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Of the causes of difference in the traffic, one of the most obvious is the coming on of evening. For example, consider the record of the traffic of nest A after 6.19 P.M., 6th September (1884), presented in Table XIV.

TABLE XIV.-Showing the Decline of Traffic with the Coming on

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The influence of Hesperus has been more fully exhibited in Tables IX and XI.

VII. Owing to the variations in the traffic which have just been proved to exist, the formula for the working population, which was proposed as rough and ready, is found to be rough indeed, since it affords only an inferior limit to the population, but not ready, since in order to secure an approximate limit, we must endeavour to observe the largest possible flow. The numbers given by the formula and by an actual census in certain instances are shown in Table XV.

24 I saw no way of taking the number without taking the lives of the inhabitants. I effected my purpose partly by intercepting individuals, usually with a second object in view (see p. 362 et seq.), either as they returned to or as they issued from the nest; partly by pouring tar oil into the nest overnight. The terms "counted outside" and "counted inside" in Table XV designate these two

methods of taking the census. The second operation was not always completely successful; hence the necessity of resorting to estimates in two of the instances in Table XV.

I should add that queens have not been included among the observed numbers in Col. 3 of Table XV; but that males have not been excluded, partly because it is difficult to distinguish them from workers, partly because I believe they may form part of the flow on which the calculated numbers in Col. 3 are based.

TABLE XV.-Showing the Correspondence between the Magnitude of the Population and that of the Traffic.

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It will be seen that the inferior limit given by the formula is very inferior. There is a rough correspondence between the

magnitude of the flow and that of the population.

The proposition that the circulation is proportioned to the numbers in a wasps' nest, is about as true or as false as the proposition that the level of prices varies as the quantity of metallic money.

I trust that the analogy of these studies with human statistics may justify their insertion in this Journal. The trade and industry which we have investigated may be petty interests, but by their regularity and orderliness they are particularly well calculated to furnish specimens of statistical methods.

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What the poet says of bees, the statistician finds true of wasys.

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I.-The present Population of the United Kingdom, 5th April, 1896. By G. B. LONGSTAFF, M.D., F.R.C.P.

TEN years ago I attempted in the pages of this Journal to estimate the then population of the United Kingdom by a consideration of the available data as to births and deaths, emigration and immigration, for the five years that had elapsed since the census of 1881.

The official estimate, based on the hypothesis of constant increase, amounted to 36,776,054, but my estimate fell short of this by 476,435.

Five years later, applying a similar but more elaborate method, I showed in the Economic Journal for June, 1891, that there was good reason to believe that the census, then recently taken, would prove the official estimate to be greatly in excess. The facts turned out to be:

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The official estimate was therefore 919,322 (or 2.44 per cent.) in excess of the facts, whereas mine was only 80,127 (or o.21 per cent.) in excess. It is obvious that these figures go far to prove the substantial accuracy of my estimate for 1886.

The requisite data for applying to the present year the method adopted in 1886 are given in the six short tables that follow:

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TABLE 1.-Population Enumerated 5th April, 1891, and Estimated for 5th April, 1896, on the assumption of the same Rate of Increase being maintained.

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TABLE 2.-Arithmetical Mean of Populations in Table 1, and Means of the Annual Birth and Death-Rates, 1881-90.

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TABLE 3.—Births, Deaths, and Natural Increase in Five Years, April, 1891, to April, 1896, calculated from Data in Table 2.

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TABLE 4. - Births and Deaths Registered in Five Years, April, 1891, to

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TABLE 5.-Excess (+) or Defect (−) of Actual Numbers in Table 4 compared with Calculated Numbers in Table 3.

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It appears from Table 5 that the births have uniformly fallen short of the calculated numbers, and that this is also true of the deaths so far as England and Wales and Scotland are concerned, but that in Ireland the deaths have somewhat exceeded anticipations. As a net result the natural increase of the United Kingdom is 279,091 less than would have resulted from a continuance of the couditions of the preceding decennium. In the quinquennium 1881-86 the corresponding defect was only 77,733, but, as has been often remarked, the dominant factor in determining the changes in the rate of growth of our population is migration.

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