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 ^ i
 
 THE 
 
 THEORY OF POLITICAL ECONOMY. 
 
 a
 
 THE 
 
 THEORY OF POLITICAL ECONOMY. 
 
 BY 
 
 W. STANLEY JEVONS, LL.D. (Edinb.), M.A. (Lond.), F.E.S. 
 
 Professor of Political Economy in University College, London, 
 Examiner in Menial and Moral Science in the University of London, 
 
 SECOND EDITION, 
 
 EEVISED AND ENLARGED, 
 
 UITH NEW PREFACE AND APPENDICES. 
 
 MACMILLAN AND CO. 
 
 1879. 
 
 [T^e riglit of translation and reproduction is reserved."]
 
 OXFOED: 
 
 BY E. PICKAED HALL, M.A., AND J. H. STACT, 
 
 PRINTEBS TO THE UNIYEESITY
 
 HB 
 
 PEEFAOE 
 
 TO 
 
 THE FIRST EDITION. 
 
 (1871.) 
 
 The contents of the following pages can hardly 
 meet with ready acceptance among those who 
 regard the Science of Political Economy as having 
 already acquired a nearly perfect form. I believe 
 it is generally supposed that Adam Smith laid the 
 foundations of this science; that Malthus, Ander- 
 son, and Senior added important doctrines ; that 
 Ricardo systematised the whole ; and, finally, that 
 Mr. J. S. Mill filled in the details and completely 
 expounded this branch of knowledge. Mr. Mill 
 appears to have had a similar notion ; for he dis- 
 tinctly asserts that there was nothing in the Laws 
 of Value which remained for himself or any future 
 writer to clear up. Doubtless it is difficult to help 
 feeling that opinions adopted and confirmed by 
 such eminent men have much weight of probability 
 in their favour. Yet, in the other sciences this 
 
 850391
 
 vi Preface. 
 
 weight of authority has not been allowed to restrict 
 the free examination of new opinions and theories ; 
 and it has often been ultimately proved that 
 authority was on the wrong side. 
 
 There are many portions of Economical doctrine 
 which appear to me as scientific in form as they are 
 consonant with facts. I would especially mention 
 the Theories of Population and Rent, the latter a 
 theory of a distinctly mathematical character, which 
 seems to give a clue to the correct mode of treating 
 the whole science. Had Mr. Mill contented himself 
 with asserting the unquestionable truth of the Laws 
 of Supply and Demand, I should have agreed with 
 him. As founded upon facts, those laws cannot be 
 shaken by any theory; but it does not therefore 
 follow, that our conception of Value is perfect and 
 final. Other generally accepted doctrines have 
 always appeared to me purely delusive, especially 
 the so-called Wage Fund Theory. This theory 
 pretends to give a solution of the main problem 
 of the science — to determine the wages of labour ; 
 yet, on close examination, its conclusion is found to 
 be a mere truism, namely, that the average rate of 
 wages is found by dividing the whole amount 
 appropriated to the payment of wages by the 
 number of those between whom it is divided. 
 Some other supposed conclusions of the science are
 
 Prefojce. vii 
 
 of a less harmless character, as, for instance, those 
 regarding the advantage of exchange (see the sec- 
 tion on ' The Gain by Exchange,' p. 153), 
 
 In this work I have attempted to treat Economy 
 as a Calcuhis of Pleasure and Pain, and have 
 sketched out, almost irrespective of previous opin- 
 ions, the form which the science, as it seems to 
 me, must ultimately take. I have long thought 
 that as it deals throughout with quantities, it must 
 be a mathematical science in matter if not in 
 language. I have endeavoured to arrive at accu- 
 rate quantitative notions concerning Utility, Value, 
 Labour, Capital, &c., and I have often been sur- 
 prised to find how clearly some of the most difficult 
 notions, especially that most puzzling of notions 
 Value, admit of mathematical analysis and expres- 
 sion. The Theory of Economy thus treated 
 presents a close analogy to the science of Sta- 
 tical ^lechanics, and the Laws of Exchange are 
 found to resemble the LaAvs of Equilibrium of a 
 lever as determined by the principle of virtual 
 velocities. The nature of Wealth and Value is 
 explained by the consideration of indefinitely small 
 amounts of pleasure and pain, just as the Theory of 
 Statics is made to rest upon the equality of inde- 
 finitely small amounts of energy. But I believe 
 that dynamical branches of the Science of Economy
 
 viii Preface. 
 
 may remain to be developed, on the consideration 
 of which I have not at all entered. 
 
 Mathematical readers may perhaps think that I 
 have explained some elementary notions, that of 
 the Degree of Utility, for instance, with unnecessary 
 prolixity. But it is to the neglect of Economists to 
 obtain clear and accurate notions of quantity and 
 degree of utility that I venture to attribute the 
 present difficulties and imperfections of the science ; 
 and I have purposely dwelt upon the point at full 
 length. Other readers will perhaps think that the 
 occasional introduction of mathematical symbols 
 obscures instead of illustrating the subject. But I 
 must request all readers to remember that, as 
 Mathematicians and Political Economists have 
 hitherto been two nearly distinct classes of persons, 
 there is no slight difficulty in preparing a mathe- 
 matical work on Economy with which both classes 
 of readers may not have some grounds of com- 
 plaint. 
 
