ation about the conditions of life in a degenerate section of a New England town, put in a quiet and forcible way by men who are thoroughly conversant with the facts under consideration; and who, moreover, besides being impartial and painstaking students, are also obviously concerned to do all that lies in their power to find some practical solution for the problems which confront them.

Mr. Robert A. Woods, the Head of the House, whose earlier book on English Social Movements will be known to many readers, contributes several very instructive chapters on "Work and Wages," "Social Recovery," and "The Total Drift"; chapters on "Population" and "Public Health" by Mr. Frederick A. Bushée and Dr. Charles D. Underhill respectively, and an anonymous chapter on "The Roots of Political Power," are also particularly interesting; and there are seven maps or diagrams which serve to illustrate the text.

The South End of Boston comprises some 40,000 inhabitants, mostly living in more or less insanitary tenement houses, and huddled together upon an area of half a square mile, which has been reclaimed from the sea. The extraordinary heterogeneous character of the people is shown by the fact that in one school every country in Europe is represented; while in another, out of 685 children, "200 are Irish, 170 are Americans, 121 Jews, 61 coloured, 9 Germans, and 124 are of other nationalities." It is by no means surprising to be told that such a district is "distinctly lacking in economic individuality as it is in any sort of local esprit de corps ;" and that, in spite of some twenty-two churches and chapels, the saloon-keeper and the political ward "boss" are the chief embodiments of such authority as is understanded of the people.

The liquor traffic "represents the largest single trade interest in the district." And, at election times, since "in each ward of such a section as this, it is safe to say that there are five or six hundred men who are more or less influenced by the political talk of the saloon," it follows that "other things being at all equal, the man who has the greater number of saloon-keepers on his side will surely be elected." The politician, it appears, has no need to deal with individuals, and finds it much easier to effect his purposes by means of the various social and political clubs which are exceedingly prolific in these parts. The tendency to organise begins with the children. Almost every boy in the tenement house quarters belongs to a gang consisting of from five to forty members. Each gang has its own "corner" or "hangout," and is controlled by quasi-officials with such expressive titles as the "bully," the "judge," and the "counsellor." As the boys grow up the more respectable form into clubs with a common meeting place for social purposes; and these, together with the regular political clubs, offer a convenient hunting ground for the political "boss" with his effective but frankly corrupt staff of lieutenants and "heelers." As a natural result, it is impossible for any one who is not "a gang man," and is without "gang-connections," to overcome the candidate of

the "Machine Club" which stands at the head of the political organisation.

However, in spite of all these extremely depressing facts, the residents of South End House are by no means in a state of despair. They see unmistakable signs of gradual improvement in the general conditions of the district. Thus, for instance, "Massachusetts legislation against the sweating system has practically abolished that iniquity in Boston; while the general legislation of the State-including the limitation of the weekly hours of work for women and minors to fifty-eight, the prohibition of child-labour under the age of fourteen, and the requirement of rather strict sanitary regulationsprevents a low order of factory industry." And they believe that the actual results of their own many-sided work are enough to justify the assurance of hope for the future. J. CARTER

The Federal Census. Critical Essays by Members of the American Economic Association, Collected and Edited by a Special Committee. (New York: The Macmillan Company. London: Swan, Sonnenschein & Co. March, 1899.)

THIS book should be of great interest to English readers, for many reasons: firstly, in view of the approaching census at home, they will find valuable critical examinations of the way in which census enumerations may fail; secondly, they are furnished with a guide to that extraordinary medley of figures, the American XIth Census; and thirdly, the critical handling of the great number of statistical problems which the Census authorities endeavour to solve, provides lessons in Practical Sociology nearly as valuable as those of Mr. Carroll D. Wright's book on that subject itself.

Apart from the admitted untrustworthiness of many of its figures, the great fault of the American Census is due to a want from which England also suffers; there is no permanent Census office, and there is an almost complete lack of continuity (from which we are fortunately saved) in the Census organisation; the tenth Census ménage was, when the eleventh began to be organised, represented by a single clerk in charge of all the documents. The new superintendent had in thirteen months to organise an army of clerks, examine their fitness, teach them their duties, and allocate their areas, decide all questions of method, erect suitable buildings, prepare all question forms, and print and distribute twenty-five million schedules. Meanwhile he was face to face with the central problem: how to extend the scope of the Census and improve its details without destroying its comparability in totals and items with the ten former reports. It is in this respect that the reports appear to have failed most completely. It is safe to say that no comparison should be made between the Census totals for different periods as they stand, but they should be studied and corrected under expert guidance till those parts which are exactly

comparable are deduced; and it is a common cause of complaint on the part of the writers of this book, that the reports, so to say, pitchfork totals at their readers with only the vaguest explanations of what they include, and that frequently the most careful search fails to reveal any exact definition of the items included.

It is perhaps ungenerous to find fault with the Census for its ample extent, for however much open to criticism many of its measurements may be, and however easy it is for unscrupulous politicians to twist the rough totals of income, wealth, products and taxation, to support any arguments they please, after all there is a serious attempt made to obtain measurements of many quantities, in their nature commensurable, the want of which is urgently felt by all economists and statisticians. The difficulties are threefold: to define the quantity which the economist wishes to measure; to choose the exact valuations which will come nearest this desideratum; and to organise the collection of the necessary returns. Any attempts to get over these difficulties are full of instruction to all statisticians who have the same ends in view, and if the government of the United States is willing to devote money and labour to these scientific experiments, all we can do is to be grateful to them, and to ask that the details of the investigation shall be given. to us, so that by study of the methods employed we may learn what can be accomplished and what mistakes should be avoided. The chief fault of these reports appears to be that this information is not given.

