *^ ^ o^? o^ ao ? d o:)ô^_z z P-4 c

t 0 GO H X WCQ b m CO ao 2se: e b O~~~~~~00 0

l~~~~~~~~~~~~~~c CD ) 04N 0 to t v0so%

S Ci O~~~~~~0 r- CQ

l C

3 ECO to

0 CD m

ul: UDo

k-

%~~~~~~~~c u -4

^ V -n 00^ OC^ oO 10 w: ;z

O l CQ O ~~~~~~00 U tO U12 'D - la m O O +

u ? Hs0O CtO I C40 1 CDX~~~~~~~~~~~~0 t. 02s:1 CD

o~~~~~~~~~~ lo qq 0 Qo0 1 o a T- I? N I ' I?

a < W I, ows, 0o0 | ~~~~~~~"om I0 'ow,n ,

O 0: C6 I: ai It:, I O

' -- L Do10s1ora|Oo|cBo

c -1 . 0 00 ms 1- ca ms 1-7 0 H i \0 4 o

t I I ~~~~~~~~~~~~rI I~ ,-b I QC

X~~~~~~~~c ._ N. k-0 N m m , .

a~~~~~~~~ . I .* . cq P- .- O. ', s r; I *' . . .~~~~~~~~~~o 4,) @

i I . . . . i t ~~~~~~~~o o I ', ^ * *. 1- ? > ! qq c

? q I I A oo



DUDFIELD-Sone Unconsidered Factors [Mar.

TABLE X.---"SUrpIUS Wives."

1851. 1861. 1871.

Total Surplus Per Total Surplus Per Total Surplus Per Married. Wives. Cenit. Married. Wives. Cent. M.Married. Wives. Cent.

England & Wales.

1- .... 22,240 1,004 4 69 29,719 1,318 4-43 34,573 1,074 310 20- .... 268,094 7,660 2-85 321,200 8,284 2-57 361,317 8,764 2,42 25--.. 450,220 12,298 2173 511,536 12,831 2-50 584,733 13,723 2-34 30- .. 468,305 10,904 2-32 528,708 11,514 2 17 598,343 12,181 2-03 35- 4. 421,597 7,297 1-73 485,070 8,423 1-73 536,598 8,532 1-59 40- 37 373,681 6,353 1P70 443,416 6,577 1,48 485,204 6,974 1 43 45- 30 300,195 4,082 1P35 355,096 4,176 1 17 404,194 4,773 1P18 50-54 249,562 2,607 1-04 286,771 2,601 0 90 337,511 3,287 0-97

Total 1,553,894. 5,245 2'04 2,961,516 55,724 iv88 3,342,473 59,307 If77

1881. 1891. 19(0.

15- .. 25,392 524 2'06 20- 447,885 12,342 2-75 25- 867,718 23,607 2-72 30- 913,304 20,493 2'24 35-.. 834,657 13,928 1P66 40- .. 714,986 10,263 1P43 45- .... 591,858 7,829 1-32 50-54 470,080 2,556 0 54

Total .... 4,865,880 91I542 188

London.

1851. 1861. 1871.

15- .... 3,4651 152 4'38 4,740 173 4-62 5,432 182 3'35 20- 39,635 1,044 2-63 48,518 1,340 2-76 57,849 1,428 2-46 25- 67,759 2,176 3 21 80,816 2,307 2-85 94,712 2,570 2 71 30- 72,374 1,991 2 75 84 394 2,128 2-52 90,686 2,452 2-56 35- 61,748 1,280 2 08 73,687 1,738 2-35 82,593 1,868 2,26 40- 53,222 1,285 2 41 66,003 1,624 2 46 72,565 1,708 2-35 45-- 38,459 810 2'10 47,644 1,190 2A49 55,061 1,207 2'19 50-54 31,011 804 2-59 36,560 1,286 3-51 44,648 1,417 3117

Total.... 367,673 9,542 2'59 442,362| 11,786 z 66 508,546 12,832 z5'z

1881. 1891. 1901.

