1.1. From the Introduction.

The history of foreign trade is inextricably bound up with the general history of the development of civilisation in the nineteenth century; without foreign trade this development could not have taken place, while progress in all directions has in turn reacted on the growth of trade.

The beginning of this progress in knowledge, power and intercourse may he traced hack to the inventions of the spinning-jenny, the steam-engine, and other mechanical appliances, which took place in the latter half of the eighteenth century. These inventions produced manufactures; manufactures needed and found purchasers, not only at home, but in the colonies, America, and the Continent; increased and profitable exchange gave renewed stimulus to science, which continually gave birth to new inventions, not only in manufacture, but in every branch of human labour; machinery superseded hand-labour, the quantity produced by the same amount of work, differently applied, was indefinitely increased; labour was spared from agriculture, and used in the manufactures and arts, placing within everyone's reach things hitherto costly or unknown, and adding to the comfort and luxury of common life in a way which we, who regard the cheap possession of the most finished products of the most complicated machinery as a matter of course, cannot well realise.

Meanwhile manufacture at home was found so profitable that England ceased to provide her own food, but in new and distant countries hardy pioneers were content to send us the fruit of virgin soil in return for the products of our machinery; both the new and old countries were enriched by this exchange, and both our colonies and the half-cultivated tracts of older States were populated and rendered prosperous. At home population was congregating into cities, and the stimulating effect of busy city life was hastening the process of the application of the forces of nature to the performance of the hard work formerly done by man, and of the consequent increase of labour needing brain-power rather than physical strength.

But these changes were not made easily, old customs, old ideas, old virtues almost, had to be rooted out and new ones planted, prejudices stood in the way. Trade was not free, many of its natural outlets were absolutely blocked in every country, and while it was not understood what benefits would accrue from freedom, classes interested in old established industries understood very well what injury might come to themselves. The development was thus hindered for half a century, till it had gathered force to overcome all resistance. With the freedom of trade came an expansion of statistical and economic knowledge, and the relative powers, populations, and resources of the nations of the world gradually became matters of common knowledge.

Thus this development of foreign trade was essential both to our manufactures and to the general furtherance of what for want of a more exact name is called civilisation. It is convenient to divide the economic results of inventions into two classes - the increase of efficiency, which would be discussed in a history of home trade, and the division of labour, which concerns us now.

2.1. Review by: Anon.
Journal of Political Economy 14 (5) (1906), 331-332.

In this revised edition of the author's essay upon England's foreign trade one does not find any material changes other than those in the charts and tables which have been brought down to 1903. In fact, the same plates have been used as for the former edition, and changes introduced in the form of an appendix of notes, in which some further statistical data are given. The author states in a prefatory note that he "does not feel bound to support every opinion he advanced at that date [1894]." and it seems unfortunate that he should not have made his revision of this new edition sufficiently thorough to save himself the necessity of making such an apology. Where the essay deals with tariff questions, the author points out that "statements which were commonplace in 1903 will in 1905 appear dogmatic." To avoid undertaking a "long historical and controversial analysis," the treatment of imperial tariff and trade relations has been left unmodified. The last chapter, upon "England's Present Position," stands as originally written, except where tables and charts are continued to a later date. The author explains that rewriting this chapter, which comprises rather more than one-quarter of the essay, "would have involved questions of too complex a nature to have a place in a book which is mainly historical, and intended to be introductory and elementary." Nevertheless, a critical treatment of England's present trade problems, and of the Chamberlain movement as a whole, by the author would have been of great interest to economists, and one cannot feel that it would have been out of place in this little treatise.

3.1. Review by: Charles J Bullock.
Journal of Political Economy 8 (4) (1900), 540-543.

This work contains what the author modestly calls "notes," prepared for lectures delivered in 1898, but "extended and entirely recast" before publication. Mr Bowley has been for some years engaged in studying the available data for the statistics of wages in the United Kingdom, and the book now presented to the public contains some matter previously published in the Journal of the Royal Statistical Society. The results here given by no means exhaust all the materials that exist, but the author trusts that the book will give a useful presentation of preliminary results, invoke helpful criticism, and "illustrate the various questions that arise in the study of wages." Mr Bowley does not attempt to write "the general history of wages" during the present century; but passes over questions of cause and effect and addresses himself to the purely statistical object of ascertaining "the total amounts and the averages of wages" from decade to decade.

3.2. Review by: George Henry Wood.
The Economic Journal 10 (37) (1900), 73-75.

In the present volume we have a further contribution to the complete history of wages in the nineteenth century. The groundwork of the book formed the Newmarch Lectures for 1898; but the material has since been so revised and expanded, that, for ordinary purposes, enough is given to provide a fairly complete view of the course of money wages in certain industries, from the time of Eden and Young to the present date. The author, however, regards this as only a preliminary contribution, and his work in this field will not be complete until he has finished his great scheme of a wage index-number throughout the century, and of which, so far, only those for agriculture and compositors have been published, in the Statistical Journal.

The theoretical portion of the book will probably be of most interest to readers of the Economic Journal. The general object is stated to be an examination of recorded facts relating to wages, from the purely statistical side, with a view to showing "the various ways in which the material can be handled, the exact meanings of the words wages, earnings and the special methods applicable for obtaining out of the scattered and vague data available, accuracy and definiteness in the result."

4.1. Review by: Roland P Falkner.
Political Science Quarterly 16 (1) (1901), 163-165.

For a number of years Mr Bowley has been an earnest and indefatigable student of the history of wages in England. He has found innumerable records fragmentary and disjointed, and it has been his task to knit them together into. consecutive history. A few years ago he found the solution of the puzzle in what he terms the "kinetic method," an elaboration of the principles of the index number. In its elements not unknown before, it is in its application to wages new with Mr Bowley and will doubtless be known as his special contribution to the methods of statistics. ...

In the present work Mr Bowley's purpose is to find for different occupations consecutive wage records, based presumably upon the same principles, to give us as many series, however fragmentary, as possible. ...

While incomplete, the volume is the product of untiring industry and patient research. It brings only tentative conclusions, and its merit lies in its method rather than in its results. In showing how the crude figures of an earlier day may be utilised for scientific purposes, despite their imperfections, Mr Bowley has performed a service for which the economist and the statistician should be duly grateful.

5.1. Review by: C P Sanger.
The Economic Journal 11 (42) (1901), 193-197.

It is somewhat remarkable that up to the present time there should be no book on the Elements of Statistics written in the English language. England possesses several statisticians of great eminence. The Statistical Society celebrated its jubilee a good many years ago, and popular magazines often contain most admirable statistical articles. What, then, is the reason why we have no elementary text-books on the subject? Probably because elementary statistics was not until recently taught as a subject at the universities; or if a course of lectures on that subject was advertised, students were not pressed to go, and were encouraged in the belief that a little common sense could easily take the place of regular training in dealing with tables of numbers. The London School of Economics has, however, since its foundation had systematic courses of lectures on the elements of statistics, and the School therefore is entitled to share with Mr Bowley the congratulations which are due to him for supplying a long-felt want. Without further ado it may be plainly stated that, whatever its shortcomings, which are dealt with later, this book is the best book on the Elements of Statistics written in English, French, German, or Italian.
...

Part I. of the book is for beginners; very little mathematics is used; but in Part II. we have the elements of the more important branches of statistical theory which demand mathematical treatment. Mr Bowley has very cleverly avoided the use of more than a very small amount of mathematics. In his object of making "clear the ground-work of the subject, so that it will be the easier for students to follow modern writers on statistics," he has been successful. There will no longer be any excuse for persons of some reputation as statisticians to show themselves ignorant of modern methods. Such an introduction has been wanted for several years.

5.2. Review by: Worthington C Ford.
Journal of Political Economy 9 (3) (1901), 443-450.

Mr Bowley is at present lecturer in statistics at the London School of Economics and Political Science, but this does not go far to describe his brilliant work in statistical studies. He has taken both the Cobden and Adam Smith prizes at Cambridge, as well as the Guy silver medal of the Royal Statistical Society, and was Newmarch lecturer in 1897-8 at University College, London. His study of wages in the United Kingdom in the nineteenth century contained examples of the application of his methods, and in the book before us he has undertaken to give a more full and better rounded account of statistical methods as they have been developed under the teachings of the mathematical school. His experience and happy results call for consideration and careful study, although his exposition as a whole may not be accepted as the best manner of illustrating the practical application of statistical methods.

It may be said at the start the book is a forbidding one, not to be hastily read, or lightly laid down, but calling for an amount of study and some knowledge of higher mathematics denied to the majority of those who have done excellent work in statistics. The entrance of the more refined methods of the pure mathematician into what passed for the province of statistics was inevitable, as so many problems in statistics admit of the application of the doctrine of chance or probability. What Quetelet began tentatively has been developed, and it is only necessary to name Edgeworth, Pearson, Galton, and Yule to show how far the study has progressed in England.

5.3. Review by: J H.
Journal of the Institute of Actuaries (1886-1994) 36 (2) (1901), 197-200.

A good English text-book on Statistics has been a long-felt want and there can he little doubt but that Mr Bowley has supplied this want in an admirable way.

Part I, the greater portion of the book, defines statistics and explains the method of investigation. For illustration the author takes the work of several of our leading Government departments. Having found how the raw material (or data) is procured, he discusses the best methods of tabulation. The next question as to how it can be summarised leads to the problem of averages and averaging, and also to graphical methods of showing the results.

Discussing a proposed definition of statistics as "the science of counting", Mr Bowley is led to draw a clear distinction between arithmetic and statistics. "Whereas arithmetic attains exactness, statistics deal with estimates, sometimes very accurate, and often sufficiently so for their purpose, but never mathematically exact."

Mr Bowley prefers, however, to regard, statistics à posteriori. And throughout his work he proceeds to discuss the different methods found necessary in dealing with large numbers descriptive of groups. He refers to different sciences which rest on statistics, particularly biology, as shown by the writings of Karl Pearson.

When we come to the study of demography (which includes not only problems of population, increase, decrease, and distribution, but questions of income, wages, foreign trade, etc., etc.), we find ourselves dependent on the central or local administration for our statistics. Mr Bowley mentions Booth's Life and Labour of the People and Leone Levi's Wages and Earnings as examples of what private enterprise has done in this direction. Equally interesting examples are the mortality statistics of Life Assurance Companies, and sickness statistics.

Hence Mr Bowley is led first to describe the objects and working of the Census Department, of the Labour Department, and the Board of Trade foreign trade statistics, as the most important and best examples of Government statistics.

Mr Bowley, however, makes many valuable suggestions as to additional information and organisation that might be supplied by the administration of the country, e.g., a quinquennial census, and a permanent staff; tabulation of market prices of stable commodities; returns of railway traffic similar to that by water, and a record of factory production.

6.1. Review by: G Udny Yule.
The Economic Journal 31 (122) (1921), 220-224.

Many of us, to whom the first edition of Dr Bowley's Elements has been familiar for twenty years, have hoped for long that he would at some time find it possible to effect an extensive revision, and in particular to deal more fully with mathematical methods. Such a revision has now been carried out and the results are before us in the Fourth Edition. The re-casting has mainly affected Part II, "Applications of Mathematics to Statistics." In the first edition of 1901, Part I, on "General Elementary Methods," occupied 258 pages; it now extends to 241 only. To Part II was given a mere 68 pages; it is now to all intents and purposes a new work of 210 pages. The whole volume appears to have been reset. ... Part II now affords a broad survey of the whole field ... Throughout, the number of sociological and economic illustrations is unequalled; but when Dr Bowley states that examples have been chosen "principally" from these fields, the term must not be taken in too strict a sense. Even Dr Bowley has had to draw on other material ... In its new, and greatly improved, form Dr Bowley's volume is assured of a long life ...

6.2. Review by: W P E.
Journal of the Institute of Actuaries (1886-1994) 52 (3) (1921), 389-392.

The whole of the first part of Professor Bowley's text book is, in a sense, arithmetical; he shows how the figures can be used to enable us to reach a simple arithmetical result whether it be an average, a mode, or index. The second part, which has been so much altered from the earlier edition that it is almost a new work, deals with the mathematical side but it is frequently arithmetical in intention.
...

