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 × 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.

"The

There is not space to review the essays on Manufactures. 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

the papers in detail, for the simple reason that they should be studied at first hand by every one who has occasion to use the American Census reports, for clues are given to the maze of figures, caution boards are erected in dangerous places, and with this help the figures are found to be prepared more soundly than would at first sight appear.

A. L. BowLEY

The Science of Finance, an Investigation of Public Expenditures and Public Revenues. By Prof. H. C. ADAMS. (New York: Holt and Co. 1898).

THE author of this work has for a long time been known to English economists as a prominent American representative of what is somewhat vaguely described as "the new school" of political economy. His reputation as a writer on financial questions has been solidly established by the standard treatise on Public Debts, which is indispensable to the student of that particular topic.

Hence the announcement that Prof. Adams had in preparation a comprehensive work covering the whole field of finance naturally aroused high expectations. After a protracted delay, the task has been achieved, and is presented to students in the book before us. It is unnecessary to say that a great deal of valuable matter and suggestive thought are contained in this "advanced text book" of "The Science of Finance." No writer of Prof. Adams' ability can handle a subject at the stage of development which financial theory has now reached without giving instruction and stimulation to learners and investigators. To contemplate the many debatable problems from the special American standpoint is by itself to perform an important service, for which we may be thankful.

But notwithstanding our sense of obligation, we must also confess to a feeling of disappointment. It may have been that we hoped for more than was reasonable; but there is, we cannot help thinking, a good deal that is unsatisfactory, and even defective, in our author's arrangement and handling of his matter. The adoption of a purely American point of view leads to limitations, and, in some cases, to positive mistakes, that detract from the great merits of the work. We miss the consistent and thorough use of the comparative method of study that is so prominent in the writings of some other American economists. Independence and originality of thought are markedly shown in Prof. Adams' work; a fuller employment of the results attained by others, and a more careful study of the mass of facts which financial institutions afford in such embarrassing abundance, would have been, we venture to think, an enhancement of the first-mentioned qualities.

The strength of the book lies, it is evident, not in development and expansion of the growing body of financial doctrine, nor, again, in its co-ordination or explanation of the financial systems of States, but