15- II II 3,857 33 1085 20- 11I 69,196 1,410 203 25- 129,334 3,358 2 59 30- I 133,936 2,913 21.7 35- I 119,682 1,957 163 40 - I I I I I I I 100,000 1,337 1P33 45- I 80,212 1,179 P46 50-54 61,201 1,384 226

'Total .... 697,418 13,571 [|94




TABLE X.-"SUrP1US Wiv'es "-Contd.

1851. 1861. 1871.

Total Surplus Per Total Surpluis Per Total Surplus Per Married. Wives. Cent. Married. Wives. Cent. Married. Wives. Cent.

Scotland.

15- ... 3,224 204 6'32 3,318 210 6'32 3,637 246 6-76 20- ... 37,463 1,492 3-98 38,943 1,430 3,67 39,682 1,544 3-89 25- ... 64,448 2,450 3'80 68,373 2,699 3 94 74,574 2,741 3-67 30- ... 66,586 2,274 3-41 71,946 2,565 3-56 78,508 2,648 3.37 35- ... 59,948 1,611 2-68 64,239 1,790 2-78 70,769 2,003 2-83 40- ... 53,737 1,447 2-69 58,707 1,590 2 70 63,827 1,662 2 60 45- 40,878 917 2,24 46,873 966 2,06 51,293 1,117 2'17 50-54 36,390 967 2-65 39,017 689 1 76 42,806 583 136

Total .... 362,669 11,362 3 I3 39i,4i6 11,939 3'o5 425,o96 12,544 2.95

1881. 1891. 1901.

15- ... 20- 25- 30- 35- 40-.. 45-.

Total

Ireland.

1851. 1861. 1871.

15- .... 7,550 587 777 5,192 310 5-97 20- ... 74,105 2,416 3-26 52,455 2,307 4 39 25- .... 105,432 2,885 2-73 98,126 3,270 3133 30- 117,468 2,608 2,22 124,362 3,136 2-52 35- . 93,555 1,869 1-99 92,414 2,013 2117 40- 128,519 3,422 2-66 104,210 2,593 2-48 45- 83,088 1,329 1 59 69,195 1,465 2'11 50-54 97,762 2,727 2-78 91,134 2,103 2'30

Total.... 707,476 17,843 | 2 5z 637,088 17,197 |269

1881. 1891. 1901.

15- 1 3,345 457 13'66 2,447 336 1373 20- 1 43,192 3,016 6-98 33,398 2,005 6 00 25- 1 78,952 3,241 4-10 66,596 2228 3'34 30- 103,428 2,681 2-59 85,384 1,895 221 35-*--. 92,077 1,657I 1-79 78,793 1,312 1-66 40- . 111,304 2,138 1P92 91,829 1,564 1 70 45- ..1 66,948 458 0-68 69,415 714 1-02 50-54 75,612 730 0-96 78,225 922 IP17

Total.... 574,858 14,378 |2 50 506,o87 10,976 z-i6



56 [Mar.

DISCUSSION on Dr. R. DUDFIELD'S PAPER.

THE PRESIDENT having presented the Guy Medal in silver to Mr. Noel A. Humphreys, I.S.O., for his paper on "The Alleged Increase of Insanity,"I

Mr. HUMPHREYS expressed his gratification at this mark of appreciation by the Society of his recent work, and said that he should like to take that opportunity of saying that the preparation of the several papers which he had contributed to the Journal of the Society during the last thirty-five years had afforded him great interest and pleasure on many grounds. They had neatly all dealt more or less directly with that branch of statistics which was, in fact, founded and created by his old friend Dr. William Farr, an eminent past President of the Society; and no one, he thought, would now venture to deny that what are called vital statistics, especially in the form initiated by him, and published from time to time in the reports of the Registrar-General, had had the most direct bearing on the promotion of sanitary organisation and progress. Most of his papers had dealt with the evidence and results of that sanitary progress, in the reduction of mortality and the increase of lonlgevity amongst the English people. He had, moreover, felt special interest in analysing those statistics by life- table methods, which afforded conclusive refutation of the frequently asserted increase of physical deterioration in the English nation.

