I find (A) the number of children of equal numbers of urban and of rural mothers. The census schedules contain returns of the names and ages of the members of each "family," by which word we are to understand those members who are alive and resident in the same house with their parents. When the mothers are young, the children are necessarily very young, and nearly always (in at least those cla.s.ses who are unable to send their children to boarding schools) live at home. If, therefore, we limit our inquiries to the census "families" of young mothers, the results may be accepted as practically identical with those we should have obtained if we had direct means of ascertaining the number of their living children.

The limits of age of the mothers which I adopted in my selection were, 24 and 40 years. Had I to begin the work afresh, I should prefer the period from 20 to 35, but I have reason to feel pretty well contented with my present data. I correct the results thus far obtained on the following grounds:--(B) the relative mortality of the two cla.s.ses between childhood and maturity; (C) the relative mortality of the rural and urban mothers during childbearing ages; (D) their relative celibacy; and (E) the span of a rural and urban generation. It will be shown that B is important, and C noteworthy, but that D and E may be disregarded.

In deciding on the districts to be investigated, it was important to choose well-marked specimens of urban and rural populations. In the former, a town was wanted where there were various industries, and where the population was not increasing. A town where only one industry was pursued would not be a fair sample, because the particular industry might be suspected of having a special influence, and a town that was increasing would have attracted numerous immigrants from the country, who are undistinguishable as such in the census returns. Guided by these considerations, I selected Coventry, where silk weaving, watch-making, and other industries are carried on, and whose population had scarcely varied during the decade preceding the census of 1871.[25] It is an open town, in which the crowded alleys of larger places are not frequent. Its urban peculiarities are therefore minimised, and its statistical returns would give a picture somewhat too favourable of the average condition of life in towns. For specimens of rural districts, I chose small agricultural parishes in Warwickshire.

[Footnote 25: It has greatly changed since this was written.]

By the courteous permission of Dr. Farr, I was enabled to procure extracts from the census returns concerning 1000 "families" of factory hands at Coventry, in which the age of the mother was neither less than 24 nor more than 40 years, and concerning another 1000 families of agricultural labourers in rural parishes of Warwickshire, under the same limitations as to the age of the mother.

When these returns were cla.s.sified (see Table I., p. 246), I found the figures to run in such regular sequence as to make it certain that the cases were sufficiently numerous to give trustworthy results.

It appeared that:

(A) The 1000 families of factory hands comprised 2681 children, and the 1000 of agricultural labourers comprised 2911; hence, the children in the urban "families," the mothers being between the ages of 24 and 40, are on the whole about 8 per cent, less numerous than the rural. I see no reason why these numbers should not be accepted as relatively correct for families, in the ordinary sense of that word, and for mothers of all ages. An inspection of the table does indeed show that if the selection had begun at an earlier age than 24, there would have been an increased proportion of sterile and of small families among the factory hands, but not sufficient to introduce any substantial modification of the above results. It is, however, important to recollect that the small error, whatever its amount may be, is a concession in favour of the towns.

(B) I next make an allowance for the mortality between childhood and maturity, which will diminish the above figures in different proportions, because the conditions of town life are more fatal to children than those of the country. No life tables exist for Coventry and Warwickshire; I am therefore obliged to use statistics for similarly conditioned localities, to determine the amount of the allowance that should be made. The life tables of Manchester [26]

will afford the data for towns, and those of the "Healthy Districts"

[27] will suffice for the country. By applying these, we could calculate the number of the children of ages specified in the census returns who would attain maturity. I regret extremely that when I had the copies taken, I did not give instructions to have the ages of all the children inserted; but I did not, and it is too late now to remedy the omission. I am therefore obliged to make a very rough, but not unfair, estimate. The average age of the children was about 3 years, and 25 years may be taken as representing the age of maturity. Now it will be found that 74 per cent. of children in Manchester, of the age of 3, reach the age of 25, while 86 per cent.

of children do so in the "Healthy Districts." Therefore, if my rough method be accepted as approximately fair, the number of adults who will be derived from the children of the 1000 factory families should be reckoned at (2681 74/100) = 1986, and those from the 1000 agricultural at (2911 86/100) = 2503.

[Footnote 26: "Seventh Annual Report of Registrar-General."]

[Footnote 27: Healthy Districts Life Table, by Dr. Farr. _Phil Trans. Royal Society_, 1859.]

(C) The comparison we seek is between the total families produced by an equal number of urban and rural women who had survived the age of 24. Many of these women will not marry at all; I postpone that consideration to the next paragraph. Many of the rest will die before they reach the age of 40, and more of them will die in the town than in the country. It appears from data furnished by the above-mentioned tables, that if 100 women of the age of 24 had annually been added to a population, the number of those so added, living between the ages of 24 and 40 (an interval of seventeen years) would be 1539 under the conditions of life in Manchester, and 1585 under those of the healthy districts. Therefore the small factors to be applied respectively to the two cases, on account of this correction, are 1539/(17 100) and 1585/(17 100).