We may return for a moment to Professor Bowley's book to point out that the actuarial reader will find much of help and interest in it; he may feel that the formula which is called the Generalised Law of Error, second approximation, is hardly suited to graduation work as it can only be relied on for graduating a few groups in many cases, and he may feel that some of the chapters on correlation are more of the nature of summaries of existing work than chapters of a self-contained textbook, but he will, at any rate, be impressed by the comprehensiveness of the summary and helped by many suggestive remarks and practical hints throughout the work.

6.3. Review by: Bruce D Mudgett.
The Annals of the American Academy of Political and Social Science 100 (1922), 210-211.

The first edition of this text was published in 1901, while mathematical statistical analysis was still relatively in its infancy. Developments of method since that time have been great and applications of the more refined methods of analysis have been still greater. In the field of economics, in particular, the first application of the method of correlation to a time series, so far as I am aware, was published in 1901, viz., Hooker's Study of the Marriage Rate and Trade. The present revised edition of Bowley's text reflects these developments. In Part I, for instance, dealing with general elementary methods, the chapter on "Application of Averages to Tabulation" has been replaced by one on "Measurements of Dispersion and Skewness."
...

It is a joy to note the expansion in this new edition - its extent and its direction. The number of economists in the United States who are using the newer methods of statistical analysis and who have anything like an adequate mathematical training is still relatively small. More texts like Bowley and Yule, which bring together and summarise the widely scattered results of researches into method, will greatly assist the extension of this knowledge to larger and larger numbers.

7.1. Review by: G Irving Gavett.
Journal of the American Statistical Association 22 (160) (1927), 523-527.

Professor Bowley's Elements of Statistics has passed to its fifth edition. The fact that a book of this class has been in constant use for over twenty-five years, outgrowing four editions, speaks very loudly for its excellence, without any further comment. So many editions have enabled the author to eliminate errors, to make additions, and to bring the material up to date. As a consequence the fifth edition is very little different from the fourth edition. And to the many persons familiar with the fourth edition little needs be said concerning the fifth.
...

Part I has given material which the high-school graduate should be able to read. Part II requires at least the first two years of ordinary college mathematics. Some writers, notably Yule, have attempted to treat statistics without differential and integral calculus. This necessarily handicaps the treatment and frequently demands such statements as: "The proof cannot be given within the limitations of the present work." Professor Bowley's Part II is not handicapped in that way. He makes constant use of the work of Professor Karl Pearson, Professor F Y Edgeworth, W P Elderton, and others. He lays but little claim to anything wholly original. Nevertheless, it is a fine piece of work to have gathered together related portions of the work of so many men and placed them in a single book so as to make a continuous, logical whole.

It would be difficult to criticise the work of Part II unless one wishes to criticise in general the work of the whole English school of statistics. It would be interesting to have the work of Charlier and the Scandinavian school alongside for comparison and study.

Every person who has to handle statistics intelligently, and every person interested in the fundamental ideas involved in the practical use of statistics and the limitations of the methods employed should make himself familiar with the contents of Part II or its equivalent.

7.2. Review by: E M N.
Journal of the Royal Statistical Society 90 (2) (1927), 372-373.

The book is meant for all who handle statistics in any branch of their application, but, as is natural, in the examples economic and social problems are given prominence, and Professor Bowley's wide knowledge and experience in this field makes his treatment here specially valuable. This economic bias is to some extent true of the subject-matter also, and the student who has to deal with biological, medical, and industrial applications in research work will need to supplement the book with a rather fuller discussion of the theory of sampling, other than simple sampling, than is given here. ...

The ground covered by Professor Bowley is, however, so wide that to demand more is perhaps hardly fair, and the book can be confidently recommended for the study of all practical statisticians not yet familiar with it.

7.3. Review by: F B.
Economica 18 (1926), 373-374.

As one reviews a new edition of Professor Bowley's Elements there comes to mind one of Alfred Marshall's letters to its author on the publication of the first edition in 1901. "In my view every economic fact, whether or not it is of such a nature as to be expressed in numbers, stands in relation as cause and effect to many other facts; and since it never happens that all of them can be expressed in numbers, the application of exact mathematical methods to those which can is nearly always waste of time, while in the large majority of cases it is positively misleading." Since those words were written statistical technique has been applied to economic problems with increasing assiduity and with worthy results; yet too often, especially in America, with the blind faith and lack of science of a witch-doctor practising his magic. While, therefore, Professor Bowley learned, or had no need to learn, what Marshall wrote to him, the advice is still opportune for those who seize the tools of the skilled statistician and wield them dangerously. The new edition of Professor Bowley's Elements is substantially the same as the last, and the book is too well known to require description. While Professor Secrist is, as his Preface reveals, greatly interested in pedagogy, the Elements is addressed, even in its first and more elementary section, to more mature students, who alone realise how rich a mine it is and with what verbal economy it is written.

The new edition has shed a considerable number of misprints which were confusing to inexperienced students of the fourth edition, while the revised and enlarged index is another welcome amendment. May we hope that some day Professor Bowley will give us a set of exercises to enable the student, by practice, to become perfect in his knowledge of those matters treated in Part II of the Elements?

8.1. Review by: M G K.
Journal of the Royal Statistical Society 101 (2) (1938), 458-459.

The present edition leaves the main text unchanged, new matter being incorporated either as notes at the ends of chapters or as supplements. Dr Bowley has wisely not departed from his original design by attempting to cover all the new results of the last sixteen years in this fresh material. He has put "in the simplest possible way those formulae and ideas which appear to be most useful in the fields of economic and social investigation and of showing their relationship to the treatment followed in the text."

The study of Statistics has been described as a type of mental discipline; and a perusal of some of the journals devoted to social problems suggests that it is a discipline to which many economists could with advantage be subjected. However, this is a free country so far as private reading is concerned, and even the courses of instruction in economics at our universities still leave Statistics as an optional subject. One can only hope that before long every student will be required, for the good of his soul and the collective benefit of social research, to get a grasp of the nature and scope of the tools which he will later have to handle. Such a student would naturally turn to Dr Bowley's "Elements" in the first instance.

9.1. From the Preface.

The present course of Lectures on the Measurement of Groups and Series deals with some of the most modern methods of statistical research. Interesting as they were to those who had the advantage of hearing them delivered, they will doubtless, when studied at leisure in printed form, prove even more interesting and useful. These Lectures are the fifth of a Series originated in 1897, designed for the assistance of Actuarial Students in connection with matters not included in the official Text Books. Three of the Series deal with legal matters, and one with the subject of Stock Exchange Securities. The present course carries the range of topics into the field of mathematics, and it is hoped that courses of lectures may be hereafter provided dealing with other subjects, practical and theoretical, relating to those branches of knowledge which it is the province of the Institute of Actuaries to promote and encourage.

10.1. Review by: F Y Edgeworth.
The Economic Journal 14 (54) (1904), 268-271.

Mr Bowley's work belongs to a small class characterised by impartial statements, which command the respect of disputants on either side of a heated economic controversy. The modesty of the true statistician contrasts favourably with the hectoring tone of political partisans. Mr Bowley's main position is thus cautiously stated:- "Our information is not sufficient to allow us to form an absolutely certain judgment as to our recent progress." "It is conceivable that the facts that we do not know may present an appearance opposite to that of the facts that we do know, as it is conceivable that the hidden hemisphere of the moon differs from that which we see; but it is prima facie improbable that the same main causes are presumably acting in the unknown as in the known." All the phenomena in the observed economic hemisphere - the changes of occupation, the progress of wages, the increase of national income, and so on - suggest that we have made considerable progress in wealth and welfare during recent years.

11.1. Review by: A W Flux.
The Economic Journal 20 (78) (1910), 268-271.

As an elementary guide to the handling of numerical statistics, this manual should perform a useful service. It fills a gap which was much in need of being filled, and, naturally, encounters the ordinary difficulties of the pioneer. That the writing of an elementary text-book is a task vastly more difficult than the preparation of a treatise for advanced students is a commonplace. The most admirable elementary manuals are those which have undergone repeated revision, and many of the points which invite criticism in the volume under consideration are such as are likely to undergo modification as opportunity arises - that is to say, they are more or less natural defects of a path-breaking textbook. Nevertheless, the suggestion that the volume was prepared, probably from lecture-notes, in some haste, forces itself on the reflecting reader of its pages, and the haste is to be regretted if it be the true cause of certain defects, small in themselves, but not negligible when considered cumulatively. The book being especially intended for beginners, the standards by which it must be judged are those that apply to a book for beginners. In such a book much importance attaches to even minor details.

The teachers who have urged their followers to observe their precepts rather than their practice have admitted a well-known failing of humanity. In general the precepts laid down in this manual are admirable, but the expenditure of sufficient time to ensure that they were uniformly observed in the couple of hundred pages of the book would have added to its value as a guide for beginners.

11.2. Review by: A W F.
Journal of the Royal Statistical Society 73 (4) (1910), 435-437.

Mr Bowley's new manual is intended for a class of readers having less special training in statistics than those to whom his former text-book on the subject was addressed. It is divided into two parts, the first of which is devoted to general principles to be followed in the use and in the interpretation of statistics, while the second forms in some sense a guide to the official statistics of the United Kingdom, showing the nature of the contents of some of the principal publications of this character. It is not necessary to say that Mr Bowley sets before his readers high ideals in matters statistical. He gives them, too, much sound advice as to things to avoid, and as to where careful analysis is essential before accepting the apparent conclusions based on statistical data. He employs in general the newest material for his illustrations, and takes advantage of the newest methods, though avoiding in this volume the technical detail which would not be intelligible to those whom he more particularly addresses. He does, however, suggest in one place the adoption of certain new notations, though he leaves them to sink into the minds of his readers, and does not venture, by their general use, to give an unfamiliar appearance to his pages, except those devoted to the examples given as exercises for students. We cannot confess to finding the new notations sufficiently attractive to regret the course taken in regard to their actual use.

11.3. Review by: J A F.
Journal of Political Economy 18 (7) (1910), 563-564.

Modern development in statistical Science has been so characteristically an elaboration of the more advanced forms of mathematical analysis that what may be called the common sense of statistics has seemed to be neglected. We have had books of ability on statistical analysis, and some excellent critical compilations of statistical results, incidentally outlining the methods by which such results are attained. But satisfactory books designed to teach the critical use of simple statistical tools and to educate the quantitative sense have been almost or quite lacking. One turns, therefore, hopefully to an Elementary Manual put forth by a writer of reputation.

Mr Bowley has stated well and compactly the purpose of his book. It "is intended for the use of those who desire some knowledge of statistical methods and statistical results without going deeply into technicalities or under taking mathematical analysis" - for the laymen who have to interpret facts which they encounter in statistical form. "It is also designed as a first course for students who wish to proceed further in the subject. ..." No one who can perceive the difficulty of making one small book serve as a fundamental treatise and also as a conspectus of miscellaneous statistical results will be surprised that Mr Bowley has not been wholly successful.
...

... the first part of the book has merits which recommend it for the use of beginners in statistics. If only Mr Bowley had developed this portion of his work to perhaps double its actual scale by clarifying and re-enforcing the exposition, it could be very warmly welcomed. As it is, it adds another to the respectable list of statistical books which are partly

11.4. Review by: Allyn A Young.
Publications of the American Statistical Association 12 (92) (1910), 385-386.

Mr Bowley's new book differs from his well-known Elements of Statistics, not only in its greatly diminished mathematical apparatus, but also in its different purpose and scope. It may be described as a handbook of statistical criticism. The first part deals with the elementary statistical processes, - averaging, tabulation, the use of diagrams and the like, but with special emphasis throughout upon the necessity of recognising and stating the limitations of the accuracy of the data used and of the processes themselves. The second part is a survey of the more important classes of English official statistics. How the statistics are gathered, what they actually mean, their inherent limitations and the kinds of inferences that safely may be based on them are all stated with clearness and precision and with pertinent concrete illustrations. The book is hardly constructive enough to serve as a formal text-book, but it is a good book to put into the hands of students or of others who are entering upon their statistical apprenticeship. Some of the fundamental criticisms of English statistics should be useful to all statisticians. We greatly need a book dealing in similar fashion with American statistics or, better yet, with official statistics in general.