Dr. R. DUDFIELD then read his paper.

Mr. YULE said he was sure they were all grateful to Dr. Dudfield for this Paper. They knew that his duties as medical officer did not give him much spare time, and the preparation of the paper must have required many hours of work. Its study had interested him extremely. Comparing it with Drs. Newsholme anid Stevenson's, and his own papers, read some two years ago, he would point out, in the first place, that Dr. Dudfield had a somewhat different idea in his mind with regard to the choice of standard fertility rates. In any discussion of the nature of the changes in the birth-rate one wanted, in the first place, to correct the crude rate in some way, so as to allow for the fact that it was affected not merely by changes in fertility, but by changes in the proportion of the married population to the whole population, and in the ages of the married women and their husbands. To perform that correction, one had to assume certain "fertility rates," i.e., the numbers of children to be expected from, say, i,ooo married women, or nmarried couples, of certain ages; and to take those standards and work out a " standard birth-rate," on the assumption that the fertility rates were constant from year

1 Journal, vol. lxx, 1907, p. 203.



1908.] Discussion on Dr. B. Dudfield's Paper. 57

to year. Then the actual birth-rate had to be reduced by dividing it by the ratio of the standard birth-rate in any given year to that in some year arbitrarily chosen as the basis of comparison. In that way a corrected birth-rate was obtained, from which the effects of changes in the ages and numbers of married people were eliminated. From his own standpoint, and that of Drs. Newsholme and Stevenson in discussing the same materials, they were not very greatly con- cerned with the nature of the standard fertility rates. They were not very particular whether the rates chosen represented the maximum possible fertility, the average fertility, or even a rather low fertility, because the corrections made by means of such standard rates was quite unaffected if all the rates for successive age groups were increased or decreased in the same proportion. But Dr. Dudfield, if he understood rightly, wanted to do rather more than this; he wanted not only to deal with the corrected birth-rates, but to get some sort of measure of the maximum natural fertility of this nation, and to compare the actual number of births at each epoch with the number to be expected if that maximum natural fertility were exerted. Consequently, in his choice of standard rates it was important that the fertility rates should represent, in the first place, the fertility of the population of Great Britain, and not of some other country; and, in the second place, that fertility at something like its maximum. For these reasons, Dr. Dudfield had to consider with particular care the rates that he chose as standards, and had finally decided on the use of the figures for Scotland in 1855-indeed, almost the only figures - e possessed for any part of Great Britain. Further, Dr. Dudfield hlad pointed out, what was an obviously important point, that the Swedish rates used by Dr. Newsholme were fecundity and not fertility rates, i.e., they were based oIn the number of confinements, not the number of children born. As Dr. Dudfield had very fairly stated, however, this did not greatly affect Dr. Newsholme's calculations. Reference might be made to an interesting table in Drs. Newsholme and Stevenson's paper,2 in which the effect of using fertility rates from different countries on the corrected birth-rates obtained was tested, and it was shown that the effect of such changes was in most cases extremely small, the difference being often only in the second place of decimals. But Dr. Dudfield had not only corrected, like his predecessors, for the changes in the proportion to the population and in the numbers at the different ages of married women, but had also dealt with a further extremely interesting point, namely, the effect of changes in the proportion of married couples at different ages, thus taking into account the changes in age distribution of husbands as well as wives. The question what effect the changes in husbands' ages might have on the birth-rate was raised during the discussion two years ago by Mr. Rosenbaum, and it was interesting to know that on the whole the effect appeared to be but small. Further, in dealing with this problem, Dr. Dudfield had had to tackle two very fidgety practical questions. First, he had to deal with those