 It is very likely that I have fallen into errors of 
 more or less importance, which I shall be glad to 
 have pointed out ; and I may say that the cardinal 
 difficulty of the whole theory is alluded to in the 
 section of Chapter IV upon the ' Ratio of Exchange,' 
 beginning at p. 91 (p. 98 of this edition). So able a 
 mathematician as my friend Professor Barker, of
 
 Preface. ix 
 
 Owens College, has had the kindness to examine 
 some of the proof sheets carefully ; but he is not, 
 therefore, to be held responsible for the correctness 
 of any part of the work. 
 
 My enumeration of the previous attempts to 
 apply mathematical language to Political Economy 
 does not pretend to completeness even as regards 
 English writers ; and I find that I forgot to mention 
 a remarkable pamphlet ' On Currency' published 
 anonymously in 1840 (London, Charles Knight and 
 Co.) in which a mathematical analysis of the opera- 
 tions of the Money Market is attempted. The 
 method of treatment is not nnlike that adopted by 
 Dr. Whewell, to whose Memoirs a reference is made ; 
 but finite or occasionally infinitesimal differences 
 are introduced. On the success of this anonymous 
 theory I have not formed an opinion ; but the 
 subject is one which must some day be solved by 
 mathematical analysis. Garnier, in his treatise on 
 Political Economy, mentions several continental 
 mathematicians who have written on the subject of 
 Political Economy; but I have not been able to 
 discover even the titles of their Memoirs.
 
 PEEFAGE 
 
 TO 
 
 THE SECOND EDITION. 
 
 In preparing this second edition certain new 
 sections have been added, the most important of 
 which are those treating of the dimensions of 
 economic quantities {])ip. 66-74, 90-1, 193-4,253-5). 
 The subject, of course, is one which lies at the 
 basis of all clear thought about economic science. 
 It cannot be surprising that many debates end in 
 logomachy, when it is still uncertain how many 
 meanings the word value has, or what kind of a 
 quantity utility itself is. Imagine the mental state 
 of astronomers if they could not agree among them- 
 selves whether Bight Ascension was the name of a 
 heavenly body, or a force or an angular magnitude. 
 Yet this would not be worse than failing to ascer- 
 tain clearly whether by value we mean a numerical 
 ratio, or a mental state, or a mass of commodity^ 
 John Stuart Mill tells us explicitly^ that 'The value 
 
 * ' Principles of Political Economy,' Book III, Chapter VI, Sec- 
 tion i. 1. This definition occurs at the beginning of a carefully 
 prepared summary of the principles of the theory of value.
 
 Preface. xi 
 
 of a thing means the quantity of some other thing, 
 or of things in general, which it exchanges for.' 
 It might of course be explained that Mill did not 
 intend what he said ; but as the statement stands 
 it makes value into a thing, and is just as phil- 
 osophic as if one were to say, ' Right Ascension 
 means the planet Mars, or planets in general.' 
 
 These sections upon the dimensions of economic 
 quantities have caused me great perplexity, espec- 
 ially as regards the relation between utility and 
 time (pp. 69-74). The theory of capital and interest 
 also involves some subtleties. I hope that my solu- 
 tions of the questions raised will be found generally 
 correct ; but where they do not settle a question, 
 they may sometimes suggest one which other 
 writers may answer. A correspondent, Captain 
 Charles Christie, R.E., to whom I have shewn 
 these sections after they were printed, objects 
 reasonably enough that commodity should not 
 have been represented by M, or Mass, but by some 
 symbol, for instance Q, which would include 
 quantity of space or time or force, in fact almost 
 any kind of quantity. Services often involve time, 
 or force exerted, or space passed over, as well 
 as mass. In this objection I quite concur, and 
 I must therefore request the reader either to in- 
 terpret M with a wider meaning than is given to it
 
 xii Preface. 
 
 in p. 69, or else mentally to substitute another 
 symbol. 
 
 In treating the dimensions of interest, I point out 
 the curious fact that so profound a mathematician 
 as the late Dean Peacock went quite astray upon 
 the subject (pp. 271-4). Other new sections are 
 those in which I introduce the idea of negative and 
 approximately zero value, showing that negative 
 value may be brought under the forms of the equa- 
 tions of exchange without any important modifica- 
 tion. Readers of Mr. Macleod's works are of course 
 familiar with the idea of negative value ; but it was 
 desirable for me to show how important it really is, 
 and how naturally it falls in with the principles of 
 the theory. I may also draw attention to the 
 section (pp. 110-115) in which I illustrate the 
 mathematical character of the equations of ex- 
 change by drawing an exact analogy between them 
 and the equations applying to the equilibrium of 
 the lever. 
 