It would doubtless be better if this Herculean labour were subdivided among different permanent offices, which, as in England, should supply periodical returns on different subjects, their frequency being proportioned to their importance. There appears to be a tendency towards this subdivision: the twelfth Census is to be very much lightened, and the officials will be able to devote themselves year by year to different sections of its undertakings, for they will be bound to publish separately a report on population ("in the terms of the English language as spoken in this country "), and afterwards to collect other information (as to mines, transportation, &c.) and publish it by July 1st, 1903.

The most important question for the statistician is, "to which of this great mass of figures do the laws of cumulative accuracy apply?" As we proceed to totals and averages, do we increase errors by simple addition, or are they eliminated in accordance with the laws of chance? This question is emphasised by Mr. Irving Fisher in what is perhaps the most valuable of these essays. He states, however, that a sum cannot be more accurate than the least accurate of its parts. If by accuracy is meant the ratio of the error to the total this is demonstrably false; and it is easy to see that the total of the population of the States is more accurately stated when a faulty estimate (e.g. for Alaska) is included (so long as this estimate is not as much as double the fact), than if no estimate is made at all; the only remedy in such a case is to give two totals, one including items which may be expected to be

correct to a certain percentage, say, 1, and another including items with a larger range of possible error. If in each of forty states the error may be expected to be one in 1,000, the error in the total may, by the theory of chance, be expected to be right to one in 1,000 x 40, say 6,300. Among these figures there must be many which have this cumulative accuracy, and it is important that the genesis of the totals. should be shown in order that the reader may form such an estimate. It may be worth noticing that if there are 100 figures in a column, each right to one in 1,000, the total will probably be right to one in 10,000; if the separate figures refer to hundreds of thousands, the last two digits will be valueless; the total will be presumably in tens of millions and the last three digits valueless. It is perhaps too much to ask that any such simple rule as this should be used in official publications; but, if it was, a great deal of space and labour could be saved by not printing figures which are admittedly wrong: so many ciphers could always be placed at the top of a column, and the results given in the nearest round numbers which were probably correct and the possibility of erroneous deductions removed. In many cases, of course, the raw material of statistics is of specific interest, but only when the figures can profess to be correct to the last digit. This discussion is not of theoretic interest only, but the necessity of some such estimates is continually shown by these essays. In instances too many to record the totals are stated to be far and demonstrably in error, while they still have some positive value. To return to Mr. Fisher's argument, averages and percentages are continually calculated in the reports and compared with one another, and with similar deductions from previous European and American Census reports, when in reality the apparently significant difference is far less than the error inherent in the figures themselves. The chief peculiarity of the American Census figures is their great inaccuracy, using the term as just defined. Mr: Fisher pleads for a lower or upper limit when it can be given; e.g., the negro death-rate as stated is known to be a lower limit, for deaths are frequently not reported. He points also to another glaring statistical error common in the reports, viz. the use of a wrong denominator in calculating rates, in particular an excessive increase in population to show a decreasing death-rate. The cumulative accuracy that is generally found in comparing rates published for different periods by the same authority, may be regarded as totally absent from the sequence of the Census reports, for the methods have constantly changed.

To come to individual papers: the problem of inter-state migration is ably handled by Mr. Willcox; he shows that the natives of the Western and Southern States tend to remain where they are, those in the Central districts to move to adjacent States, and those in the Atlantic division to migrate to a greater distance. He gives a very useful caution against studying conjugal condition or the birth-rate without a correcting factor for the very different distribution by age

and sex in the East and West and in the North and South. Mr. Ripley puts in a plea for treatment by "areas of characterisation instead of in arbitrary topographical divisions. Mr. Holmes suggests an age-grouping, 3-7, 8-12, 13-17, &c., years, to eliminate erroneous returns. Prof. Mayo-Smith's criticism of the statistics of occupations is searching. He shows "that it would be comparatively easy with a very slight stretching of terms to transpose large bodies of men from one occupation to another," making "comparison between different Censuses in regard to the number of men of a specified occupation extremely uncertain," and he gives several examples of such uncertainty; e.g., the number of woodchoppers are returned as having increased 165 per cent., against a 30 per cent. increase in all gainful occupations. The division by grand groups of occupations produces some anomalous results. "A book-keeper in a cotton-mill may be said to belong to trade, a porter in a brewery to transportation, and a labourer in any of these undertakings to be rendering personal service." His analysis of the building up of totals in various occupations by members of various classes (native whites, coloured, immigrants, and according to age and sex) is very interesting. One example of a simple explanation of an apparently surprising fact may be given: "In plain words, this great tendency of females of foreign parentage to go into gainful occupations is due simply to the demand for domestic servants."

Mr. Irving Fisher's paper, already referred to, should be studied by all interested in mortality figures. His view of the Census figures in this department may perhaps be sufficiently shown by his remark: "The ordinary reader is certainly excusable if he expects a book of figures to be fact, not fiction;" and the ordinary reader may be very grateful to Mr. Fisher for showing how to extract the facts on which this fiction is founded.

Passing by the studies of the statistics of crime and pauperism, it is a relief to find some words of praise in Mr. Kinley's review of the mortgage figures; the complete methods of research employed are for once described in the reports, and the resulting volumes "are easily among the best portions of the census." On pp. 239 seq. there is an interesting criticism of the method of sampling as applied to the selection of counties for the examination of mortgages.

There is not space to review the essays on Manufactures. "The statistics of manufactures are among the weakest in the whole range of census reports, although more carefully compiled than most," says Mr. North; from which we may deduce that there is a very solid substratum of fact in the volumes, but that the English reader should make a careful study of these essays before attempting to use the Census figures, and even then he should leave the wage statistics severely alone. Similar remarks apply to the papers on Valuation and Taxation.

On the whole we must hold this book to be of the very greatest importance. It has not been necessary to review the technicalities of