(D) I have no trustworthy data for the relative prevalence of celibacy in town and country. All that I have learned from the census returns is, that when searching them for the 1000 families, 131 bachelors were noted between the ages of 24 and 40, among the factory hands, and 144 among the agricultural labourers. If these figures be accepted as correct guides to the amount of celibacy among the women, it would follow that I must be considered to have discussed the cases of 1131 factory, and 1144 agricultural women, when dealing with those of 1000 mothers in either cla.s.s.

Consequently that the respective corrections to be applied, are given by the factors 1000/1131 and 1000/1141 or 88.4/1000 and 87.6/ 1000. This difference of less than 1 per cent, is hardly worth applying, moreover I do not like to apply it, because it seems to me erroneous and to act in the wrong direction, inasmuch as unmarried women can obtain employment more readily in the town than in the country, and celibacy is therefore more likely to be common in the former than in the latter.

(E) The possible difference in the length of an urban and rural generation must not be forgotten. We, however, have reason to believe that the correction on this ground will be insignificant, because the length of a generation is found to be constant under very different circ.u.mstances of race, and therefore we should expect it to be equally constant in the same race under different conditions; such as it is, it would probably tell against the towns.

Let us now sum up the results. The corrections are not to be applied for (D) and (E), so we have only to regard (A) (B) (C), that this--

2681 74/100 1539/1700 1796 77 ------------------------- = ---- = -- 2911 86/100 1585/1700 2334 100

In other words, the rate of supply in towns to the next adult generation is only 77 per cent., or, say, three-quarters of that in the country. This decay, if it continued constant, would lead to the result that the representatives of the townsmen would be less than half as numerous as those of the country folk after one century, and only about one fifth as numerous after two centuries, the proportions being 45/100 and 21/100 respectively.

[Transcriber's Note: In the original ma.n.u.script, Table I occupied two facing pages. This is the left-hand (sinister) page; the right-hand (dexter) page is immediately below.]

TABLE I. -- _Census Returns of 1000 Families of Factory Hands in Coventry, and 1000 Families of Agricultural Labourers in Warwickshire, grouped according to the Age of the Mother and the Number of Children in the Family._

---------------------------------------------------

NUMBER OF CHILDREN IN FAMILY.

---------

---------

---------

----------

--------

0.

1.

2.

3.

4.

---------+---------+---------+----------+--------

F

A

F

A

F

A

F

A

F

A

a

g

a

g

a

g

a

g

a

g

c

r

c

r

c

r

c

r

c

r

t

i

t

i

t

i

t

i

t

i

o

c

o

c

o

c

o

c

o

c

r

u

r

u

r

u

r

u

r

u

Age of Mother

y

l

y

l

y

l

y

l

y

l

.

t

.

t

.

t

.

t

.

t

--------------------------------------------------- 24 to 25

28 17 40 31

24 32 12 10 2

+-------------------+

26 " 27

19 18 36 24 36 28 23 26

8 8

28 " 29

18 17 32 16 20[A] 33 36 23

14 23

30 " 31

13 4 23 18 24 21 28[A] 31

18 22

32 " 33

18 11 16 14 19 13 22[A] 27

23 26

---------+

34 " 35

14 15

11 6 17 16 28 18

31 34

+-------------------+

36 " 37

12 17 4 11 10 13

22 14

16 20

+---------+

38 " 39

8 6 9 15 14 17 16 21 22 23

40

8 7 3 10 8 9 13 14 8 10

===============

=================================================

Total within

outline

96 67 258 109 116 111 171 149

Total between

outlines

42 45 16 36 56 71 29 35 142 166

Total beyond

outline

===============

=================================================

Total

138 112 174 145 172 182 200 184 142 166

===============

=================================================

[Footnote A: These three cases are anomalous, the Factory being less than the Agricultural. In the instance of 20-33, the anomaly is double, because the sequence of the figures shows that neither of these can be correct; certainly not the first of them.]

_Note_.--It will be observed to the left of the outline, that is, in the upper and left hand of the table, where the mothers are young and the children few, the factory families predominate, while the agricultural are the most numerous between the outlines, that is, especially in the middle of the table, where the mothers are less young, and the family is from four to five in number. The two are equally numerous to the right of the outlines, that is, to the right of the table, where the families are large.

[Transcriber's Note: In the original ma.n.u.script, Table I occupied two facing pages. This is the right-hand (dexter) page; the left-hand (snister) page is immediately above.]