11.5. Review by: Wm B Bailey.
The Economic Bulletin 3 (4) (1910), 422-423.

In this manual, we have a textbook for the use of students who desire an elementary course in the theory and practice of statistics. The first nine chapters, comprising 82 pages, are devoted to statistical method. The subjects treated are: Nature and Use of Statistics; Accuracy and Approximation; Averages; The Accuracy of Averaging and Other Arithmetical Processes; Tabulation; Sampling; Rules for Using Published Statistics; Methods of Statistical Analysis.

The remaining hundred pages contain a splendid study of the contents and accuracy of the principal official statistical publications of Great Britain with some suggestions as to the results which may be obtained from their use. ....

It would be difficult to name a work in which the contents and reliability of British official publications are described more clearly than in the second half of this work. Taken as a whole, this manual is perhaps the best elementary textbook upon statistics which can be put in the hands of the beginner. It would be of great value to American students if a volume were prepared showing the reliability of the statistical material in the official publications in this country and pointing out the sources of the most reliable information upon our social and industrial life. The value of the volume as a textbook is much increased by the addition of a number of questions upon the points covered in the different chapters. Professor Bowley in this and his previous work upon statistics has done much to provide the teacher of statistics with suitable textbooks.

12.1. Review by: Anon.
Journal of the Institute of Actuaries (1886-1994) 50 (1) (1916), 70-71.

Although intended primarily for beginners Dr Bowley's Elementary Manual is a book that may be read with advantage by every student of statistics. Perhaps its chief merit is that in Part II it introduces the reader to actual statistical data by giving some account of the official statistics relating to such subjects as population, trade, prices and employment. But Part I, which deals with the elements of statistical method, contains useful information on various practical matters which might escape the student who approaches the subject exclusively from the mathematical side, e.g., the use (or abuse) of percentages, the use of diagrams, the necessity for precision in the headings of tables, and, the main points to be kept in view in considering published statistics. And, in view of the difficulty of obtaining examples for self-examination, the collection of exercises in Appendix I is a useful feature.

13.1. Review by: W P E.
Journal of the Institute of Actuaries (1886-1994) 59 (3) (1928), 424-425.

An earlier edition of this book was reviewed in Vol 50. The first part of it is unaltered but, consequent on the war, the author has re-written Part II., which deals with statistical work in connection with population, vital statistics, trade, wages, employment, etc. The reader will notice that the statistics discussed vary between mere enumeration (e.g., in Censuses) and ingenious estimates (e.g. the figures given for aggregate of incomes) : he will appreciate that statistical work covers the whole range between these extremes and he will probably feel, as he finishes the book, that it is the ingenious estimate, rather than the mere enumeration, that encourages and attracts.

14.1 From the Preface.

This book is the result of an attempt to bring within two covers a wide region of pure mathematics. Knowledge is assumed of that part of mathematics usually required for matriculation, namely algebra to simultaneous quadratic equations and the substance of the first four books of Euclid, together with a very slight acquaintance with graphic algebra, mensuration, and solid geometry. From this stage the work is carried forward in algebra to the logarithmic series; in coordinate geometry to the nature of the general conicoid; in trigonometry to the use of Euler's expressions for the sine and cosine, with a careful treatment of imaginary quantities; in calculus to definite integration and the maxima of a function of n independent variables; together with the pure geometry which is necessary for the other subjects. It has been the intention to include the bulk of the results obtained in pure mathematics which admit of rigid proof of a fairly easy character, and are needed by those who use pure mathematics as an instrument in mechanics, engineering, physics, chemistry, and economics. For this purpose a very great deal that is ordinarily contained in text-books has been thrown aside, and only those theorems and formulas which are of direct practical application or which are necessary to lead to others of direct practical application are retained.

It has also been the intention to give exact definitions and strict proofs, of a more careful nature than those found in many of the more diffuse and elementary books; only two difficulties have been intentionally glossed over, viz., the nature of continuity and the nature of irrationals.

14.2. Review by: Anon.
The Mathematical Gazette 7 (108) (1913), 214-215.

Perhaps the only adverse criticism that can be made against this excellent volume is that one is not clear as to the section of the public for which it is intended. It is admittedly not for the mathematical specialist; for the engineering student, it is, more's the pity, liable to be considered too rigorous, preference being given to one or other of the advanced treatises labelled "Advanced Practical Mathematics"; and, apparently, in England these two classes alone are worth consideration! The volume starts from an assumed knowledge of "Matriculation Mathematics" and extends to and slightly beyond "Scholarship Mathematics."
...

After finishing the perusal of such a book as this, we feel what a pity it is that, leaving higher work out of the question, we fail to convince the non-mathematical student that he requires a knowledge of the theoretical side, even of Matriculation Mathematics.

14.3. Review by R D Carmichael.
Bull. Amer. Math. Soc. 21 (1) (1914), 39-40.

The considerable number of topics, the discussion of which is brought together in this one book, are treated in separate sections and probably in a larger degree of isolation from each other than most readers would expect in a single volume in which all of them find a place. The exposition, on the whole, is fairly satisfactory; some of the sections are excellent. The section on limits and series is the least satisfactory of all; some of the statements in it are properly characterised as awkward

The book as a whole is a contribution of some value to the pedagogy of that part of the mathematical curriculum with which it is concerned. Some of the controlling ideas in its preparation might well be adapted to the needs of American institutions; but the book itself is probably not well suited to such purposes.

14.4. Review by: Anon.
The Mathematics Teacher 6 (3) (1914), 182.

Beginning with indices and ending with solid analytical geometry the author has in one book covered in a scholarly manner the principal body of the pure mathematics a student will want for the pass examination in the universities. It comprises algebra after quadratics, similar figures and projection in one plane in geometry, trigonometry, plane coordinate geometry, calculus and solid analytical geometry.

15.1. Review by: E Brabrook.
Charity Organisation Review, New Series 38 (225) (1915), 309-312.

This work is one of the publications of the Ratan Tata foundation for the study of problems of poverty. It follows on the similar investigations of Mr Charles Booth, Mr Rowntree, and others by extending the methods of those workers to another series of towns, and by introducing some new processes of inquiry and some other fields of research. The keynote was given to it by the paper which Dr Bowley had contributed to the Royal Statistical Society on the methods and results of his observations on Working-class Households in Reading, where his residence for some years had given him the opportunity of acquiring intimate personal acquaintance with the condition of the population. The chapters relating to Northampton, Warrington, and Stanley are contributed by Mr Burnett-Hurst; for the summary of the principal conclusions both authors are responsible, and Dr Bowley furnishes a criticism of the accuracy of the results.

15.2. Review by: B S Rowntree.
The Economic Journal 25 (99) (1915), 427-430.

The book now under review is devoted to four towns: Northampton, Warrington, Stanley, and Reading. It is of exceptional interest, not only because it substantially increases the number of towns investigated, and thus helps us to gauge the extent to which results already obtained may be regarded as typical, but because the methods of research which it describes differ from those hitherto employed. Former investigators set to work to make a complete scrutiny of the town under investigation, going from house to house for their information, a process which, though having an element of completeness, involved much time and expense. Messrs Bowley and Burnett-Hurst have adopted the sampling method, only visiting about 5 per cent. of the houses in each town. They carefully estimate the probable margin of error involved in using this method, and show that it cannot materially affect the conclusions to be drawn from the given data. Thus with comparatively small expenditure of time and money the vital facts with regard to the social conditions may be ascertained, even in a town of considerable magnitude.

Their inquiry deals with four aspects of social life, and deals with them both vitally and comprehensively. Those aspects are housing; the constitution of the family, distinguishing between earners and dependents, men, women, and children; wages and the standard of life of the workers; and the immediate causes of poverty. The whole of the work has obviously been done with conscientious care and complete impartiality

15.3. Review by: Anon.
The Irish Monthly 46 (539) (1918), 300-301.

A study of the economic conditions of working class households in Northampton, Warrington, Stanley and Reading. The investigation, made on a basis of average, is very thorough and the tabulation of results showing clearly the interaction of the various economic factors is well done. With what justification a certain Scriptural quotation about "whited sepulchres" and "dead men's bones" could be applied to our social fabric which some people find "so fair to outward view" a single conclusion from this study may illustrate. Taking a "poverty line standard" which considers "only the minimum expenditure needed to maintain physical health and which makes allowance for those items of expenditure for which the ordinary man or woman will, in practice, postpone the purchase of certain necessaries," and defining "Primary poverty" to mean a condition in which "the actual earnings (including pensions) of the family pooled together are insufficient to give all members food and clothing up to the poverty line standard," the authors find that in Northampton one person in 11, in Warrington one in 7, in Stanley one in 16, and in Reading more than one in every 4 persons were living in "Primary poverty."

15.4. Review by: A D W.
Journal of the Royal Statistical Society 78 (3) (1915), 455-456.

Dr Bowley has, we believe, what may be called a paternal interest in the theory of sampling. In the book before us are given the results of a practical application of that theory, and they are very valuable. Dr Bowley and Mr Burnett-Hurst have sampled (in 1912 and 1913) the populations of the four towns named, taking, roughly, one household in twenty, to ascertain the conditions respecting rents paid by the working-classes, their housing, the composition of their families, and their earnings and poverty. The results as regards Reading have appeared in this Journal (June, 1913), but a summary of them is included in the present volume. The theory of sampling is a sound one, and the authors are satisfied that the present example of it affords, on the whole, a representative picture of working-class conditions in the towns investigated. Where the results of the sample are compared with complete data the differences, in most cases, are well within two or three times the probable error, and where this is not the case special explanations are suggested. ...

The work is a considerable contribution to the growing literature on the conditions of life of the working classes, and students and social workers are indebted to the Ratan Tata Foundation for its publication.

15.5. Review by: Frank H Streightoff.
The American Economic Review 5 (4) (1915), 899- 901.

The Ratan Tata Foundation "to promote the study and further the knowledge of methods of preventing and relieving poverty and destitution" is responsible for the publication of this book which is interesting not only for the statistical method employed, but also for its conclusions. In 1912 Dr Bowley made an experimental study of the working-class families in the city of Reading, and the experience there gained served to economise energy in the surveys in the other towns made the following summer by Mr Burnett-Hurst. In order to obtain an accurate sample of the working-class population, the tax lists in Stanley and Warrington and the directories in Northampton and Reading were carefully checked over, every twentieth building being noted. These buildings were then visited, and information was collected from all that were inhabited by working-class families. The only case in which another building might be substituted was that of a house found vacant, when the next dwelling on the left was to be approached. By this means schedules were filled out at almost exactly one house in twenty. Wherever it was possible to check the results thus obtained by figures in the census or Board of Trade reports, the comparison showed that the statistics gathered by the investigators were quite accurate. It seems possible to accept with confidence Dr Bowley's well-argued conclusion that the deductions drawn from the statistics are truly representative of the four cities in question. ...

Cautiously written, thoroughly considered, well founded upon carefully planned tables, this book is one which inspires confidence. It is full of interesting facts and fertile suggestion.

15.6. Review by: Edward Porritt.
Political Science Quarterly 30 (3) (1915), 518-520.

The object of the Ratan Tata Foundation, of which the headquarters are at the School of Economics, Clare Market, Kingsway, London, W. C., is to promote the study of methods of preventing and relieving poverty and destitution. The Foundation makes inquiries into wages and cost of living, methods of preventing and diminishing unemployment and measures affecting the health and well-being of the wage-earning classes. The results are published in pamphlet or book form. In addition to disseminating information, the officers of the Foundation "will, as far as is in their power, send replies in individual inquiries relating to questions of poverty and destitution, their causes, prevention, and relief, whether at home or abroad." Livelihood and Poverty is the sixth in the series of the publications of the Foundation, and it is an admirable example of the work which the Foundation is undertaking.

Northampton with its shoe industry, Warrington with its iron and steel, its chemical and its brewing industries, Stanley, as a centre of the coal trade in the great mining county of Durham, and Reading, a large centre in the biscuit trade, are typical English industrial towns. Only Stanley, however, can be described as a labour camp; for Northampton, Reading and Warrington are old market towns, with the usual market-town trades and commercial activities, and each was a place of some commercial and social importance centuries before the industrial era and the days of labour camps, of which England has now its full quota. In each of these large towns - at least three of them would be called cities in this country - the method of investigation has been to take a certain proportion of the working-class homes and make house-to-house inquiries in accordance with a uniform schedule of queries ...
...