 Two or three correspondents, especially Herr 
 Harald Westergaard of Copenhagen, have pointed 
 out that a little manij)ulation of the symbols, in 
 accordance with the simple rules of the differential 
 calculus, would often give results which I have 
 laboriously argued out. The(whole question is one 
 of maxima and minima, the mathematical condi-
 
 Preface. xiii 
 
 tions of which are familiar to mathematicians. 
 But, even if I were capable of presenting the subject 
 in the concise symbolic style satisfactory to the 
 taste of a practised mathematician, I should prefer 
 in an essay of this kind to attain my results by a 
 course of argument which is not only fundamen- 
 tally true, but is clear and convincing to many 
 readers who, like myself, are not skilful and pro- 
 fessional mathematicians. In short, I do not write 
 for mathematicians, nor as a mathematician, but as 
 an economist wishing to convince other economists 
 that their science can only be satisfactorily treated 
 on an explicitly mathematical basis. When mathe- 
 maticians recognise the subject as one with which 
 they may usefully deal, I shall gladly resign it into 
 their hands. I have expressed a feeling in more 
 than one place that the whole theory might prob- 
 ably have been put in a more general form by 
 treating labour as negative utility, and thus bring- 
 ing it under the ordinary equations of exchange. 
 But the fact is there is endless occupation for an 
 economist in developing and imj)roving his science, 
 and I have found it requisite to reissue this 
 essay, as the bibliopoles say, ' with all faults.' 
 I have, however, carefully revised every page of 
 the book, and have reason to hope that little 
 or no real error remains in the doctrines stated.
 
 xiv Preface. 
 
 The faults are in the form rather than the 
 matter. 
 
 Among minor alterations, I may mention the 
 substitution for the name Political Economy of the 
 single convenient term Economics. I cannot help 
 thinking that it would be well to discard, as quickly 
 as possible, the old troublesome double-worded 
 name of our Science. Several authors have tried 
 to introduce totally new names, such as Plutology, 
 Chrematistics, Catallactics, &c. But why do we need 
 anything better than Economics ? This term, besides 
 • being more familiar and closely related to the old 
 term, is perfectly analogous in form to Mathematics, 
 Ethics, ^Esthetics, and the names of various other 
 branches of knowledge, and it has moreover the 
 authority of usage from the time of Aristotle. Mr. 
 Macleod is, so far as I know, the re-introducer of 
 the name in recent years, but it appears to have 
 been adopted also by Mr. Alfred Marshall at Cam- 
 bridge. It is thus to be hoped that Economics will 
 become the recognised name of a science, which 
 nearly a century ago was known to the French 
 Economists as la science eco7iomique. Though em- 
 ploying the new name in the text, it was obviously 
 undesirable to alter the title-page of the book. 
 
 When publishing a new edition of this work, 
 eight years after its first appearance, it seems
 
 Preface. xv 
 
 natural that I should make some remarks upon 
 the changes of opinion about economic science 
 which have taken place in the interval. A re- 
 markable discussion has been lately going on in 
 the reviews and journals concerning the logical 
 method of the science, touching even the question 
 whether there exists any such science at all. Atten- 
 tion was drawn to the matter by Mr. T. E. Cliffe 
 Leslie's remarkable article ^ ' On the Philosophical 
 Method of Political Economy,' in which he en- 
 deavours to dissipate altogether the deductive 
 science of Ricardo. Mr. W. T. Thornton's writings 
 have a somewhat similar tendency. The question 
 has been further stirred up by tlie admirable 
 criticism to Avhich it was subjected in the masterly 
 address of Professor J. K. Ingram, at the last 
 meeting of the British Association. This Address 
 has been reprinted in several publications^ in 
 England, and has been translated into the chief 
 languages of Western Europe. It is evident, 
 then, that a spirit of very active criticism is 
 
 ^ Hermathena, No. iv, 1876, pp. 1-32. Republished in Mr. 
 Leslie's collected 'Essays in Political and Moral Philosophy,' 
 Dublin, 1879, pp. 216-242. 
 
 c Journal of the London Statistical Society, December, 1878, 
 vol. xli, pp. 602-629. Journal of the Statistical and Social In- 
 quiry Society of Ireland, August, 1878, vol. vii, Appendix. Also 
 as a separate publication, Longmans, London 1878.
 
 xvi Preface. 
 
 spreading, which can hardly fail to overcome in 
 the end the prestige of the false old doctrines. 
 But what is to be put in place of them? At the 
 best it must be allowed that the fall of the old 
 orthodox creed will leave a chaos of diverse 
 opinions. Many would be glad if the supposed 
 science collapsed altogether, and became a matter 
 of history, like astrology, alchemy, and the occult 
 sciences generally. Mr. Cliffe Leslie would not go 
 ■quite so far as this, but would reconstruct the 
 science in a purely inductive or empirical manner. 
 Either it would then be a congeries of miscel- 
 laneous disconnected facts, or else it must fall in 
 as one branch of Mr. Spencer's Sociology. In any 
 case, I hold that tliere must arise a science of the 
 development of economic forms and relations. 
 
 But as regards the fate of the deductive method, 
 I disagree altogether with my friend Mr. Leslie; 
 he is in favour of simple deletion; I am for thorough 
 reform and reconstruction. As I have previously 
 explained d, the present chaotic state of Economics 
 arises from the confusing together of several 
 branches of knowledge. Subdivision is the remedy. 
 We must distinguish the empirical element from 
 
 V d 'The Future of Political Economy,' Fortnightly Review, 
 November 1876, vol. viii, N. S. pp. 617-31. Translated in the 
 Journal des Economistes, March 1877, 3™^ Serie, vol. xlv, p. 325.
 