2 Jourtnal, vol. lxix, p. 42.



58 Discu4ssion [Mar.

husbands whose ages were not returned on the same schedules as their wives; and, secondly, with the question of how to deal with the "surplus wives," i.e., the number of wives in excess of the whole number of husbands, an excess which was always very considerable, and might, or might not, represent wives whose husbands were abroad. Dr. Dudfield had also attempted to allow for the amount of non-registration of births; a difficult subject to deal with, for they were almost entirely thrown back on simple estimates or guesswork, as it was very difficult to get accurate knowledge. All these points were important, and had not before been fully treated. Proceeding now to compare Dr. Dudfield's results with his own, he had, in the first place, one difficulty, namely, that while Dr. Dudfield gave in the final summary (Table 13) index-numbers showing the changes in the population and the estimated births, he gave no index-number for anything directly equivalent to the corrected birth-rate, such as his predecessors had used. But an index-number -of fertility or corrected birth-rate might be very readily deduced from Dr. Dudfield's figures, viz., by simply taking the given index- number for legitimate births, dividing that by the index-number for the estimated births in any one of the four columns on the right of 'Table 13, and multiplying the result by ioo. For the whole period, 1851-1901, he could only compare corrected birth-rate index-numbers -so obtained from Dr. Dudfield's data with figures obtained from the corrected legitimate birth-rates in his own paper (Table V).3 They ran as follows:

Index Nunibers for Corrected Leqitimate Birth-Rate.

Dr. Dudfield. Mr. Yule (Table V), Journal of the

Year. On Fecund Married On Husbands and Wives Royal Statistical Society, Womiien as Eiiiiiiierated. in Comnbination. vol. lxix, p. 118.

1851. . 100 100 100 '61. 97 97 100 '71 . . 100 99 102 '81 . ... 97 - o '91 .. . 91 97

1901 . .81 81 85

Over the whole period, Dr. Dudfield's figures gave a drop of I9 per cent. in the fertility of the population, and7his figures a drop of I5 per cent.; but half of the difference was accounted for, not by differences of method in calculating the effect of changes in the married population, but simply by the fact that Dr. Dudfield had added 5 per cent. to the recorded births of 1851, and only 21 per cent. to those of 1901 to allow for non-registration. The differences in intermediate years were partly accounted for in the same way (cf. the added percentages as stated in Dr. Dudfield's Table 9), and on the whole, considering the entire difference in details of method, he thought the agreement very satisfactory. The only divergence that troubled him was that in 1891. If

3 Journal, vol. lxix, p. 118.



1908.] on Dr. B. Dudfeld's Paper. 59

instead of taking the whole period from 1851 we took only the period since 1861, we could compare Dr. Dudfield's conclusions with those of Drs. Newsholme and Stevenson as well, and here, again with the exception of 1891, the agreement was really striking. Using 1861 as the base = IOO, the figures were as follows:

Index Nunubers for Corrected Legitimate Birth-Rate.

Drs. Newsliolme and Dr. Dudfield Stevenson Mr. Yule (Table V),

Year. On Fecunid Womlen (App. Table I), Journal of the as Enumerated. Journal of the Royal Statistical Society,

Royal Statistical Society, vol. lxix, p. 118. vol. lxix, p. 72.

1861 .100 100 100 '7 .103 102 102 '81 .99 101 101 '91 .93 97 97

1901 ....... 84 84 85

There was no doubt, then, comparing 1861 with 1901, that there was a drop of between I 5 and i6 per cent. in the fertility of the married population. Making all possible allowance for ages, and the number of different corrections which Dr. Dudfield had quite rightly entered into, on the whole the results confirmed each other in a most remarkable way.