Some of the surprises of Livelihood and Poverty are the bad housing conditions that still survive in these English towns, and the fact that the old domestic method of shoe manufacturing has still some survivals in Northampton. It is cheering to note that machinery is displacing hand labour - mostly the labour of women and girls - in the monotonous and exhausting work of fustian-cutting in Warrington, one of the largest centres of the velveteen industry in England. Moreover, as was to a great extent the case when nearly thirty years ago machine composition began to take the place of the method that was as old as letter-press printing, fustian cutting by machinery seems likely to result in comparatively few additions to the ranks of the unemployed.

16.1. Review by: G G C.
Journal of the Royal Statistical Society 78 (4) (1915), 614-616.

This essay, a prefatory note states, contains the substance of four lectures delivered at the London School of Economics and Political Science in January and February, 1915. It is an attempt, at least, to set out the data so far available for forming a forecast of the character of British external trade during the continuance of the war. Professor Bowley examines the monthly returns of British trade from 1906 to 1914 with the view of having some light thrown on the question of what changes were to be anticipated in the latter part of 1914 apart from the war, so as to eliminate these from those which the war may be held to have brought about. His conclusion is that in July, 1914, trade as a whole was still on a level that would have been reckoned extremely high in any year before 1913, although there were then immediate signs of weakness in the cotton trade, with reference to which he refers to the Paper by Professor Chapman and Mr Kemp in the March number of this Journal. But, however large a part of the decline in trade may be due to other causes than the war, the reader will agree with Professor Bowley in thinking that it is well to bring into prominence the fact that the diminution in value of the exports of manufactured goods in 1914 as compared with 1913 has been greater than if the entire cotton export trade had ceased to exist. An important part of the essay is devoted to the consideration of the balance of trade, including an explanation of how the greatly enhanced excess of imports since the war has arisen and how it has probably been met. This question is necessarily one of values, but one of the chapters is devoted to the important question of changes in the quantity of trade, for after all it is quantities that we consume. In estimating these changes Professor Bowley relies chiefly on the familiar method of computing the total quantity of trade on the assumption that the value of the total trade has changed with reference to a standard period in the same proportion as such change has been ascertained for commodities making up the larger part of the trade (or the trade in different classes), and then calculating values for the periods in which there were different values on the basis of the standard prices.

16.2. Review by: E J R.
Studies: An Irish Quarterly Review 4 (15) (1915), 508-509.

In this work Dr Bowley points out that, as his analysis of the external trade of the United Kingdom only covers a period ending with the year 1914, it is much too soon to forecast the lines of growth or the probable quantity and quality of trade during the continuance of a state of war; but, nevertheless, it is still of great importance to set out the data we have and to envisage the problem. This he does with considerable lucidity. Beginning with a table showing the movement of imports and exports in each year from 1901-1914, he traces the significance of the fluctuations which occurred, and explains many of the ambiguities which are to be met with when one endeavours to master the intricacies of these very involved returns. His analysis is of a comprehensive character and. should prove valuable as an introduction to the study of this subject in its rapidly changing phases, as week by week new conditions arise which cause the student to reconsider his deductions. At the end of the book will be found two useful diagrams showing the value of imports, exports, and re-exports at United Kingdom ports during the years 1906-1914.

16.3. Review by: C K Hobson.
The Economic Journal 25 (100) (1915), 585-586.

In this little book Professor Bowley examines the foreign trade statistics of the United Kingdom during the critical months August to December, 1914. The outbreak of war was accompanied by a violent shock to trade, and followed by a gradual recovery to a position of fresh though unstable equilibrium, from which the author (rightly, as events have shown) anticipates a healthy development. Professor Bowley begins by discussing the values of imports and exports in the aggregate, considering the statistics of foreign trade before the war, and describing succinctly the basis on which the accounts are compiled. He points out that the value of enemy cargoes sold in the United Kingdom is included in the statistics of imports, though the ships themselves are excluded, and that such gifts to the Government as that of wheat from Canada are excluded. Attention is also called to the fact that goods taken out of the British Government's stores and depots, whether for the use of the British or the Allied forces, and goods bought by the Government and shipped directly on Government vessels, are not counted as exports. Professor Bowley, however, omits to mention the fact that military and naval stores brought into the country on Government vessels are not counted as imports, and that information is withheld in regard to some other goods brought in on ordinary merchant vessels.
...
Professor Bowley goes on to examine the course of trade in the principal commodities, the question of quantities and prices, and in the last chapter the course of trade with special countries. The most striking feature of the import trade was the way in which the steady supply of foodstuffs was maintained during these most critical months. ... On the whole, Professor Bowley concludes that the enemy's efforts to check our supplies from countries not actually at war have had less effect than a minor trade crisis, and about as much as a moderately serious strike of transport workers.

17.1. Review by: Anon.
Charity Organisation Review, New Series 37 (222) (1915), 317-318.

Professor Bowley is well known as a past-master in the art of social statistics; and at a time when 'investigations' are so numerous, and carried out by persons of such very various qualifications, it is important to have from an expert such guidance as is contained in this little volume. The author has skilfully avoided for the most part the use of technicalities which would be incomprehensible to the reader untrained in mathematics; but the subject makes difficult reading, and is not illuminated by the genius which made Sir E Giffen's Essays at once so instructive and so absorbing, even to the layman. Perhaps that is inevitable in lectures dealing rather with the grammar than with the sub- stance of statistics. We should like to have a book from Professor Bowley on a slightly different subject, i.e., the interpretations of social statistics, in which he would show us how to handle and interpret the existing statistics, and teach us to ward off the undigested lump of figures with which the journalist and the amateur philanthropist are apt to bombard the patient public. would be an expansion of a wise saying of his own measurements 'are, after all, means of forming judgments not the judgments themselves.'

17.2. Review by: Anon.
The British Medical Journal 1 (2940) (1917), 582.

A book which may be mentioned is Professor Rowley's work on the Nature and Purpose of the Measurement of Social Phenomena, founded on a course of lectures given in the Faculty of Economics at London University in 1914. Its appeal to the general public is likely to be limited, but it deserves the careful attention of social workers and investigators. In the whole sphere of science there is probably no subject so rife with ambiguities of definition and other pitfalls for the unwary as modern statistical sociology. Regarding society as an organic whole, the statistician endeavours to give a quantitative description of all its parts, in the first place as a contribution to pure science, and secondly, with a view to the modification of unsatisfactory conditions in conformity with some social ideal." On the one side, measurement should result in accurate and comprehensible description that makes possible the visualisation of complex phenomena; on the other, it is necessary to the practical reformer that he may know the magnitude of the problem before him." The scope of the book can best be briefly indicated by the following list of main headings: The nation or society; relation of persons to areas; classification, industrial, by degree of dependence, by social position; classification by order, by incomes, individual family, nature of family income; production and consumption; the standard of living, conventional, minimum, the poverty line. Having analysed the available methods of classifying the individuals and families of a society as previously defined, the author shows how families typical of classes or occupying a numerically defined position in the economic scale are to be identified. In his last chapter he deals with economic progress, of which he considers there is no better test than that which shows what proportion of a nation are in poverty.

17.3. Review by: James A Field.
Journal of Political Economy 24 (4) (1916), 408- 409.

The formidable name of this book must not be taken too seriously. Mr Bowley himself hastens to say so in a prefatory note which is pretty nearly an apology for the title-page. Without such a warning the reader might expect to find here a systematic treatise, somewhat in the German manner, profound, abstract, and impersonal. What he does find is a small volume of large print in which a versatile and accomplished statistician, talking of British conditions to a British university audience, discusses practically and in the light of his own experience some of the methods and aims of a comprehensive social survey.
...

Throughout the book it is apparent that Mr Bowley is discussing not statistical problems at large but the concrete statistical problems he has himself encountered. He is giving some of his statistical reminiscences. This quality of his work, in one sense a limitation, is at the same time perhaps its most interesting feature and even its cardinal merit. For here is a book of statistical experience; and statistical experience is not easy to put into books. Raw data, good and bad, we have in plenty. Of competent treatises on pure statistical theory there are not a few. But to bring together the facts in harmony with the principles we need statistical insight and a sense of statistical values that only experience can originally give, and that only the experienced teacher can impart.

17.4. Review by: M G.
Journal of the Royal Statistical Society 78 (4) (1915), 616-617.

The concluding paragraph of this book opens with the sentence: "We ought to realise that measurement is a means to an end: it is only a childish mind that delights in numbers for their own sake." The spirit of this apophthegm informs the whole of Dr Bowley's work. He has given us, in fact, a careful study of the aims a sociological investigator has in view when he compiles or analyses statistics, of the difficulties which will be encountered, and of how they may be in part at least overcome. Those who are familiar with Dr Bowley's more technical writings will not find in the present volume much that they had not already learned from him, but even they will welcome this succinct presentation of his ideas, while to a large class of readers it will be of the greatest value. It is exceedingly difficult to bring home to untrained users of statistics not only the fact that the interpretation of data is frequently doubtful, but the reason for this as well. An attentive perusal of the chapter entitled The Standard of Living should save many readers from committing themselves to definite and erroneous statements. It need not be supposed that Dr Bowley confines himself to the utterance of warnings and that his readers will conclude that the best thing to do with statistics is to leave them alone. On the contrary, particularly perhaps in the passages dealing with the use of classifications by rank, many practical hints are given as to the possibility of instituting valid and useful comparisons. The application of such ideas in the gauging of economic progress is especially valuable. We also desire to commend Dr Bowley's criticism of standard dietaries and the deductions made therefrom. We concur with him in thinking that, valuable as are the results of physiological and chemical inquiries into the subject, the superstructure of sociological and economic inference which has been reared upon them is a trifle top-heavy.

17.5. Review by: Robert E Chaddock.
Political Science Quarterly 31 (2) (1916), 334-335.

This book presents the material covered in five public lectures given in the Faculty of Economics of the University of London in 1914. The author recognises the fact that the title offers promise of more than he has been able to fulfil in this brief exposition, but it seemed desirable to publish the lectures promptly because they "deal with matters of immediate importance to social workers and investigators." Especially those who gather data, but also those who seek to weigh the significance and limitations of facts already gathered, will find these pages full of illuminating suggestions and timely warnings, meant to promote the scientific character and practical results of their work.

Measurements are frankly regarded as means to an end, i.e., "accurate and comprehensible description that makes possible the visualisation of complex phenomena." It is this that the scientific investigator, the social worker, or the social reformer needs in order to comprehend the magnitude of his problems and their relations. The reading of the latter part of the book will promote a better understanding and a more common-sense discussion of the problems connected with standards of living and economic progress. Economic phenomena are included under the term "social," which is to be distinguished from biological phenomena. The task is to "determine what are the facts which it is essential to know and devise a means of ascertaining them."

17.6. Review by: H Sanderson Furniss.
The Economic Journal 25 (99) (1915), 430-431.

This book contains "the substance of five public lectures given in the Faculty of Economics in the University of London in April and May, 1914." (Prefatory Note.)

There are now available for economists, and for others who care to use them, vast official and private collections of statistics, and Professor Bowley thinks that the time has come to take stock of the activities which have produced them, and" to assign (them) their place in an organic body of science, to consider from the beginning the general objects and methods of social investigation, and to inquire how far these objects have been or are in the way of being attained."

The book is full of suggestions, both as to the best methods of obtaining statistics in various fields of inquiry, and as to the uses to which they may legitimately be put when obtained; and throughout its pages the author points out numerous pitfalls of a kind which are not always successfully avoided even by those most skilled in the collection and in the use of statistics.
...

The author's hope for the book is that "the result of the examination will be to appraise, if indirectly, the value, relevancy and reasonableness of the general existing stock of statistical results, and to suggest some lines of further progress", a hope that should certainly be realised.

18.1. Review by: W P E.
Journal of the Institute of Actuaries (1886-1994) 54 (3) (1923), 298-299.

A second edition of Dr Bowley's book on "The Measurement of Social Phenomena" has been brought out and it contains many hints on statistical matters which are of value to students. It is one of those books of lectures which retains in its printed form much of the attractiveness associated with the spoken word.