 Preface, xvli 
 
 the abstract theory, from the applied theory, and 
 from the more detailed art of finance and ad- 
 ministration. Thus will arise various sciences, 
 such as commercial statistics, the mathematical 
 theory of economics, systematic and descriptive 
 economics, economic sociology, and fiscal science. 
 There may even be a kind of cross subdivision of 
 the sciences; that is to say, there will be division 
 into branches as regards the subject, and division 
 according to the manner of treating the branch of 
 the subject. The manner may be theoretical, em- 
 pirical, historical, or practical ; the subject may be 
 capital and labour, currency, banking, taxation, 
 land tenure, &c. — not to speak of the more fun- 
 damental division of the science as it treats of 
 consumption, production, exchange, and distri- 
 bution of wealth. In fact, the whole subject is so 
 extensive, intricate, and diverse, that it is absurd 
 to suppose it can be treated in any single book or 
 in any single manner. It is no more one science 
 than statics, dynamics, the theory of heat, optics, 
 magneto-electricity, telegraphy, navigation, and 
 photographic chemistry are one science. But as 
 all the physical sciences have their basis more or 
 less obviously in the general principles of me- 
 chanics, so all branches and divisions of economic 
 science must be pervaded by certain general 
 
 b
 
 xviii • Preface. 
 
 principles. It is to the investigation of such 
 principles — to the tracing out of the mechanics of 
 self-interest and utility, that this essay has been 
 devoted. The establishment of such a theory is a 
 necessary preliminary to any definitive drafting of 
 the superstructure of the aggregate science. 
 
 Turning now to the theory itself, the question is 
 not so much whether the theory given in this 
 volume is true, but whether there is really any 
 novelty in it. The exclusive importance attributed 
 in England to the Ricardian School of Economists, 
 has prevented almost all English readers from 
 learning the existence of a series of French, as 
 well as a few English, German, or Italian econo- 
 mists, who had from time to time treated the 
 science in a more or less strictly mathematical 
 manner. In the first edition (pp. 14-18), I gave 
 a brief account of such writings of the kind as 
 I was then acquainted with ; it is from the works 
 there mentioned, if from any, that I derived the 
 idea of investigating Economics mathematically. 
 To Lardner's 'Railway Economy' I Avas probably 
 most indebted, having been well acquainted with 
 that work .since the year 1857. Lardner's book 
 has always struck me as containing a very able 
 investigation, the scientific value of which has not 
 been sufficiently estimated; and in chapter xiii
 
 Preface. xix 
 
 (pp. 286-296, &c.) we find the Laws of Supply 
 and Demand treated mathematically and illus- 
 trated graphically. 
 
 In the preface to the first edition (p. xi) ^, I re- 
 marked that in his treatise on Political Economy, 
 M. Joseph Garnier mentioned several continental 
 mathematicians Avho had WTitten on the subject 
 of Economics, and I added that I had not been able 
 to discover even the titles of their memoirs. This, 
 however, must have been the result of careless 
 reading or faulty memory, for it will be found 
 that Garnier himself f mentions the titles of several 
 books and memoirs. The fact is that, writing as 
 I did then at a distance from any large library, 
 I made no attempt to acquaint m3^self with the 
 literature of the subject, little thinking that it was 
 so copious and in some cases so excellent as is 
 now found to be the case. With the progress of 
 years, however, my knowledge of the literature of 
 political economy has been much widened, and the 
 hints of friends and correspondents have made me 
 aware of the existence of many remarkable works 
 which more or less anticipate the views stated in 
 this book. While preparing this new edition, it 
 
 e See p. ix of this edition. 
 
 f 'Traite d'Economie Politique . . . ,' 5me Edition, Paris, 1863, 
 pp. 700-2. 
 
 b 2
 
 XX Preface. 
 
 occurred to me to attempt the discovery of all 
 existing Avritings of the kind. With this view I drew 
 up a chronological list of all the mathematico-econo- 
 mic works known to me, already about seventy in 
 number, which list, by the kindness of the editor, 
 Mr. Giffen, was printed in the Journal of the London 
 Statistical Society for June 1878 (vol. xli, pp. 398- 
 401), separate copies being forwarded to the leading 
 economists, with a request for additions and cor- 
 rections. My friend M. Leon Walras, Rector of the 
 Academy of Lausanne, after himself making con- 
 siderable additions to the list, communicated it to 
 the Journal des ficonomistes (December 1878), 
 to the editor of which we are much indebted 
 for its publication. Copies of the list were also 
 sent to German and Italian economical journals. 
 For the completion of the bibliographical list I 
 am under obligations to Professor W. B. Hodgson, 
 Professor Adam son, Mr. W. H. Brewer, M.A., H. M. 
 Inspector of Schools, the Baron d'Aulnis de Bou- 
 rouill. Professor of Political Economy at Utrecht, 
 M. N. G. Pierson of Amsterdam, M. Vissering of 
 Leiden, Professor Luigi Cossa of Pavia, and others. 
 
 All reasonable exertions have thus been made 
 to render complete and exhaustive the list of mathe- 
 matico-economic works and papers, which is now 
 printed in the first appendix to this book (pp.
 
