TABLE 6.-Excess of Emigrants over Immigrants, British and Irish

Table 6 shows a great falling off in the net emigration, amounting to no less than 416,251.

We have therefore the population unduly increased by defect of emigration, and unduly decreased by defect of natural increase, resulting in a net increase amounting to 137,160 in excess of the estimate.

It will be observed that the emigration figures in Table 6 are for calendar years, and as emigration in the first quarter of 1891 was more active than for the corresponding quarter of the present year, a correction should be made. As, however, the complete figures are not published for quarters, this is difficult to do. Assuming the proportion of net emigration to gross emigration to have remained constant, 2,544 should be added to the estimate to allow for this:

Therefore the method adopted in 1886 indicates that the growth of the population of the United Kingdom is now more rapid than in the past decade, my estimate indicating an excess in the five years of 139,804 over the official estimate of the Registrar-General.

But since 1886 great improvements have been made in the record of migration, the exchange between this country and the continent of Europe, which was formerly neglected, being now known approximately. The returns now give a new datum, viz., the Summary of the General Passenger Movement. This has resulted in a net balance outwards in each of the five years under consideration amounting in all to 379,125, so that we can make a direct estimate, thus:

Natural increase in five years, April, 1891, to
April, 1896

Balance of passenger movement, 1891-95, }

outwards

Correction for 1st quarter, 1896

Increase in five years......

+ 2,113,980

379,125

+ 1,734,855
2,644

+ 1,737,499
+ 1,578,556

Increase of official estimate.

I have applied the same correction to the figures for emigration, since it happens that the number of "alien immigrants not stated to be en route to America" is almost identical for the two quarters, viz., 6,586 and 6,553.

.

as to the

The second estimate is higher than the first, but only exceeds it by 19.139. It might appear to be the more trustworthy of the two, since it does not depend upon assumptions or calculations, and its errors are consequently only those of the official figures upon which it is based. Sir Courtenay Boyle says in his last report: "There is every reason to believe that the figures numbers of passengers in each direction are approximately complete; any slight omissions that may possibly exist would apply on both sides of the account, and would not materially disturb the balance, which is no doubt sufficiently accurate for all practical purposes." But, as Sir Courtenay Boyle has pointed out, a large number of seamen are included amongst the immigrant aliens, but these, when putting to sea as part of the crews of English ships, are not reckoned as emigrants. The total number of such seamen recorded in the last five years amounts to 49,621. It has been suggested that these should all be deducted; but it should be mentioned that the number of foreign seamen enumerated in England and Wales increased from 9,978 in 1881 to 15,083 in 1891. There would seem to be no means of getting at the exact facts until the simple process is adopted of recording the total numbers carried, crews as well as passengers, upon all vessels arriving from or clearing for foreign or colonial ports. However, we must do the best we can with the facts at our disposal; I shall therefore deduct 10 per cent. from the 49,621 to allow for men on board ships in British ports and unemployed. Thus :

This number falls short of the first estimate by 25,520, but is 114,284 above the official estimate of the Registrar-General. Supposing it to be correct, and I do not see how it can err by more than 25,000, it does not prove that the British and Irish population has increased more rapidly than in the last decade (for that is not the case), but that it has been more stay-at-home. In proportion as the United Kingdom has gained, the colonies, and still more the United States, have lost.

To apportion the increase between the three kingdoms is a much more difficult matter. The Registrar-General of Ireland estimates the population of that island for the middle of each year from the recorded births, deaths and migration. The number for April, 1896, can be obtained by interpolation:

If we distribute this population between England and Wales and Scotland in the proportions which prevailed in 1891, we get-

We know, however, that the natural increase in Scotland has not fallen off quite so much as in England. Scotland in this way has gained about 1,000. On the other hand the Scotch emigrants have fallen off much more than the English, so as to result in a gain of some 12,000 to Scotland. We know, however, nothing as to the immigration into Scotland, or the movements of the Scots into England. I have transferred 10,000 from England and Wales to Scotland, and finally get this result, using round. numbers::

The difference between my estimate and that of the RegistrarGeneral is much less than in the case of the corresponding estimates ten years ago, and it is of opposite sign. My estimates of the several divisions of the United Kingdom are far more doubtful than the total, an error of 50,000, or even more, would not surprise me.

It may be noted that the population of the United Kingdom probably passed that of France in 1894, or even in 1893.