18.2. Review by: A Z.
Journal of the Royal Statistical Society 88 (2) (1925), 281.

The first edition of this book was published in 1915, and was reviewed in the .Journal for July of that year. In the present edition the text has been revised and some notes and references added. (Incidentally, one of these notes deals with the minor point of criticism raised in the review referred to above.) It is perhaps unfortunate that the 1911 Census figures had to be retained for the statistics given by way of illustration, since the 1921 arrangements included important changes; but we certainly agree that it was not worth while holding up the issue of this volume on this account until the 1921 results had all been published.

Interest in statistics and statistical methods as a means towards the study of sociological conditions has grown considerably since 1915, and it is all the more necessary, therefore, that sure guidance should be available as to the proper uses, trustworthiness and limitations of the instrument. Dr Bowley's book provides this, and his clear exposition should be valuable to .many. In particular, the chapters on the standard of living and economic progress give timely advice on the carrying out of investigations into these pressing problems of the day.

19.1. Review by: Edwin Cannan.
The Economic Journal 29 (114) (1919), 207-213.

No reader of the Journal with any serious interest in the distribution of income is likely not to have read Professor Bowley's masterly contribution to the subject by this time, so that I need not waste space in summarising his conclusions, which appear to be eminently sound, though they have excited some indignation in minds of undue optimism which find the atmosphere under his wet blanket somewhat suffocating.

19.2. Review by: Willford I King.
The American Economic Review 9 (3) (1919), 617-620.

In this brief monograph Professor Bowley incidentally sets forth the salient facts concerning the national income of the United Kingdom just before the World War, but his chief purpose in so doing is apparently to answer the queries of socialists and others as to how much income might safely or unsafely be diverted from the existing share of the rich and added to the wages of the labouring class. He considers what might be done under the existence of the present competitive regime and also what might be accomplished if a socialistic state were substituted for the present order.

The work is a thoroughly well balanced and scientific treatise. It, like most English statistical studies, however, contains too many figures in the text and it could be made more attractive and intelligible to the general public if accompanied by a set of graphs illustrating the essential features. As it is, the less-careful readers are likely to fail to differentiate unimportant items from figures of major importance. The author has been wise in not confusing his reader with superfluous details concerning the sources of his information and yet he has given sufficient reference to show the basis of the estimates set forth. No one familiar with the careful work of Professor Bowley need question the fact that the figures presented are as accurate as the materials at hand make possible.

19.3. Review by: E Brabrook.
Charity Organisation Review, New Series 45 (270) (1919), 163-164.

Professor Bowley brings to this difficult and pressing question the qualifications of a master of statistical method who has made the subject of labour and its remuneration matter of long-continued study and research. In 1989 he showed that in the United Kingdom, France, and the United States of America alike, real wages had doubled in less than fifty years and increased by one half in less than twenty years. In 1901 to 1908, as secretary of a committee of the British Association, he rendered great public service by investigating and drawing up reports on Women's Labour. His presidential address to the Section of Economic Science and Statistics in 1906 dealt with statistical method in its application to labour problems.

20.1. Review by: F Y E.
Journal of the Royal Statistical Society 83 (3) (1920), 482-484.

Professor Bowley's latest study on the division of national income enhances the value of his penultimate contribution to the subject. The observations which he lately recorded with respect to the division of the national dividend at a particular epoch become now more trustworthy when it is shown that the proportions observed in one year are apt to remain constant for a series of years. The new observations perform the part of inductions fitted to be the test of others, to use the phraseology of Mill. Comparing the evidence against the existence of black swans and against that of men whose heads grow beneath their shoulders, Mill justly observed "it was more credible that a bird should vary in its colour than that man should vary in the relative position of his principal organs." Previous experience showed that the negative evidence against the black swans, though more unanimous, was less trustworthy. Now this is the sort of induction about inductions which Professor Bowley's new brochure supplies. An experience extending over more than thirty years leads us to expect that the proportions in which the national income is distributed will, in ordinary times at least, change very slowly.

21.1. Review by: A D Webb.
The Economic Journal 31 (124) (1921), 498-501.

The division of Economics and History of the Carnegie Endowment for International Peace has planned an "Economic and Social History of the World War," and the present monograph by Dr Bowley is among the first of the series arranged by the British editorial board. Its subject is the movement of prices and rates of wages in the United Kingdom from the out-break of war in 1914 down to about the middle of 1920, the latter date, as it happens, marking the culmination of the upward movement characteristic of the period.

The data are for the most part derived from official records already published, and Dr Bowley, as we should expect, presents them with admirable skill. The result is a highly valuable epitome, critical and appreciative, of the facts about prices and wages during the war period, so far as they have been made public.

Prices and wages are, of course, pre-eminently subject to treatment by the method of Index Numbers, and Dr Bowley has a good deal of criticism to offer of the validity, under war conditions, of the well-known Index Numbers of prices and the Cost of Living. ...
...
Dr Bowley has done a very valuable piece of work, and if the companion volumes of the series are as well done and as informative, the series will be indispensable to all who take an interest in the social and economic history of this country.

21.2. Review by: J F Rees.
The Scottish Historical Review 19 (76) (1922), 313-315.

Le Vicomte Georges d'Avenel declares that the history of prices is "la plus grosse part de l'histoire des hommes." Prices according to him afford the key to great secular changes which would otherwise remain mysteries to the historian. To tabulate records of prices and reduce them to some common denominator is to prepare the way for important discoveries. Here there is no need for hypotheses, nor can the human fallibility of the researcher lead to error. Figures cannot lie. This is an alluring prospect. But in spite of the enthusiasm of d'Avenel, and the assiduity with which he and his collaborators have collected prices, historians remain somewhat sceptical. Per haps they find it easier to form hypotheses and more adventurous to be liable to fall into error. If, however, they are inclined to put d'Avenel's principles to the test, they would do well to consider the period treated in this volume.

The War concentrated into a few years changes which normally work themselves out very slowly. For these years there is a great abundance of material. In fact, the difficulty is to take into due consideration the wealth of available evidence. Professor Bowley's book is one of the series planned by the Division of Economics and History of the Carnegie Endowment of International Peace in order to lay the foundation for the Economic and Social History of the World War. It is confined to an account of the principal movements of prices and of rates of wages.
...
This book is worthy of Professor Bowley's reputation as a statistician. He writes with intimate knowledge of the War conditions, for, although he does not tell us so, he was in constant touch with the Government departments during the period of strain which he here dispassionately describes.

21.3. Review by: E C S.
Journal of the Royal Statistical Society 85 (1) (1922), 119-121.

In the Foreword to this volume the publishers state that it gives an account of the principal movements in prices and rates of wages in the United Kingdom from the beginning of the War to the summer of 1920. "Without turning aside to discuss the reasons for particular regulations and the methods of administration (which will be the subject of other volumes of the series), Professor Bowley exhibits and analyses the economic results." In his Introduction Dr Bowley remarks: "this volume deals with results, not with causes."

The portion of the book dealing with prices follows the lines well known to students familiar with Dr Bowley's previous publications on the subject. Movements in wholesale and retail prices are followed with a wealth of detail, and the student will find collected in this part of the book full particulars for the period under review of most of the price quotations for food and materials which are readily obtainable. There is also a comprehensive account of the various indices of cost of living.

The second part of the book, dealing with wages, follows similar lines. It collects in convenient form a large mass of statistics concerning wages in many industries, dealing in detail with the Cotton, Wool, and Iron and Steel Industries as well as Agriculture, Coal Mines, Building, Railways, and Docks. Being in the main a collection of facts, the book does not lend itself to a detailed review. It is a pity, however, that the scheme under which the series of monographs referred to in the heading, above is being produced did not allow greater scope to Professor Bowley in his handling of the problem of wages between 1914 and 1920. The period under review produced more schemes of wages regulation than probably the whole of industrial history previously can show. It would have been invaluable to have had a critical account from Dr Bowley's detached point of view of the economic soundness and consequences of the various methods of paying bonuses on wages, and of the various sliding scales - according to some index of the cost of living or of the selling price of the product produced - brought into being during the War. To the present reviewer it appears that those industries which have not been fettered with sliding scales, but which adopted the flexible method of regular conferences between employers' and employees' representatives and adjusted themselves to the circumstances immediately confronting them, have been the ones best able to adapt themselves without strife or the threat of strife to the unprecedented alteration in industrial conditions which has occurred. For example, a sliding scale dependent upon some index of cost of living is now seen to be quite unsuited for an industry manufacturing a product which has to compete with similar products manufactured abroad.

Dr Bowley mentions the notorious $7\large\frac{1}{2}\normalsize$ per cent and $12\large\frac{1}{2}\normalsize$ per cent bonuses - a history of these and of their consequences was surely worthy of a separate chapter in a book dealing with War Wages - but does not mention specifically the Industrial Courts Act and other legislation which performed such invaluable service in the field of wages regulation during the War and afterwards. It may be, however, that it is the intention of those responsible for this series of monographs to include an account of these in the monograph on "Labour Supply and Regulation," though the student of the future may be excused if he looks for information of these in a book title of the one under review rather than the one just quoted.

22.1. Review by: Lewis Meriam.
Quarterly Publications of the American Statistical Association 17 (136) (1921), 1040-1041.

One's first reaction on examining this little book of sixty-three pages, less than four hundred words on a typical page, is a sense of disappointment that it is not for trained students of economics and statistics. They would welcome a book under this title written by the author for them, but they are nor the readers the author had in mind when he prepared the present essay. It appears in The World of Today Series, and although the purpose of the series and of the book itself is not specifically set forth, they are obviously designed for persons with a definite interest in public questions but with no special training and experience in their study. One who is familiar with the work of our large government statistical offices knows of the almost amazing popular demand for statistics, and the frequent failure to appreciate the almost inevitable limitations to their use. For this type of British citizen Dr Bowley has written. A similar work designed for American readers would be distinctly worthwhile.

23.1. Review by: M Tappan.
Economica 15 (1925), 334-338.

Many of us who are economists would be prepared, I think, to say of ourselves as Henry Adams said of himself, "At best he could never have been a mathematician; at worst he would never have cared to be one; but he needed to read mathematics like any other universal language, and he never reached the alphabet." Professor Bowley's excellently proportioned book is not for us, if we have not reached the alphabet of mathematics. But suppose that we have gone so far - and it is a very little way after all - then with the assistance of the Appendix to the present treatise, which gives the relevant theorems of the Calculus, we may follow the system of pure economics which is developed in symbolic form in the text. With a little practice, we may even follow it with sufficient ease to appreciate its harmony. For the first time, with possibly one exception, a number of the propositions and proofs of analytical economics which have found expression in symbols imbedded here and there in economic writings, appear as a single, co-ordinated and independent mathematical structure. Like a skeleton it is closely articulated, bare of softer parts and white, with the white light of reason.

Professor Bowley explains in his Preface that he has "attempted to reduce to a uniform notation and to present as a properly related whole, the main part of the mathematical methods used by Cournot, Jevons, Pareto, Edgeworth, Marshall, Pigou and Johnson, so far as these are applied to the fundamental equations of exchange and to the elementary study of taxation." And after modestly disclaiming originality in economic theorems and mathematical results, he adds: "Perhaps, however, there is in my analysis a more definite attempt than has been usual to deal equally with the hypothesis of competition and of monopoly, to find a place for incomplete monopoly, and to indicate how perfect competition and perfect monopoly are, mathematically, the extreme cases of a more general conception." Professor Bowley, needless to say, knows what he is about; and what others have been about becomes clear as the disguises of differing notations, divergent premises, and cross-drawn issues, fall away in his hands.
...

If "no Roman lost his life because he was absorbed in the contemplation of a mathematical diagram," no economist shall gain his life until he shall have been so absorbed. He cannot better seek grace than by turning to Professor Bowley's book; unless he has had the reviewer's greater privilege of hearing Professor Bowley present his exposition in lectures.