The question then arose, why did all the different methods of correction. as illustrated by Dr. Dudfield's Table 13, lead to the same results--a question which, at first, puzzled him a good deal. He confessed he had not given as much time to it as he should like to, because a great deal of time was really r equired for working out arithmetic. But it appeared to him to be chiefly due to the facts (1) that the fall in fertility was large, so that we were not much troubled by small differences in conclusions, and (2) that all corrections were relatively small, leading in the end to only comparatively small alterations, so that over the period 1861-1901 the fall in the crude birth-rate was little different from that of any corrected rate. To go into the matter further, they could regard the corrections as being made in two steps; they could imagine that they made a correction, first of all, for changes in the proportion of married persons to the whole population oIly; secondly, they might proceed to make an additional correction for the changes in the age-distribution of the married population. Now the change in the mere proportion of married persons to the population was very considerable. Taking the number of married women per million, they increased from i68,212 in 1851, to 1 75,774 in 1901, which was an increase in the ratio of from I,000 to 1,045. But the second correction was small. If you took the effect of the changes in the ages of married women you found that the number of births that could be produced from ioo,ooo married women in 1851 (using Dr. Dudfield's standard rates), was 230io6, and in 1901, 22,763. In other words, the effect of the changed age-distribution of married women on their possible fertility had



60 Discussion [Mar.

been comparatively small, only about I 5 per cent., as compared with 4-5 per cent. in the effect of the changed proportion of married women to the population. He had not been able to go into the further question of the effect of age of husbands, but was fairly certain it would prove to be a comparatively small effect. Consequently they got but little differences when taking the more elaborate corrections into account, because the changes in the factors considered were small as compared with changes in the whole fertility, and as compared with changes in the proportion of married people to the whole population of the Kingdom.

He had no general criticism to offer on the processes adopted by Dr. Dudfield, and he should not like to conclude without expressing his great indebtedness to the author for the very valuable material given in the Appendix, material which would be of great service for more extended work in the future.

The PRESIDENT here left the Chair, which was taken by Sir J. ATHELSTANE BAINES.

Mr. WALFORD thought the conclusions of Dr. Dudfield very serious, not only for England, but for the Empire in general, and it was a great pity that they could not be brought more fully before the public. He thought the time had now arrived when it was their duty to endeavour in some way to prevent the ,decrease of our population. If not, it was only a question of time when this country would descend to the position of a third-rate power. But what is absolutely necessary is legislation against advertisements of means of preventing conception and for procuring abortion.

Mr. ROSENBAUM said he should have liked more opportunity to study the Paper before makiing any remarks upon it. So far as he had seen and heard it, he agreed absolutely with Mr. Yule that it was an extraordinarily valuable contribution to the subject of the birth-rate. He should like to raise just one question affecting not only that Paper itself, but also Mr. Yule's criticism, and that was, whether there was any reason to suppose that fertility-rates at different ages were constant. There might be an effect produced by the postponement of marriage to which Dr. Newsholme referred in his Paper two years ago. It was quite conceivable that the average fertility is a function of the age at marriage; the average fertility of a woman at 35 may depend to a quite appreciable extent on whether she was married at 20 or 30. Both in this Paper and in previous ornes, it appeared to have been assumed that the fertility-rates at various ages were constant. Again, he felt that, since they were getting on to these refinements in examination of the birth-rate-and there could be no better test of the advances made in statistical study-they ought to make some attempt to have fertility-rates for each year instead of for five-year periods. The observed differences between the Swedish and Scotch fertility-rates might then be fully accounted



1908.] on Dr. R. Ducdfield's Paper 61

for by differences in the age-grouping in each five-year period. He believed Mr. Coghlan had produced tables for Australia giving the fertility-rates for each year. He had not examined the Scotch figures very closely, but it seemed to him that they might be made to yield the fertility-rates for, at any rate, the main middle years of the fertile period; and it would be very desirable to get together such materials. He felt they were all indebted to the author for his valuable contribution to this important subject.