 Preface. xxi 
 
 301-310). It is hardly likely that many additions 
 can be made to the earlier parts of the list, but 
 I shall be much obliged to any readers who can 
 suggest corrections or additions. I shall also be 
 glad to be informed of any new publications 
 suitable for insertion in the list. On the other 
 hand it is possible that some of the books men- 
 tioned in the list ought not to be there. I have 
 not been able in all cases to examine the publi- 
 cations m3^self, so that some works inserted at the 
 suggestion of correspondents may have been named 
 under misconception of the precise purpose of the 
 list Economic works, for instance, containing 
 numerical illustrations and statistical facts nu- 
 merically expressed, however abundantly, have 
 not been intentionally included, unless there was 
 also mathematical method in the reasoning. With- 
 out this condition the whole literature of numerical 
 commercial statistics would have been imported 
 into my list. In other cases only a small portion 
 of a book named can be called mathematico- 
 economic ; but this fact is generally noted by the 
 quotation of the chapters or pages in question. 
 The tendency, however, has been to include rather 
 than to exclude, so that the readei* might have 
 before him the whole field of literature requiring 
 investigation.
 
 xxii Preface. 
 
 To avoid misapprehension it may be well to 
 explain that the gronnd for inserting any publica- 
 tion, or part of a publication in this list, is its 
 containing an explicit recognitioyi of the mathe- 
 matical character of economics, or the advantage 
 to he attamed hy its symbolical treatment. I con- 
 tend that all economic writers must be mathe- 
 matical so far as they are scientific at all, because 
 they treat of economic quantities, and the relations 
 of such quantities, and all quantities and relations 
 of quantities come within the scope of the mathe- 
 matics. Even those who have most strongly and 
 clearly protested against the recognition of their 
 own method, continually betray in their language 
 the quantitative character of their reasonings. 
 What, for instance, can be more clearly mathe- 
 matical in matter than the following quotation from 
 Cairnes' chief works: — 'We can have no difficulty 
 in seeing how cost in its principal elements is to be 
 computed. In the case of labour, the cost of 
 producing a given commodity will be represented 
 by the number of average labourers employed in 
 its production — regard at the same time being 
 had to the severity of the work and the degree 
 of risk it involves — multiplied by the duration of 
 
 ■s ' Some Leading Princii»le3 of Political Economy Newly Ex- 
 pounded,' pt. 1, chap, iii, p. 97.
 
 Preface. xxiii 
 
 their labours. In that of abstinence, the principle 
 is analogous : the sacrifice will be measured by the 
 quantity of wealth abstained from, taken in con- 
 nection with the risk incurred, and multiplied hy 
 the duration of the abstinence.' Here we deal 
 with computation, multiplication, degree of severity, 
 degree of risk, quantity of Avealth, duration, &c., 
 all essentially mathematical things, ideas, or ope- 
 rations. Although my esteemed friend and pre- 
 decessor has in his preliminary chapter expressly 
 abjured my doctrines, he has unconsciously adopted 
 the mathematical method in all but appearance. 
 
 We might easily go further back, and discover 
 that even the father of the science, as he is often 
 considered, is thoroughly mathematical. In the 
 fifth chapter of the First Book of the ' Wealth of 
 Nations,' for instance, we find Adam Smith con- 
 tinually arguing about ' quantities of labour,' 
 ' measures of value,' ' measures of hardship,' ' pro- 
 portion,' ' equality,' &c. ; the whole of the ideas in 
 fact are mathematical. The same might be said of 
 almost any other passages from the scientific parts 
 of the treatise, as distinguished from the historical 
 parts. In the first chapter of the Second Book 
 (29th paragraph), we read — ' The produce of land, 
 mines, and fisheries, when their natural fertility is 
 equal, is in proportion to the extent and proper
 
 xxiv Preface. 
 
 application of the capitals employed about them. 
 When the capitals are equal, and equally well 
 applied, it is in proportion to their natural fer- 
 tility.' Now every use of the word equal or equality 
 implies the existence of a mathematical equation ; 
 an equation is simj)ly an equality; and every use 
 of the word proportion implies a ratio expressible 
 in the form of an equation. 
 
 I hold, then, that to argue mathematically, 
 whether correctly or incorrectly, constitutes no 
 real differentia as regards writers on the theory 
 of economics. But it is one thing to argue and 
 another thing to understand and to recognise 
 explicitly the method of the argument. As there 
 are so many who talk prose without knowing it, 
 or, again, who syllogise Avithout having the least 
 idea what a syllogism is, so economists have long- 
 been mathematicians without being aware of the 
 fact. The unfortunate result is that they have 
 generally been bad mathematicians, and their 
 works must fall. Hence the exj^licit recognition 
 of the mathematical character of the science was 
 an almost necessary condition of any real improve- 
 ment of the theory. It does not follow, of course, 
 that to be explicitly mathematical is to ensure 
 the attainment of truth, and in such writings as 
 those of Canard and Whewell, we find plenty of
 
 Preface. xxv 
 
 symbols and equations with no result of value, 
 owino- to the fact that they simply translated into 
 symbols the doctrines obtained, and erroneously 
 obtained, Avithout their use. Such writers mis- 
 understood and inverted altogether the function 
 of mathematical s3'mbols, which is to guide our 
 thoughts in the slippery and complicated processes 
 of reasoning. Ordinary language can usually ex- 
 press the first axioms of a science, and often also 
 the matured results ; but only in the most lame, 
 obscure, and tedious way can it lead us through 
 the mazes of inference. 
 