23.2. Review by: W L Crum.
The Quarterly Journal of Economics 39 (2) (1925), 313-319.

Professor Bowley states in his preface to The Mathematical Groundwork of Economics: "I have attempted to reduce to a uniform notation, and to present as a properly related whole, the main part of the mathematical methods used by Cournot, Jevons, Pareto, Edgeworth, Marshall, Pigou, and Johnson, so far as these are applied to the fundamental equations of exchange and to the elementary study of taxation." In the seven chapters, covering 77 pages of the work, he appears to have accomplished this principal purpose very successfully. The analysis throughout is well planned and carefully executed, and there is a minimum of those mechanical obstacles which frequently impede the study of a text in applied mathematics. The mathematical work of these chapters is illustrated by occasional well-chosen diagrams, and through it all runs a thread of verbal interpretation designed to assist the reader in linking up the symbolic expressions and equations with familiar concepts and principles of economic theory. The reviewer hazards the suggestion that the average reader might have been helped considerably if such verbal interpretation had been used more extensively, particularly in the first five chapters. Certain it is that the reader following the steps of the mathematical analysis must often interpolate descriptive phrases from his general knowledge of economic theory if he is to have a continuous picture of the bearing of the mathematics upon the economics.

23.3. Review by: F Y Edgeworth.
The Economic Journal 34 (135) (1924), 430-434.

A long-felt want is satisfied by this clear, concise and correct statement of the leading propositions and methods which mathematics contributes to Political Economy. A saving knowledge of that doctrine may be acquired here more readily than in any other treatise, English or foreign, with which we are acquainted. The learner is led from the simplest species of transaction on to "multiple exchange," and thence to dealings in products and the factors of production. By steps that are neither violently abrupt nor tediously circuitous he reaches the heights from which the mutual dependence of all economic quantities can best be contemplated. At those heights, too, are observed some curiosities of theory, like Alpine flowers, found only at great altitudes. The treatise is not merely introductory. The maturer student will be edified by it. He will be confirmed in the belief that his study is worth pursuing. The authorship of the treatise guarantees the importance of the subject. The author is a statistician of the hard-headed English type, who walks in the way of Tooke and Newmarch and Giffen; applying ascertained facts to important practical problems. Measuring the growth of wages and the proportions in which the national income is distributed, he has contributed more than most economists to the formation of intelligent opinion about popular schemes for the reconstruction of industry. It is not to be supposed that such a man would turn from investigations of national importance to formulate the mathematical theory of economics if with the literary economists he regarded that theory as moonshine. If challenged to show what fruit our branch of science bears we can at least reply that it is assiduously cultivated by one who knows what good fruit is, having produced it in great quantities. The importance of particular theorems as well as of the general theory is enhanced by Professor Bowley's work.

23.4. Review by: W P E.
Journal of the Institute of Actuaries (1886-1994) 56 (1) (1925), 107-110.

Prof Bowley has collected and reduced to a uniform notation the mathematical methods used by economic writers (Marshall, Edgeworth and others) so far as they are applied to the fundamental equations of exchange and taxation. The book will be helpful to those who are interested in this side of economics and the increasing use of mathematical expressions in economic literature is ample justification for Prof Bowley's work. It is unfortunate that the first figure in the book is so crowded as to give the reader an unhappy feeling at the start and we regret the use of $D_{x}$ for $\large\frac{d}{dx}\normalsize$. There are objections to the latter but they have been removed by frequent use and an unaccustomed symbol introduces similar objections.

23.5. Review by: Allyn A Young.
Journal of the American Statistical Association 20 (149) (1925), 133-135.

The readers of this Journal are familiar with Professor Bowley's high attainments in the field of statistics. His latest book reveals him as an adept in the difficult field of mathematical economics. He has attempted, he tells us, "to reduce to a uniform notation and to present as a properly related whole, the main part of the mathematical methods used by Cournot, Jevons, Pareto, Edgeworth, Marshall, Pigou, and Johnson, so far as these are applied to the fundamental equations of exchange and to the elementary study of taxation."

In this attempt, there is no room for doubt, Professor Bowley has been successful. His book is the one best guide available to the student who seeks to acquaint himself with the methods and results of modern mathematical economics. For this purpose it is vastly better than books about mathematical economics, such as those of Boven and Moret. Up to now, Zadwadski's able work, Les Mathématiques appliquées à l'économie politique, has afforded the best general survey of the field, but Professor Bowley's book is broader in scope and more systematic. Further, Professor Bowley is the first to weld the scattered parts of mathematical economics into a consistent whole. His modest disclaimer of intent to advance new theorems in economics should not be permitted to obscure the distinctly fresh and original quality of his own contribution. To relate two previously unrelated theorems is, in effect, to advance a new theorem. No small amount of pains and skill has gone into the making of this book.

23.6. Review by: A W F.
Journal of the Royal Statistical Society 87 (4) (1924), 619-621.

In this volume Dr Bowley has presented in a connected and systematic form mathematical expressions of some of the more important problems discussed by economic writers. His preface indicates that a desire is expressed by students for such of material which, as he says, as had to be sought in manly places and, when found, presents some difficulty owing to the variations in the notations adopted by the writers whose work is to be consulted. Even in Dr Bowley's volume there is found a necessity for using at the outset a notation which is varied later on. Of the notations selected we can only say that the needs of the case have caused them to be somewhat complex. If one began one's work with these notations and used them consistently, doubtless the significance of each symbol would be clear when the more involved problems were under discussion. ...
...

Dr Bowley has endeavoured to escape the cumbrous expressions of some of his forerunners, but he has been unable to avoid the use of a multiplicity of symbols, the task of following which is inevitably laborious. If those whose knowledge of mathematics is slight are tempted, by the assistance which this volume offers, to practise the use of mathematical formulae, they may gain less than they anticipate. ...
...

Dr Bowley has done his work well, but it may be matter for regret that economic students who are novices in the use of mathematical symbols should be encouraged in the practice of floundering among masses of formulae.

23.7. Review by: F H H.
The Journal of Social Forces 3 (1) (1924), 185.

Bowley's work is designed to give a degree of system and uniformity of notation to a vast amount of work on the mathematical treatment of value, exchange and taxation. He borrows freely from his predecessors, Cournot, Jevons, Pareto, Edgeworth, Marshall and Pigou, with little claim to originality. His will be an impossible book, however, for all but a few students of economics who have a penchant for mathematical forms. The usefulness of the book would have been greatly enlarged by a fuller text and less exclusive attention to mathematical formulae.

23.8. Review by: W F S.
The Mathematical Gazette 12 (174) (1925), 292.

An elementary study of economics involves a certain amount of graphical or algebraical reasoning. Professor Bowley's book deals with the more advanced stages, and aims at coordinating the mathematical methods which have been developed in modern times by leading economists, particularly in relation to exchange, production, and taxation. The treatment is quite general, the reader being usually left to make his own applications. A good many graphs are given, and the reader's interest might have been increased if the facts represented by these graphs had been stated.

23.9. Review by: C M D.
Transactions of the Faculty of Actuaries 10 (98) (1924-1925), 369-371.

From the Preface to this book we learn that Professor Bowley's aim has been to present in a coherent form the mathematical treatment of the theory of political economy which has been developed during the past eighty years or more. The book is intended for the advanced student, and a knowledge both of economics and mathematics is demanded. The actual number of mathematical theorems used however is small, and Professor Bowley has assisted the student by bringing them together in an Appendix of nineteen pages.

In mathematical application economists have been greatly indebted to Cournot, whose work entitled Recherches sur les Principes Mathématiques de la Théorie des Richesses was first published in 1838. Unfortunately this work was not fully appreciated until some years after Cournot's death in 1877, but it remains as the first authority on the application of continuous functions. Jevons who may be regarded as the English pioneer, first published his Theory in 1871. Since that time considerable use of mathematics has been made, but the results are scattered in the different works of the writers and in journals; the subject is also complicated for the student by the employment of different methods and of different notation. Professor Bowley has done a great service by collecting these results, and setting them out in proper relation; at the same time he attempts to reduce them to a uniform notation. He makes a general acknowledgment to the works of Cournot, Jevons, Pareto, Edgeworth, Marshall, Pigou, and Johnson, but it must be recognised that in the skilful presentation of the text a good proportion of original matter appears. A certain selection has been exercised in methods of approaching a proposition, and in some cases there is no doubt others would have made a different choice, but the name of the author alone is sufficient to stamp the book as a work of value. Professor Bowley, one of our most eminent statisticians, has always shown an active interest in the promotion of mathematical study, and has had much to do with the general advancement of mathematical economics as a subject in University studies. So far back in 1906, in his address to the British Association, he drew attention to the need of mathematical reasoning in statistics, and claimed that more attention should be given to the study of statistics in the Universities. His appreciation of statistical process is clearly evident in the present work.

24.1. Review by: E Abbott.
Social Service Review 1 (1) (1927), 149-151.

Three notable attempts have been made in England to determine by intensive field inquiries the percentage of the population of a selected community living "in poverty." The first of these was Mr Charles Booth's great study of London poverty, the results of which were published at intervals from 1887 to 1902 as papers in the Journal of the Royal Statistical Society and in the seventeen volumes of Life and Labour of the People in London. In 1901 Mr B Seebohm Rowntree published his statistics for York (Poverty: a Study of Town Life); and in 1915 Professor Bowley and his students added in Livelihood and Poverty statistics for five other English towns: Northampton, Warrington, Stanley, Reading, and Bolton." The present volume is a sequel to Livelihood and Poverty, but for both volumes the line of descent may be traced directly back to the earlier English poverty studies.
...

It was significant therefore that a distinguished statistician like Professor Bowley adopted, more than a decade later, the Rowntree method of securing data. The new features of Professor Bowley's plan were the introduction of a method of random sampling and the securing of information regarding the composition of working-class households. Professor Bowley's plan involved the scheduling of every twentieth house on every working-class street in each of the towns selected for study. The result, he believed, constituted a random sample of the population. As a matter of fact, instead of every twentieth house, "approximately one working-class house" in twenty-three was visited in Northampton, one house in nineteen at Warrington, one house in seventeen at Stanley, and one house in twenty-one at Reading. This new method of Professor Bowley's, which yielded results more rapidly and less expensively than the Rowntree method, was useful also because comparative data could be obtained from time to time with relatively little difficulty.

Professor Bowley attempts to answer the question "Has poverty diminished?" by investigating the same towns after an interval of approximately ten years, using as nearly as possible the same methods.

24.2. Review by: B S Rowntree.
The Economic Journal 36 (142) (1926), 228-233.

Students of social reform will remember the publication, in 1915, under the auspices of the University of London, of a book entitled Livelihood and Poverty, which contained the results of an investigation, conducted mainly in 1913, into the economic conditions of working-class households in certain urban districts. Dr Bowley and Miss Hogg are to be congratulated on the service they have rendered in producing a post-war sequel to that volume, in which they chronicle the results of an investigation undertaken about ten years later, and as far as possible following the same methods. The ground covered is likewise the same. The towns with which they deal in Has Poverty Diminished?, namely, Northampton, Warrington, Reading, Bolton and Stanley, are those which were included in the volume concerned with pre-war data, and thus the authors reach a basis of comparison whereby the effect of the past ten years on working-class conditions can be gauged with some degree of accuracy. Dr Bowley and Miss Hogg would be the last to over-estimate the importance of the results here set forth. Not all the house- holds in the above towns were investigated, but samples were taken, the size of sample aimed at being 800 to 1200 working-class households for each town. Thus the ratio of the households examined varied with the size of the town, and was expected to comprise about 1200 addresses, of which perhaps 200 were excluded as non-working class.

24.3. Review by: Amy Hewes.
Journal of the American Statistical Association 21 (155) (1926), 367-369.

Professor Bowley and Miss Hogg have presented the results of a study of the changed position of the poverty line in England which will arrest attention both on account of the significance of the findings and the methods employed Poverty has diminished in at least four of the five towns in which investigations were made in 1924 and compared with earlier and similar investigations in the same towns made in 1913 and 1914.
...