Mr. NOEL HUMPHREYS said he agreed with Mr. Yule that the facts which had been industriously collected and dealt with by the author would be very useful to future students of the subject. On reading the Paper, he could not avoid regret that Dr. Dudfield had based his calculations and conclusions on the facts, for Scotland, in 1855, which was the first year of birth registration in that country. There could be little doubt that in the first year of birth registration, not only was there a deficiency of births registered, but he doubted very much, from his experience of registration in England, whether the wives' ages, given for the first time in those early returns, were trustworthy. That touched on another of the corrections which Dr. Dudfield had applied to his calculations; the deficiency in registration of births in England, as estimated by Dr. Farr in 1851, on the basis of the Census Returns, was 5 per cent., but Dr. Dudfield had assumed a continuing deficiency at the present time equal to 2- per cent. partly attributable to the desire to evade vaccination. This correction did not much affect the value of Dr. Dudfield's figures, but there did not appear to him that there was any sufficient ground for the assumption of such a great deficiency which implies the non-registration of more than 20,000 births annually in England and Wales. It was true that the anti-vaccination craze had affected birth registration in England, but the effect had been mainlv that parents, with a view to evade vaccination, often gave a wrong place of birth. The value of birth registration f.or many purposes was now so fully appreciated by all classes that his experience led him to doubt whether there was at present any large deficiency of birth registration in England, and to- feel certain that such deficiency was not as much as 2 per cent.

Mr. R. H. HOOKER would have liked to know a little more concerning the points touched on by Mr. Yule, and would have been glad if the author could have indicated more succinctly the precise effect that his calculations had upon the results obtained by Drs. Newsholme and Stevenson, and by Mr. Yule, two years ago. He would like to know, in fact, to what extent their earlier work was modified or superseded. He understood that the effect of the three factors examined was relatively small, and had rather gathered that they were not as important as the author himself had anticipated they would prove to be. In this case he desired to express his gratitude to the author for having, nevertheless, presented his work to the Society; as a careful analysis of the work done, even



62 Discussion LMar.

if no very startling results were apparent, was always of great value for study and example. One small statement had attracted his attention, viz., that the census schedule did not provide for a true enumeration of married couples, and that persons appeared as "married" who, for purposes of the legitimate birth-rate, would rank among the unmarried. He rather doubted if this were the case, and was inclined to think that there might be quite as much tendency for a child to be wrongly described as " legitimate " in the r egistrar's returns as for the woman to describe herself as " married" in the census returns.

Mr. BAILEY said he very much doubted how far the accuracy could be depended upon of the ages stated in these public documents, which is so essential for this investigation. Several years ago he had thought of endeavouring to get out a table of the rate of mortality at different ages and comparing it with Dr. Farr's English Life-table. He and a friend of his used for this purpose the families of the peerage, believing that there would be a sufficient number of that class to arrive. at some general laws; because there you really had the dates of birth and marriage, the number of children and the ages of the children; and no correction whatever was required. He thought if someone would take the trouble to get an old Peerage, and use it for the objects of Dr. Dudfield's paper, they could take out as many cases as were required, and would get a sufficient number of facts which could be absolutely depended upon to arrive at certain definite results without the necessity of corrections.

Sir ATHELSTANE BAINES, in moving a vote of thanks to the author of the Paper, said that the labour involved in handling so great a mass of figures would be recognised by all, and Dr. Dudfield was entitled to credit, also, for confining himself as strictly as he had done, to the issues he set out with, defining, not yielding to the temptation of straying into the attractive questions which his figures suggested, outside those issues. The effect of postponing marriage on the birth-rate had been estimated recently by the Registrar- General of England at about 20 per cent. of the decrease in the last thirty years, whilst the average age of the married men had risen by about 3, and of the wives by about 4 vears. The ages had been tabulated, he thought; in smaller groups by Mr. Kiaer, of Christiania. But the question most prominently before the meeting was the merit of the hypothetical corrections applied by the author. He (the speaker) always regarded with admiration the discernment and moderation with which such selection had to be made, as it was one of the most difficult of statistical operations, and might, if not well managed, lead to results very different from those anticipated by the operator. He had not himself had experience in applying corrections to the birth. returns of so ancient a date as those in question, but, so far as he could judge, the author had proceeded upon sound methods, and had made the most of the available material for his basis of calculation.