TABLE I. -- _Census Returns of 1000 Families of Factory Hands in Coventry, and 1000 Families of Agricultural Labourers in Warwickshire, grouped according to the Age of the Mother and the Number of Children in the Family._

NUMBER OF CHILDREN IN FAMILY.

-------------------------------------------------

5.

6.

7.

8.

9.

---------+---------+---------+---------+---------

F

A

F

A

F

A

F

A

F

A

a

g

a

g

a

g

a

g

a

g

c

r

c

r

c

r

c

r

c

r

t

i

t

i

t

i

t

i

t

i

o

c

o

c

o

c

o

c

o

c

r

u

r

u

r

u

r

u

r

u

y

l

y

l

y

l

y

l

y

l

Age of Mother

.

t

.

t

.

t

.

t

.

t

---------+---------+---------+---------+---------

------------

1 1

24 to 25

26 " 27

6 6

4 1 2

28 " 29

12 15

2 5 2 1

30 " 31

21 25

9 5 1 2

32 " 33

14 18

12 9 5 3 1

34 " 35

15 25

12 10 4 5 5 2

36 " 37

14 22

10 15 6 7 2 1

38 " 39

7 11

3 9 7 7 2 1

40

=================================================

--------------------

Total within outline.

90 123

Total between outline

52 54 24 25 7 9 1

Total beyond outline.

=================================================

=====================

90 123 52 54 24 25 7 9 1

Total.

TABLE II.

----------------------------------------------------------------------

Number of Families

Number of Children

--------+--------------+------------------------

Factory

Agricultural

Factory

Agricultural

Within outline

541

436

903

778

Between outlines

375

476

1233

1562

Beyond outlines

84

88

545

571

=============================================+========================

Total

1000

1000

2681

2911

======================================================================

C -- AN APPARATUS FOR TESTING THE DELICACY WITH WHICH WEIGHTS CAN BE DISCRIMINATED BY HANDLING THEM.

[_Read at the Anthropological Inst.i.tute_, Nov., 1882.]

I submit a simple apparatus that I have designed to measure the delicacy of the sensitivity of different persons, as shown by their skill in discriminating weights, identical in size, form, and colour, but different in specific gravity. Its interest lies in the accordance of the successive test values with the successive graduations of a true scale of sensitivity, in the ease with which the tests are applied, and the fact that the same principle can be made use of in testing the delicacy of smell and taste.

I use test-weights that mount in a series of "just perceptible differences" to an imaginary person of extreme delicacy of perception, their values being calculated according to Weber's law. The lowest weight is heavy enough to give a decided sense of weight to the hand when handling it, and the heaviest weight can be handled without any sense of fatigue. They therefore conform with close approximation to a geometric series; thus-- _WR0, WR1, WR2, WR3_, etc., and they bear as register-marks the values of the successive indices, 0, 1, 2, 3, etc. It follows that if a person can just distinguish between any particular pair of weights, he can also just distinguish between any other pair of weights whose register-marks differ by the same amount. Example: suppose A can just distinguish between the weights bearing the register-marks 2 and 4, then it follows from the construction of the apparatus that he can just distinguish between those bearing the register-marks 1 and 3, or 3 and 5, or 4 and 6, etc.; the difference being 2 in each case.

There can be but one interpretation of the phrase that the dulness of muscular sense in any person, B, is twice as great as in that of another person, A. It is that B is only capable of perceiving one grade of difference where A can perceive two. We may, of course, state the same fact inversely, and say that the delicacy of muscular sense is in that case twice as great in A as in B. Similarly in all other cases of the kind. Conversely, if having known nothing previously about either A or B, we discover on trial that A can just distinguish between two weights such as those bearing the register-marks 5 and 7, and that B can just distinguish between another pair, say, bearing the register-marks 2 and 6; then since the difference between the marks in the latter case is twice as great as in the former, we know that the dulness of the muscular sense of B is exactly twice that of A. Their relative dulness, or if we prefer to speak in inverse terms, and say their relative sensitivity, is determined quite independently of the particular pair of weights used in testing them.

It will be noted that the conversion of results obtained by the use of one series of test-weights into what would have been given by another series, is a piece of simple arithmetic, the fact ultimately obtained by any apparatus of this kind being the "just distinguishable" fraction of real weight. In my own apparatus the unit of weight is 2 per cent.; that is, the register-mark 1 means 2 per cent.; but I introduce weights in the earlier part of the scale that deal with half units; that is, with differences of 1 per cent.

In another apparatus the unit of weight might be 3 per cent., then three grades of mine would be equal to two of the other, and mine would be converted to that scale by multiplying them by 2/3. Thus the results obtained by different apparatus are strictly comparable.