The present study does not follow closely the English tradition in investigations of this kind, which usually puts more emphasis than is customary in this country on the testimony of individuals called as witnesses rather than upon extended statistical measurement. This was the method used in the investigations in connection with the establishment of the wage boards in England and the earlier procedure in connection with the factory acts. The advantages of getting a picture in its human terms with all the realistic appeal which the individual witness makes has been more relied upon than the weight of cumulative experience. In the present study, on the contrary, the attempt has been to make a statistical presentation, but so much particularisation is still held to that it is difficult and sometimes impossible to discover in the tabular form the central tendency which is its only excuse for being.

24.4. Review by: A B H.
Journal of the Royal Statistical Society 89 (2) (1926), 350-352.

In 1913 Professor Bowlev and Professor Burnett-Hurst carried out an investigation into the economic status of the working-classes in five towns in England. The results of this inquiry (published in 1915 under the title of Livelihood and Poverty), which comprised a detailed analysis of the composition of the family as regards wage-earning capacity, number of children and other dependants, and a commentary upon the state of housing, enabled the authors to reach approximate conclusions as to the number of families in poverty - as measured by the number failing to reach a certain minimum standard of livelihood.

In 1924 Professor Bowley and Miss Hogg (with the assistance of investigators in each town) repeated this inquiry in the same towns and as nearly as possible with the same methods. The present book gives an analysis of the data obtained in this second investigation, and compares the conclusions reached in 1924 with those of 1913.

The years 1913 to 1924 have been witnesses of such great changes in the social phenomena of England that such comparison of the position of working-class households in pre-war and post-war days is of peculiar interest. "The dominating events so far as these studies are concerned," say the authors, "have been the fall of the birth-rate, the loss of life by the war, the rise in prices and the more rapid rise of weekly money wages for unskilled labour and unemployment, ... and there have been no means of estimating how far the changes in wages and in personnel have affected the proportion of persons who are in a condition of poverty."

24.5. Review by: Frank H Hankins.
Social Forces 5 (3) (1927), 527-528.

In 1915 was published the work to which this one is the sequel. That earlier work was in turn suggested by and largely patterned after the work of Rowntree, Poverty, A Study of Town Life, 1901, and used the same minimum standard. There is thus available a remarkably interesting and accurate series of studies of the trends of living standards among the working classes of certain English cities. Since the studies of 1915 and 1925 relate to the same towns it is possible to make comparisons for the two dates with a high degree of confidence. In the first place there has been an increase in wages above the increase in the cost of living; wages have about doubled while prices have advanced about 70 per cent. There has been an especially marked improvement for the unskilled even when the great amount of unemployment is taken into account.

24.6. Review by: Anon.
Journal of the Royal Society of Arts 75 (3868) (1927), 223-224.

This is a work detailing a rather special case of somewhat laborious research, the full value of which it is extremely difficult to appraise; although on the principle that any carefully collected and tabulated records of social conditions may ultimately prove of value, we welcome the book as an addition to our knowledge. About twelve years ago a detailed study was made in certain localities as to living conditions, and ten years afterwards a similar house-to-house enquiry was made by the authors of the present work.
...

The general question, whether poverty now tends to increase or to diminish, is scarcely elucidated: indeed many uncertainties make elucidation difficult or even hopeless.

24.7. Review by: Edwin Cannan.
Economica 17 (1926), 221-222.

The time intended to be covered by the question in the title is roughly the ten years from 1914 to 1924, and the place is England and Wales. The investigation is made by taking Reading, Northampton, Warrington, Bolton, and Stanley as samples of the whole, and from 800 to 1,000 working-class households as samples in each of these towns.

The method of making a random selection of households is explained in Chapter II, and little uneasiness need be felt about it. But the selection of the five towns to represent England and Wales is much more open to question. The authors hope that it is fair because though Bolton is too favourable a specimen of the cotton area, Stanley, which is a Durham colliery district, and Warrington, should be sufficient to counterbalance the rather too favourable effect of the inclusion of the- other three towns. But a gloomy reader may shake his head over the absence of ship- building and agriculture, and doubt whether the bigger towns are quite as prosperous as the smaller ones which alone appear in the sample.

24.8. Review by: Paul H Douglas.
The American Economic Review 16 (4) (1926), 730-731.

This excellent investigation of the composition and income of 4,000 families in 5 English industrial towns, - namely, Reading, Northampton, Warrington, Bolton, and Stanley, - is a continuation of a similar investigation made by Bowley and Burnett-Hurst in 1914 for their book Livelihood and Poverty. The earlier study had shown that no less than 12.6 per cent of the persons covered had an income insufficient to secure that minimum standard of life which Rowntree had prescribed as Poverty. In 1924, however, only 3.6 per cent of the persons would have been below such a standard had the bread-winners been able to work the full-time week. Even with the amount of unemployment, which with the exception of Stanley approximated that for the country as a whole, only 6.5 per cent of the persons fell below this minimum of subsistence. It seems therefore to be established definitely that despite the long period of unemployment, the working classes with the exception of the coal miners and their families, are less in want today than they were before the Great War.

25.1. Review by: A W Flux.
The Economic Journal 37 (146) (1927), 255-257.

For an account of the National Income we may seek the answer to either of two questions: What do we receive? or What do we spend? If we include savings with spendings the two roads of approach should lead us to the same end. The former line of inquiry was adopted by Dr Bowley in his estimate of our National Income for 1911, and the monograph now issued follows in the main the same method. An interesting estimate of the total to be reached by the latter method forms part of the material reviewed in testing the conclusions reached. It is, of course, based on assumed average rates of price increase for the main sections of goods and services which form the equivalent of the part of income which is spent. Whether a more definite estimate of these price changes will result from a survey of the results of the Census of Production for 1924 is a question, the answer to which must await the completion of the publication of those results. In the meantime it would be rash to challenge any such carefully considered estimate as that given by the authors of the monograph before us. We note, by the way, that in their references to the First Census of Production the authors have relied on treacherous memories, and in referring to 1906 and 1906-7, they may have recalled the date of the Act of Parliament without remembering that the Census related to a period not begun when the Act was passed.

25.2. Review by: H W M.
Journal of the Royal Statistical Society 90 (2) (1927), 376-378.

It appears to the present writer that Professor Bowley and Sir Josiah Stamp have under-estimated the social income of 1911 and over-estimated that of 1924; but in neither case in a serious degree. ... The writer has not put forward his estimates as of superior validity, but has given them rather as a measure of the amount of variation which may be allowed to figures which, when set out in a table, appear to have a greater degree of precision than the authors give them in the text.

25.3. Review by: G P Watkins.
Journal of the American Statistical Association 22 (159) (1927), 404-405.

In this book the authors bring down to date, as of 1924, a previous estimate of national income. It is, as well might be expected, and excellent example of skilful statistical work. The task calls for ingenuity in finding and filling deficiencies and gaps in quantitative data by estimates that are well grounded and well-reasoned guesses, rather than applications of formally mathematical ideas. Skilful work in such matters supposes not only familiarity with available data, but also a high degree of conversance with the underlying concrete facts, the latter requirement being especially exacting, even when thus qualified for degree. An acceptable result also supposes rare powers of statistical analysis.

26.1. Review by: W P E.
Journal of the Institute of Actuaries (1886-1994) 59 (3) (1928), 422-423.

The late Professor Edgeworth began to write on mathematical statistics in 1883 and continued his work on the subject up to the time of his death in 1926: his papers were published in various journals and the present volume by Professor Bowley not only enumerates the papers with notes on some of them but gives a connected account of Edgeworth's work. Edgeworth's interest in the subject was philosophical rather than arithmetical and his starting point was the "metaphysical conception of probability." Following the line of thought natural to him, Edgeworth studied such points as the "best" values of constants and variations from those values; a distinction may be drawn between "best" and "most probable" and he tried to find ways of passing from the measurements to their unknown source. Several of his papers deal directly with "the law of error " and many of the others refer to it. To Edgeworth's mind the "law of error" had to be obtained from a priori conditions and given these conditions the claim is made that the expression he reached is the "true and unique law that represents the frequency curve of a magnitude that depends on a number of independent elements."...
...

Professor Bowley's task has been by no means easy: Edgeworth's papers were seldom self-contained and his interjectory remarks, though in many ways attractive, gave the reader a feeling of discontinuity. To many of us statistics is an arithmetical subject and the mathematical work is wanted for an arithmetical end, but Edgeworth's thoughts ran in a different way and his philosophical attitude did not always help him to express his examples in a way most helpful to his less philosophical readers. These remark. are made to indicate that to some extent Edgeworth did not, perhaps could not, give himself the best chance of appealing to the average statistical reader: and, as the present labour of love brings Edgeworth's work a little nearer to us, it wins our gratitude. One remark may be added, even though it may appear inappropriate in a notice on mathematical statistics: those of us who met Edgeworth will remember the charm of old-world courtesy so naturally associated with a scholar and a gentleman.

26.2. Review by: Mark H Ingraham.
The American Economic Review 19 (4) (1929), 738-739.

Mr Bowley has written a notable epitome of Mr Edgeworth's work pertaining to mathematical statistics. Three phases of the work stand out in the reviewer's mind: first, the emphasis on a priori probabilities in the applications of the theory of probabilities; secondly, a discussion of the "law of error" and the theories dependent upon it; and finally, the discussion of the "best mean."

The amount of misunderstanding about the roll of a priori probabilities is enormous. The number of foolish statements that have been made about such works as R A Fisher's brilliant papers in Metron concerning the coefficient of correlations of a population where the coefficient of correlation for a sample is known, and kindred subjects is amazing. Hence the clarity with which the limitations of the "genuine inverse method" is developed is refreshing. This method picks from a class of frequency curves that of a population from which the probability of drawing a given sample is a maximum rather than the frequency distribution from which it is most probable that the sample was drawn. The second distribution is without meaning unless some arbitrary and probably false assumption about the nature of the universe is made.

27.1. Review by: P Sargant Florence.
The Economic Journal 41 (164) (1931), 600-602.

At times of general elections it is becoming the custom for each political party to issue a handbook of " facts for speakers." These facts are largely, in the form of figures, and have all the appearance of accuracy; but those listeners - and perhaps speakers, too - who may feel qualms about accepting and retailing the selections and summaries of admittedly biased organisations must rejoice in the appearance of this new and somewhat novel addition to the Home University Library.

True, the title is misleading; for the book is essentially a chronicle of such facts and events of the years from 1919 to 1929 as are statistically measurable, and not an analysis of the degree to which the war was responsible for events, whether measurable or not. Many of the events that are recorded of the post-war decade, such as the fall in birth and death rates and the progress of new industries based on technical invention, were not primarily a consequence of the war, as Professor Bowley himself admits; and many of the more important economic consequences of the war are not statistically measured, and some even appear to be happening after 1929. In 1931 it is surprising to read that the complete stabilisation of European currencies was only reached in June 1928."

Wisely, Professor Bowley reaches few final conclusions, and confines himself to a very complete yet happily summarised statistical account of the recent progress of the nations.

27.2. Review by: H V H.
International Affairs (Royal Institute of International Affairs 1931-1939) 10 (1) (1931), 122.

This valuable addition to the Home University Library covers an extraordinarily wide field - population, national debts and taxation, the condition of capital and the distribution of income, the displacement of labour, foreign trade and unemployment, currency and prices. Dr Bowley has analysed and summarised the available statistics regarding the principal changes that were caused by the War; he has added, besides a running commentary, some discussion of the broader issues involved. Different readers will find the greatest interest in different chapters, no doubt, but it would be impossible not to rank high the chapter on population, in which Dr Bowley explains that "the population of working age [in the belligerent countries] is older and more feminine. ... The age distribution will not be even approximately normal (in the sense of appropriateness to a stationary or regularly increasing population) for more than half a century;" and the chapter on displacement of labour, which contains an illuminating table showing how far we have yet to go in adjusting our labour force to post-War conditions.

28.1. Review by: J Marschak.
The Economic Journal 46 (183) (1936), 485-489.

The relationship between the level of income and the structure of consumption is obviously important for both economic policy and theory. Mr Allen and Professor Bowley study this relationship, not by comparing income and consumption changes through time, but by comparing, at a given time-period, the consumption of families with different incomes. They thus eliminate, to a great extent at least, the disturbing influence of temporal changes of prices and tastes.