 The bibliographical list, of which I am speaking, 
 is no doubt a very heterogeneous one, and may 
 readily be decomposed into several distinct classes 
 of economical works. In a first class may be placed 
 the writings of those economists who have not at 
 all attempted mathematical treatment in an express 
 or systematic manner, but who have only incidentally 
 acknowledged its value by introducing symbolic or 
 graphical statements. Among such writers may be 
 mentioned especially Ran (1868), Hagen (1844), 
 J. S. Mill (1848), and Courcelle-Seneuil (1867). 
 ]\Iany readers may be surprised to hear that John 
 Stuart Mill has used mathematical symbols; but, 
 on turning to Book III, chapters xvii and xviii, of 
 the ' Principles of Political Economy,' those difficult
 
 xxvi Preface. 
 
 and tedious chapters, in which Mill leads the 
 reader through the Theory of International Trade 
 and International Values, by means of yards of 
 linen and cloth, the reader will find that Mill at last 
 yields, and expresses himself concisely and clearly ^^ 
 by means of equations between 771, n, p, and q. 
 His mathematics are very crude; still there is 
 some approach to a correct mathematical treat- 
 ment, and the result is that tliese chapters, 
 however tedious and difficult, will probably be 
 found the truest and most enduring parts of the 
 whole treatise. 
 
 A second class of economists contains those who 
 have abundantly employed mathematical appa- 
 ratus, but, misunderstanding its true use, or being 
 otherwise diverted from a true theory, have built 
 upon the sand. Misfortunes of this kind are not 
 confined to the science of economics, and in the 
 most exact branches of physical science, such as 
 mechanics, molecular physics, astronomy, &c., it 
 would be possible to adduce almost innumerable 
 mathematical treatises, which must be pronounced 
 nonsense. In the same category must be placed 
 the mathematical writings of such economists as 
 Canard (1801), Whewell (1829, 1831, and 1850), 
 
 1' Book III, chajoter xviii, section 7.
 
 Preface. xxvii 
 
 Esmenard du Mazet (1849 and 1851), and perhaps 
 Du Mcsnil-Marigny (1860). 
 
 The third class forms an antithesis with the 
 second, for it contains those anthors who without 
 any parade of mathematical language or method, 
 have nevertheless carefully attempted to reach 
 precision in their treatment of quantitative ideas, 
 and have thus been led to a more or less complete 
 comprehension of the true theory of utility and 
 wealth. Among such writers Francis Hutcheson, 
 the Irish founder of the great Scotch School, and 
 the predecessor of Adam Smith at Glasgow, pro- 
 babl}^ stands first. His employment of mathematical 
 symbols i seems rather crude and premature, but 
 the precision of his ideas about the estimation of 
 quantities of good and evil is beyond praise. He 
 thoroughly anticipates the foundations of Ben- 
 tliam's moral system, showing that the Moment 
 of Good or Evil, is in a compound proportion of 
 the Duration and Intenseness, affected also by the 
 Hazard or uncertainty of our existence k. As to 
 BenthanV s ideas, they are adopted as the starting 
 point of the theory given in this work, and are 
 quoted at the beginning of chapter ii, (pp. 30-31.) 
 Bentham has repeated his statement as to the mode 
 
 > 1720. Hutcliesoii. 'Au luquiiy,' 1729, &c., pp. 186-198. 
 ^ 1728. lb. 'An Essay,' &c., pp. 34-43, and elsewhere.
 
 xxviii Preface. 
 
 of measuring happiness in several different works 
 and pamphlets, as for instance in that remarkable 
 one called ' A Table of the Springs of Action/ 
 (London, 1817, p. 3;) and also in the 'Codification 
 Proposal, addressed by Jeremy Behtham to all 
 nations professing Liberal opinions' (London, 1822, 
 pp. 7-11.) He here speaks explicitly of the appli- 
 cation of arithmetic to questions of utilit3^ meaning 
 no doubt the application of mathematical methods. 
 He even describes (p. 11) the four circumstances 
 governing the value of a pleasure or pain as the 
 dimensions of its value, though he is incorrect in 
 treating prDjyinquity and certainty as dimensions. 
 
 It is worthy of notice that Destutt de Tracy, one 
 of the most philosophic of all economists, has in a 
 few words recognised the true method of treatment, 
 though he has not followed up his own idea. 
 Referring to the circumstances which, in his 
 opinion, render all economic and moral calculations 
 very delicate, he says i ' On ne pent guere employer 
 dans ces matieres que des considerations tirees de 
 la theorie des limites.' So well known an English 
 
 1 ' Elemens d'ldeologie/ iv, et v^ Parties. ' Traite de la Vo- 
 lonte et de Ses EfFets,' Paris, 1815, 8vo, p. 499. Edition of 1826, 
 J). 335. American Edition, ' A treatise on Political Economy, 
 translated from the unpublished French original,' Georgetown, 
 D.c. 1817, p. xiii.
 
 Preface. xxix 
 
 economist as Malthiis has also sliown in a feAV 
 lilies his comjilete appreciation of the mathematical 
 nature of economic questions. In one of his ex- 
 cellent pamphlets"' he remarks 'Many of the 
 questions, hoth in morals and politics, seem to be 
 of the nature of the problems de maxiinis and 
 minimis in Fluxions; in which there is always a 
 point where a certain effect is the greatest, while 
 on either side of this point it gradually diminishes.' 
 But I have not thought it desirable to swell the 
 bibliographical list by including all the works in 
 which there are to be found brief or casual remarks 
 of the kind. 
 