A sufficient number of test-weights must be used, or trials made, to eliminate the influence of chance. It might perhaps be thought that by using a series of only five weights, and requiring them to be sorted into their proper order by the sense of touch alone, the chance of accidental success would be too small to be worth consideration. It might be said that there are 5 4 3 2, or 120 different ways in which five weights can be arranged, and as only one is right, it must be 120 to 1 against a lucky hit. But this is many fold too high an estimate, because the 119 possible mistakes are by no means equally probable. When a person is tested, an approximate value for his grade of sensitivity is rapidly found, and the inquiry becomes narrowed to finding out whether he can surely pa.s.s a particular mistake. He is little likely to make a mistake of double the amount in question, and it is almost certain that he will not make a mistake of treble the amount. In other words, he would never be likely to put one of the test-weights more than one step out of its proper place. If he had three weights to arrange in their consecutive order, 1, 2, 3, there are 32 = 6 ways of arranging them; of these, he would be liable to the errors of 1, 3, 2, and of 2, 1, 3, but he would hardly be liable to such gross errors as 2, 3, 1, or 3, 2, 1, or 3, 1, 2. Therefore of the six permutations in which three weights may be arranged three have to be dismissed from consideration, leaving three cases only to be dealt with, of which two are wrong and one is right. For the same reason there are only four reasonable chances of error in arranging four weights, and only six in arranging five weights, instead of the 119 that were originally supposed. These are--

12354 13245 13254 21345 21354 21435

But exception might be taken to two even of these, namely, those that appear in the third column, where 5 is found in juxtaposition with 2 in the first case, and 4 with 1 in the second. So great a difference between two adjacent weights would be almost sure to attract the notice of the person who was being tested, and make him dissatisfied with the arrangement. Considering all this, together with the convenience of carriage and manipulation, I prefer to use trays, each containing only three weights, the trials being made three or four times in succession. In each trial there are three possibilities and only one success, therefore in three trials the probabilities against uniform success are as 27 to 1, and in four trials at 81 to 1.

_Values of the Weights_.--After preparatory trials, I adopted 1000 grains as the value of _W_ and 1020 as that of _R_, but I am now inclined to think that 1010 would have been better. I made the weights by filling blank cartridges with shot, wool, and wads, so as to distribute the weight equally, and I closed the cartridges with a wad, turning the edges over it with the instrument well known to sportsmen. I wrote the corresponding value of the index of _R_ on the wad by which each of them was closed, to serve as a register number. Thus the cartridge whose weight was _WR4_ was marked 4'. The values were so selected that there should be as few varieties as possible. There are thirty weights in all, but only ten varieties, whose Register Numbers are respectively 0, 1, 2, 3, 3-1/2, 4-1/2, 5, 6, 7, 9, 12. The reason of this limitation of varieties was to enable the weights to be interchanged whenever there became reason to suspect that the eye had begun to recognise the appearance of any one of them, and that the judgment might be influenced by that recognition, and cease to be wholly guided by the sense of weight.

We are so accustomed to deal with concurrent impressions that it is exceedingly difficult, even with the best intention of good faith, to ignore the influence of any corroborative impression that may be present. It is therefore right to take precautions against this possible cause of inaccuracy. The most perfect way would be to drop the weights, each in a little bag or sheath of light material, so that the operatee could not see the weights, while the ratio between the weights would not be sensibly changed by the additional weight of the bags. I keep little bags for this purpose, inside the box that holds the weights.

_Arrangement of the Weights_.--The weights are placed in sets of threes, each set in a separate shallow tray, and the trays lie in two rows in a box. Each tray bears the register-marks of each of the weights it contains. It is also marked boldly with a Roman numeral showing the difference between the register-marks of the adjacent weights. This difference indicates the grade of sensitivity that the weights in the tray are designed to test. Thus the tray containing the weights _WR0_, _WR3_, _WR6_ is marked as in Fig. 1, and that which contains _WR2_, _WR7_, _WR12_ is marked as in Fig. 2.

[Ill.u.s.tration: Fig. 1.]

[Ill.u.s.tration: Fig. 2.]

The following is the arrangement of the trays in the box. The triplets they contain suffice for ordinary purposes.

=========================================

Just

perceptible

Grade of

Sequences

Ratio.

Sensitivity

of Weights

-------------+-------------+-------------

1.020

I.

1, 2, 3

1.030

I.1/2

2, 3-1/2, 5

1.040

II.

3, 5, 7

1.050

II.1/2

2, 4-1/2, 7

1.061

III.

0, 3, 6

1.071

III.1/2

0, 3-1/2, 7

1.082

IV.

1, 5, 9

1.082

IV.1/2

0, 4-1/2, 9

1.104

V.

2, 5, 7

1.127

VI.

0, 6, 12

=========================================

But it will be observed that sequences of 1/2 can also be obtained, and again, that it is easy to select doublets of weights for coa.r.s.er tests, up to a maximum difference of XII., which may be useful in cases of morbidly diminished sensitivity.