28.2. Review by: Henry Schultz.
Journal of the American Statistical Association 31 (195) (1936), 613-617.

This investigation differs from all previous family budget studies in that it is based definitely on some of the preconceptions of modern mathematical theory of utility and exchange. That theory enables us to explain the pattern of consumption of an individual in terms of his tastes, his income, and market prices. Its application to family budget data should yield useful and interesting results.

More specifically, the purposes of this investigation are, in the words of the authors, "... to discover how far the expenditures of individual families or of groups of families can be described by rules and formulae, to relate any rules that are found to the postulates of economic theory and to describe the variations from the averages that result from the different choices of individual families."

The theory is severely mathematical in form and is summarised in a mathematical appendix of nineteen pages. It cannot conveniently be condensed further. All that it is possible to give within the limits of a review are (1) the major steps by which the authors reach their most important formula, and (2) the uses to which this formula is put.
...

Family Expenditure is an important contribution to econometrics. It may very well be that sociologists, psychologists, advertisers, and others who are interested in consumer behaviour will have to turn to mathematical economics if they are to understand future researches in this field.

28.3. Review by: Faith M Williams.
Journal of the American Statistical Association 31 (195) (1936), 610-613.

This study of variations in family expenditures presents an interesting and valuable example of the possibilities of mathematical analysis in the field of consumption. The volume is divided into four quite distinct sections. The first chapter analyses data from 21 different studies of family expenditures ...
The second chapter presents an original contribution to the techniques of measuring variations in family expenditures by analysing the differences between the actual expenditures of individual families and the expenditures which would be expected on the basis of regression equations expressing the average behaviour of their group. The third chapter is devoted to a theoretical analysis of the distribution of expenditure which develops theses, presented by one of the authors with Mr J R Hicks in Economica. The fourth section, the appendix, sets forth the mathematical basis for the third chapter. The third and fourth sections, which represent about one-third of the volume, build upon the work of Edgeworth and Pareto and seek to develop theories of the marginal rate of substitution for competitive consumers' goods. The volume is somewhat marred by the looseness with which it uses certain economic terms.

28.4. Review by: Gerhard Tintner.
Economica, New Series 3 (11) (1936), 345-346.

It should be pointed out that the authors are free from the bias of pure statisticians which spoils many similar studies. They never calculate statistical parameters for their own sake but are well aware of the economic problems which their study tries to solve. They always give economic interpretations of the statistical results and this is certainly not the least merit of their work. The very nature of the study makes it impossible that many new and striking features should have been detected. But the results which in general are not new are often for the first time established by correct economic and reliable statistical methods. And the quantitative specifications contained in the book, however subject to random variation, are far more reliable than anything previously worked out in the same field. The numerous tables are well arranged and can easily be used by anybody who is interested in budget studies.

Mr Allen's and Professor Bowley's book should encourage all those who try to apply mathematics and statistics in economics. It shows how it can be done successfully, not by aping the natural scientists but by the development and application of methods which are particularly fitted for the difficult task of economic and social problems.

29.1. Review by: A C Pigou.
Economica, New Series 5 (18) (1938), 230-233.

For the writer of this notice to attempt a review, in the sense of a technical criticism, of Dr Bowley's latest publication would be merely impertinent. Even among professional statisticians, a fortiori among general economists, there are very few qualified to do that. Among persons over the age of - no, I will not name the age at which omniscience ceases! - there are very few who would even think themselves so qualified. My task is a much humbler one: on my own behalf and that of many others to congratulate and thank the author. It is a great privilege to be allowed to do this, more especially to be allowed to do it in the Journal of the School on which Bowley's name, over so long a period, has shed an unique lustre.
...

It is up to the statistician not only to devote immense care and labour to the figures that he sponsors, but also, so to speak, always to decry his own wares, advertising not so much what they can as what they cannot do. To read Bowley's book is to be given an object lesson in these virtues. In this single-minded search for truth, this avoidance of all sensation, this overcoming of many obstacles and frank recognition of others that cannot be overcome, there is an austere but compelling beauty. Economists and statisticians alike are under a heavy debt to Dr Bowley not merely for the yield of his researches, massive and imposing as these are, but also, perhaps even more, for the manner in which he has conducted them, and for the high standard that he has always set alike for himself and others. May the torch be carried on !

29.2. Review by: Frederick Brown.
The Economic History Review 9 (2) (1939), 215-217.

Professor Bowley, in his book, summarises a lifetime's original work on statistics of wages and income in the United Kingdom, subjects in which he was a pioneer and still occupies a unique position of authority. ...

Professor Bowley thinks that working-class conditions in the United Kingdom have not deteriorated. Between 1860 and 1899 "real" wages rose steadily and doubled in the period; from 1899 to 1914 they were stationary or declined slightly; and in 1936 they were about one-third higher than in 1914. "The increase in real wages has at no time in the past forty years been rapid"; the change in them is "not enough to account for the progress that is evident to anyone who has observed the wage-earning classes during the period." (Professor Bowley, through the various social surveys which he has directed, has observed them.) "The development of social expenditure ... through old-age pensions and the many insurance services; ... a great advance of knowledge, as the younger generations have matured in an environment of more general education; ... the reduction of the hours of work in 1919-20; ... the reduction of stringency in making the income meet necessary expenses, due to the smaller number of children"; all these factors have contributed to the progress of the working classes, although the progress has not been uniform, since "some groups [districts and industries] have had exceptional good fortune, while others have barely preserved their standard."

29.3. Review by: H W M.
Journal of the Royal Statistical Society 101 (2) (1938), 461-463.

"This book," says the author, "is an attempt to bring into a coherent whole the investigations that I have made on the subject of wages and income at various dates during the past forty years." How thorough and painstaking his efforts have been is shown by the fact that in the appended Bibliography of ninety-one items sixty-five are contributions by himself, including eight in which he collaborated with colleagues. Fifteen of these have appeared in our Journal and ten in the Economic Journal. It is superfluous to say how useful to the student it is to have the results of all this work brought together and summarised in brief compass. Those who are concerned with obtaining general measurements or with acquiring the main technique for handling wage problems will find all that they require in this short book, while the Bibliography will enable specialists to refer to more elaborate tables and more detailed analysis.

29.4. Review by: D Caradog Jones.
The Economic Journal 48 (190) (1938), 291-294.

When a statistician of Professor Bowley's eminence gathers together in a single work the threads of investigations he has made over a long period of years, the book is bound to be indispensable to all students of the subject. In order to be as sure of Professor Bowley's conclusions as the author himself has been careful in stating them, the reader will find it necessary to concentrate his attention seriously; otherwise important qualifications will be missed which may have a significant influence on the ultimate results. Fortunately, Professor Bowley, in a dozen introductory pages, has sketched the broad outline of his conclusions, and the general reader will find there the essential matter to which this review is but an introduction. How much better off is the British workman to-day than he was fifty or sixty years ago'? That is an important question upon which an authoritative opinion would be valuable. But, without a definition of terms, no answer is possible. To be "better off " is a state of mind that we have not learnt how to measure. Men may have higher rates of wages, and they may be able to buy with those wages a greater quantity and variety of commodities than was possible in times past, yet they may feel "worse off," because they take as standards for comparison the lives they see others enjoying to-day, rather than the lives experienced by their predecessors years ago.

29.5. Review by: Simon Kuznets.
Journal of the American Statistical Association 33 (202) (1938), 456-458.

This book presents a compact summary of Professor Bowley's studies on the subject of wages and their share in the national income in the United Kingdom. Utilising largely his own writings, which date back to 1895 and cover the period since 1880, revising them at points where such revision can easily be made in the light of recent data, and supplementing them by a few references to other studies, the author discusses briefly money wages, real wages, some aspects of the distribution of earnings, the relation of earnings to needs, the total wage bill, and the share of total wages in the national income. Six appendices present some of the more technical aspects of the measures. An extensive bibliography of the author's writings, supplemented by a brief bibliography of the more important studies by other authors, provides references to the statistical groundwork of the summary estimates discussed in the text.

29.6. Review by: Witt Bowden.
The American Historical Review 44 (3) (1939), 620-621.

The author's purpose was to bring into a coherent whole his numerous earlier studies of wages and income, with emphasis on papers now out of print or not readily accessible. Recommendation of the work to specialists would be superfluous. Students of the trends of British wages, income, and prices have long found Professor Bowley's writings outstanding sources of information. The reader who is not acquainted with statistical techniques may have difficulty in viewing the volume as a "coherent whole", especially unless he keeps in mind the author's statement that the essence of his studies is not the obtaining of absolute figures but the measuring of changes. The linking of relatives for tracing the trends of British wages and prices (for the volume deals with real as well as money wages) gives comparatively adequate results because of the comparative homogeneity and the limited area of the United Kingdom. The book is much more than a compilation of statistics, for the author brings to bear his wide knowledge and mature judgment on such important subjects as earnings and needs, labour costs, and shifts in occupations and industries.

It is surprising that so eminent a statistician as Professor Bowley has used ambiguous terms in his tables, the meaning of which can be ascertained only by careful reading of the text. Many of the tabulations standing alone might mean either rates, or hourly earnings, or daily earnings, or full-time weekly or annual earnings, or the actual averages of weekly or of annual earnings when account is taken of part time and overtime.

29.7. Review by: E M Bernstein.
Southern Economic Journal 5 (4) (1939), 548.

This small volume of 150 pages contains a summary of the significant findings of Dr Bowley on money wages, real wages, occupational distribution, wage rates, and the national income. Not only does it bring together the scattered writings of Dr Bowley on these questions, but it also contains critical observations on the wage and income estimates of other investigators, and on the technical difficulties of making wage and income estimates.

The essays show clearly that precise measurement of wages and income is extremely difficult, although reasonably accurate approximations can be made of changes in wages and income. This difficulty of precise measurement is particularly apparent when such controversial matters as poverty or adequate working class budgets are considered. The concept of a satisfactory diet changes steadily, not only because the social attitude towards standards of consumption changes, but because scientific discoveries shift the emphasis from bulk to calories and more recently to vitamins.

Perhaps for most economists Dr Bowley's book will be of greatest interest not so much for the light it throws on questions of statistical method, as for the information it makes available on such fundamental questions as the rise in real wages and the growth of income.

29.8. Review by: Willford I King.
The American Economic Review 28 (3) (1938), 605-607.

In this little book, Professor Bowley has summarised and synthesised the studies of wages and income in the United Kingdom in the preparation of which he has been intermittently engaged during the last forty years. The work is characterised throughout by that carefulness of statement for which the author is noted.

Dr Bowley emphasises two, facts: first, that it is not possible to measure with exactitude the income of a nation at any given time; second, that every change in definition results in a change in the estimate of the total. It follows that the importance and dependability of estimates attach mainly to relative comparisons for different dates. These can be made with a reasonable degree of precision; and it is such comparisons which are stressed in this work.

30.1. Review by: Simon Kuznets.
The Review of Economics and Statistics 26 (2) (1944), 99-100.

This volume assembles the results of several investigations originally intended as part of "a comprehensive study of income as a whole and of its distribution, together with examination of definitions and of such special topics as depreciation". The outbreak of the war led to the suspension of the original undertaking and the curtailment of some of the investigations. The book is thus an interim report on parts of what is essentially an incomplete job. This circumstance undoubtedly explains both the lack of cohesion and the differences in quality among the several parts.

30.2. Review by: Milton Gilbert.
Journal of the American Statistical Association 38 (224) (1943), 473-475.

This volume is the result of a study initiated in 1938 under the auspices of the National Institute of Economic and Social Research. Professor Bowley was Director of the investigation and, although others were associated with him on the project, he takes full responsibility for the methods followed and the opinions expressed. The outbreak of war forced curtailment of the original program and, as work cannot be resumed in the immediate future, the results obtained to date are being issued. While it is unfortunate that the intended plan could not be realised, the work as it stands is a major contribution to national income literature.

30.3. Review by: Willford I King.
American Sociological Review 8 (5) (1943), 612-613.

This book is the first to be issued of a series of studies projected by the National Institute of Economics and Social Research. The volume is the result of work done by a committee of the London School of Economics acting under the direction of Dr Bowley.
...

The volume under review contains an extensive bibliography of books and articles dealing with income. It covers numerous publications in the various leading nations. Like all of Bowley's books, this study has all the earmarks of a very scholarly piece of work.