 I may here remark that all the writings of 
 Mr. Henry Dunning Macleod exhibit a strong 
 tendency to mathematical treatment. Some of his 
 works or papers in which this mathematical spirit 
 is most strongly manifested have been placed in 
 the list. It is not my business to criticise his 
 ingenious views, or to determine how far he really 
 has created a mathematical system. While I cer- 
 tainly differ from him on many important points, 
 I am bound to acknowledge the assistance which 
 I derive from the use of several of his works. 
 
 ni ' Observations on the Effects of the Corn Laws, and of a rise 
 or fall in the price of corn on the Agriculture and General Wealth 
 of the Country,' London, 1814, p. 30; 3rd Edition, 1815, p. 32.
 
 XXX Preface. 
 
 In the fourth and most important class of 
 mathematico-economic writers must be placed 
 those who have consciously and avowedly at- 
 tempted to frame a mathematical theory of the 
 subject, and have, if my judgment is correct, 
 succeeded in reaching a true view of the Science. 
 In this class certain distinguished French philo- 
 sophers take precedence and priority. One might 
 perhaps go back with propriety to Condillac's 
 work, ' Le Commerce et le Gouvernement/ first pub- 
 lished in the year 1776, the same year in which 
 the ' Wealth of Nations ' appeared. In the first 
 few chapters of this charming philosophic work 
 we meet perhaps the earliest distinct statement 
 of the true connection between value and utility. 
 The book, however, is not included in the list 
 because there is no explicit attempt at mathe- 
 matical treatment. It is the French engineer 
 Dupuit who must probably be credited with the 
 earliest perfect comprehension of the theory of 
 utility. In attemi)ting to frame a precise measure 
 of the utility of public works, he observed that the 
 utility of a commodity not only varies immensely 
 from one individual to another, but that it is also 
 widely different for the same person according to 
 circumstances. He says ' nous verrions que I'utilite 
 du morceau de pain pent ci'oltre pour le meme
 
 Preface. xxxi 
 
 iiidividu depiiis zero jiisqii'aii cliiffre de sa fortune 
 entiere' (1849 Diipiiit, ' De rinflueiice des Peages/ 
 etc., p. 185). He establishes, in_fect, a theory of 
 the gradation of utility,^ beautifully and perfectly 
 expounded by means of geometrical diagrams, and 
 this theory is undoubtedly coincident in essence 
 with that contained in this book. He does not, 
 however, follow his ideas out in an algebraic form. 
 Dupuit's theory was the subject of some contro- 
 versy in the pages of the ' Annales des Ponts et 
 Chaussees,' but did not receive much attention 
 elsewhere, and I am not aware that any English 
 economist ever knew anj^thing about these re- 
 markable memoirs. 
 
 The earlier treatise of Cournot, his admirable 
 * Recherches sur les Principes Mathematiques de 
 la Theorie des Richesses' (Paris, 1838), resembles 
 Dupuit's memoirs in being, until within the last 
 few years, quite unknown to English economists. 
 In other respects Cournot's method is contrasted 
 to Dupuit's. Cournot did not frame any ultimate 
 theory of the ground and nature of utility and value, 
 but, taking the palpable facts known concerning 
 the relations of price, production and consumption 
 of commodities, he investigated these relations 
 analytically and diagraphically with a power and 
 felicity which leaves little to be desired. This
 
 xxxii Preface. 
 
 work must occupy a remarkable position in the 
 history of the subject. It is strange that it should 
 have remained for me among Englishmen to dis- 
 cover its value. Some years since (1875) Mr. Tod- 
 hunter wrote to me as follows : — ' I have sometimes 
 wondered whether there is anything of importance 
 in a book published many years since by M. A. A. 
 Cournot, entitled " Recherches sur les Principes 
 Mathematiques de la Theorie des Richesses." 
 I never saw it, and when I have mentioned the 
 title, I never found any person who had read the 
 book. Yet Cournot was eminent for mathematics 
 and metaphysics, and so there may be some merit 
 in this book.' I procured a copy of the work as far 
 back as 1872, but have only recently studied it 
 with sufticient care to form any definite opinion 
 upon its value. Even now I have by no means 
 mastered all parts of it, my mathematical power 
 being insufficient to enable me to follow Cournot 
 in all parts of his analysis. My impression is that 
 the first chapter of the work is not remarkable; 
 that the second chapter contains an important 
 anticipation of discussions concerning the proper 
 method of treating prices, including an anticipation 
 (p. 21) of my logarithmic method of ascertaining varia- 
 tions in the value of gold ; that the third chapter, 
 treating of the conditions of the foreign exchanges.
 