1908.] on Dr. P. Dudfield's Paper. 63

Dr. DUDFIELD in replying to the vote of thanks and to the discussion, expressed his appreciation of the kindly manner in which the Paper had been received. As he could not claim to be more than a very junior student of the statistical science, he had hesitated to bring the results of his work before the Society, as the end achieved had by no means fulfilled his expectations.

With reference to Mr. Yule's remarks, the only point to which he would allude was the peculiarity attaching the figures for 1891. The census results for that year differed in some (at present, to him, unknown) manner from those of 1881 and 1901. To that cause he attributed the departure from the general agreement with the results obtained by Mr. Yule and Drs. Newsholme and Stevenson. The line of enquiry taken by him (Dr. Dudfield) had been so distinct from that of those authors, that he had not endeavoured to. ascertain, as Mr. Hooker desired, the effect of his own work on that of the authors mentioned. He was seeking a concrete estimate of the loss, or deficit, of births, not a relative rneasure of the change of rate. The whole of his calculations depended on an assumption of constant fertility, a point referred to by Mr. Rosenbaum. He thought that there was no reason to believe that the national fecundity had altered at all, but, undoubtedly, owing to postponement of marriage to later ages, that fecundity was not fully effective, and hence the apparent fertility was reduced. He believed that with a reversion to the principles and practices of the middle of the last century, the birth-rate would return to its former level.

Mr. Humphreys's objection to the use of the records of the first year of registration was a valid one. If, however, the Scotch figures for 1855 were rejected, there remained no data at all for this. country. As regards his correction figures for non-registrationl of births, his experience, as a medical officer of health, had convinced him that such non-registration was more common than generally suspected. It was in part due to fear of the operation of the Vaccination Acts, although the last shred of real compulsion had been removed from the Statute Book. Quite recently he had learned of the existence of popular delusion as to relief from registration. It was thought by some people that -the holding of an inquest on a child, prior to registration of the birth, absolved the parents from all liability for such registration. He had also. brought to the notice of the Registrar-General a number of births which were reported by midwives, but never registered. Under the most favourable conditions these observations could extend to only a comparatively small proportion of all the births in his district,. but he had little doubt that the cases investigated formed a fair sample of the whole.

He should have liked to have included " specific " fertility-rates, namely, rates for each age of the mothers, as Korbsi did for Buda- Pesth, but while the births in Scotland were available for that purpose, he doubted whether the ages of married women in single years could be obtained, except by laborious and costly tabulation. Graphic interpolation was, doubtless, possible, but the trustworthi- ndss of results so obtained would be more than uncertain.



64 Discussion on Dr. R. Dudfield's Paper. [Mar.

The small effect on the fertility produced by the introduction of husbands' ages was at first sight remarkable. Some explanation was to be found by contrasting the changes for each quinquennial period, when examined vertically (for fathers) and horizontally (for mothers). (See Appendix.) The maternal age was the principal factor affecting fertility. It appeared to him to be desirable that the mean ages should be determined for each H.W. Table, not only for married men and women en masse, but for wives at each (quinquennial) age of husbands, and vice verse. Similarly the mean ages required to be taken out for the H.W. table of marriages published annually.

The uniformity of the index-numbers in Table 13 was, he thought, largely due to the causes indicated by Mr. Yule. The numbers of the total population of married women, &c., were so large, and the corrections made, relatively, so small, that the general tendency of the former would inevitably discount the results of any convictions introduced.

The following were elected Fellows of the Society: Bailey, Frederick. Furniss, Henry Sanderson, M.A. Drake, E. T., Government Statist of Webb, Augustus Duncan, B.Sc.

Victoria.



Documents

Some Unconsidered Factors Affecting the Birth-Rate