[Since the above was printed the result of the recent Census of London has been published. The revised figures show an increase of 200,900 in five years, this being 13,289 less than the estimate based upon constant rate of increase, and 29,877 less than the natural increase, but quite doable the estimate based upon the number of inhabited houses. The falling off in the natural increase has been counterbalanced by a falling off in the net emigration. But the population of the administrative County of

London has little bearing upon that of the United Kingdom, since it so largely depends upon intra-migration.-G.B.L.]

II.-Application of the Method of Percentiles to Mr. Yule's Data on the Distribution of Pauperism. By FRANCIS GALTON, F.R.S.'

WHEN any large group of statistical cases is sorted into a hundred classes equal in number, and progressively increasing in value, the dividing values between the classes are called Percentiles; or, if into ten classes, they are called Deciles; or if into four classes, they are called Quartiles. The fiftieth percentile, the fifth decile, and the second quartile are consequently the same as the median. All other deciles, &c., are calculated on the same principle as the median, and in the way that Mr. Yule has already explained. Still, it will be convenient to workers to possess a form by which a complete set of deciles may be compactly worked out, so Table A is printed as an illustration. Its headings sufficiently explain the process, with perhaps the following exceptions: In the first column the entries at either end of the series have been thrown into the separate lumps of below 175 and above 1025, while instead of the remaining entries appearing as in Table I (p. 347), under the form of 20, 25, &.. they are written as 175 to 2.25; 2.25 to 2.75, and so on, those being the values to which the former figures really reter. The small number of cases that fell exactly on the dividing lines had been sorted, as I am informed by Mr. Yule, as equally as might be into the adjacent compartments. The multiplier o'5 is introduced into column F, because the intervals between the successive lines refer to differences of o'5 per cent. Usually I calculate the o ̊5th and 9.5th deciles in addition to those given in the table. If the ends of the series were abrupt, the o'1st and the 99th might also appear. The deciles being merely a condensed method of description, those additional values should be selected that are most suitable to the intercomparison of the particular series that are to be dealt with. The 25th decile is identical with the 1st quartile and the 75th with the 3rd; they are not used here. The quartile (irrespectively of its or sign) in a normal (symmetrical) series, is identical with its "probable error. Table B contains the deciles 1 to 9, for each of the five years. The

1 For Mr. Galton's remarks in the discussion which followed Mr. Yule's paper, see p. 350.

2 The principles of the method of percentiles, and the ogival curve by which I commonly expressed them, are fully explained in my Natural Inheritance, p. 46 (Macmillan, 1889); the particular form under which percentiles or deciles are here used, was employed in a paper by me on "Assigning Marks for Bodily Efficiency," see Report British Association, 1889, p. 475.

diagram is drawn from the contents of Table B, to afford a graphic view of the changes during the period under discussion. Table C contains three selections for each year from Table B, namely the median, and the values of the deciles 2 and 8 after the median has been subtracted from them; it contains two simple deductions from these, and it also utilises the mean (its value having been taken from Mr. Yule's Paper). The result is that four entries for each year give all the necessary data for such quantitative comparisons as statisticians want, between that and the remaining years. Two other entries which have been deduced from the above are added for convenience, making six entries in all for each year. The diagram and the small Table C appear to me simpler and more distinct, and to be as useful and accurate in the present instance for the ordinary purposes of the statistician, as are the five plates and the results of the elaborate calculations that accompany Mr. Yule's paper. The former were compiled with ease; they show the changes of the median and mean from year to year; they measure the spread of each series by means of the difference between the 2nd and 8th deciles (which forms an excellent measure of the spread), and they give a fairly good indication of the symmetry or skewness of the curve (by the ratio which is entered in the bottom line) between the deviations of deciles 2 and 8. In a symmetrical curve those deviations being equal, the ratio is 1; in a skew-curve it is less than I when the mode is to the left of the median, greater than 1 when it is to the right. Besides this, the data contain materials for applying the empirical method of Professor Yule by which, in numerous cases, the node may be determined, namely that mode = (mean 3x (mean median)} or, using u to express the entries in the second line of Table C, mode = = mean 3u, but, as the mean = median + u, this may be changed into mode = median Anyhow the line u gives a second measure of asymmetry. Whenever the series to be dealt with are more symmetrical than these, there is yet another result obtainable from such data as those in Table C, namely, the power of approximately

2u.