 Preface. xxxiii 
 
 is highly ingenious if not particularly useful ; but 
 that by far the most important part of the book 
 commences with the fourth chapter upon the ' Loi 
 du debit/ The remainder of the book, in fact, con- 
 tains a wonderful analysis of the laws of supply and 
 demand, and of the relations of prices, production, 
 consumption, expenses and profits. Cournot starts 
 from the assumption that the debit or demand for a 
 commodity is a function of the price, or D =3 F (2?) ; 
 and then, after laying down empirically a few 
 conditions of this function, he proceeds to work 
 out with surprising power the consequences which 
 follow from those conditions. Even apart from its 
 economic importance this investigation, so far as 
 I can venture to judge it, presents a beautiful 
 example of mathematical reasoning, in which 
 knowledge is apparently evolved out of ignorance. 
 In reality the method consists in assuming certain 
 simple conditions of the functions as conformable 
 to experience, and then disclosing by symbolic 
 inference the implicit results of these conditions. 
 But I am quite convinced that the investigation is 
 of high economic importance, and that, when the 
 parts of political economy to which the theory 
 relates come to be adequately treated, as they 
 never have yet been, the treatment must be based 
 upon the analysis of Cournot, or at least must 
 
 c
 
 xxxiv Preface. 
 
 follow his general method. It should be added 
 that his investigation has little relation to the 
 contents of this work, because Cournot does not 
 recede to any theory of utility, but commences 
 wdth the phenomenal laws of supply and demand. 
 
 Discouraged apparently by the small amount of 
 attention paid to his mathematical treatise, Cournot 
 in a later year (1863) produced a more popular 
 non-symbolic work on Economics; but this later 
 work does not compare favourably in interest and 
 importance with his first treatise. 
 
 English economists can hardly be blamed for 
 their ignorance of Cournot's economic works when 
 we find French writers equally bad. Thus the 
 authors of Guillaumin's excellent Dictionnaire de 
 I'Economie Politique, which is on the whole the 
 best work of reference in the literature of the 
 science, ignore Cournot and his works altogether, 
 and so likewise does Sandelin in his copious Reper- 
 toire General d'Economie Politique. M. Joseph 
 Garnier in his otherwise admirable text-book » 
 mixes up Cournot with far inferior mathema- 
 ticians, saying — ' Dans ces derniers temps M. 
 Esmenard du Mazet, et M. du Mesnil-Marigny ont 
 aussi fait abus, ce nous semble, des formules alge- 
 briques ; les Recherches sur les Principes Mathema- 
 
 " 'Trait6 d'Economie Politique,' Cinqui^me Edition, p. 701.
 
 Preface. xxxv 
 
 tiqiies des Riclicsses de M. Couriiot, ne nous ont 
 fourni aucun moyen d'eliicidation.' MacCiilloch of 
 course knows nothing of Cournot. Mr. H. D. Macleod 
 has the merit at least of mentioning Cournot's 
 work, but he misspells the name of the author, and 
 gives only the title of the book, which he had pro- 
 bably never seen. 
 
 We now come to a truly remarkable discovery in 
 the history of this branch of literature. Some years 
 since my friend Professor Adamson had noticed 
 in one of Kautz' works on Political Economy o 
 a brief reference to a book said to contain a 
 theory of pleasure and pain, written by a German 
 author named Hermann Heinrich Gossen. Although 
 he had advertised for it, Professor Adamson was un- 
 able to obtain a sight of this book until August 
 1878, when he fortunately discovered it in a German 
 bookseller's catalogue, and succeeded in purchasing 
 it. The book was published at Brunswick in 1854 ; 
 it consists of 278 well-filled pages, and is entitled, 
 ' Entwickelung der Gesetze des menschlichen Ver- 
 kehrs, und der daraus fliessenden Regeln fur mens- 
 chliches Handeln,' which may be translated — ' De- 
 velopment of the laws of human Commerce and of 
 the consequent Rules of Human Action.' I will 
 
 « ' Theorie und Geschichte tier National-Oekonomik,' 1858, vol. i. 
 p. 9. 
 
 C 3
 
 xxxvi Preface. 
 
 describe the contents of this remarkable volume as 
 they are reported to me by Professor Adamson. 
 
 Gossen evidently held the highest possible opinion 
 of the importance of his own theory, for he com- 
 mences by claiming honours in economic science 
 equal to those of Copernicus in astronomy. He 
 then at once insists that mathematical treatment, 
 being the only sound one, must be applied through- 
 out ; but, out of consideration for the reader, the 
 higher analysis will be explicitly introduced only 
 when it is requisite to determine maxima and 
 minima. The treatise then opens with the consi- 
 deration of Economics as the theory of pleasure 
 and pain, that is as the theory of the procedure 
 by which the individual and the aggregate of in- 
 dividuals constituting society, may realise the 
 maximum of pleasure with the minimum of painful 
 effort. The natural law of pleasure is then clearly 
 stated, somewhat as follows : — Increase of the same 
 hind of consumption yields ^pleasure continuously dimi- 
 nishing up to the point of satiety. This law he 
 illustrates geometrically, and then proceeds to 
 investigate the conditions under which the total 
 pleasure from one or more objects may be raised 
 to a maximum. 
 
 The term Werth is next introduced, which may, 
 Professor Adamson thinks, be rendered with strict
 
 Preface. xxxvii 
 
 accuracy, as utility , and Gossen points out that the 
 quantity of utility, material or immaterial, is mea- 
 sured by the quantity of i:>leasure which it affords^ 
 He classifies useful objects as, (1) those which '>^fl/'-'-"i,^y'^' 
 possess pleasure-giving powers in themselves ; 
 (2] those which only possess such powers when^*^**^'*^'^ 
 in combination with other objects; (3) those which»uAn.ji>/«^ ' 
 only serve as means towards the production of 
 pleasure-giving objects. He is careful to point out 
 that there is no such thing as absolute utility, 
 utility being purely a relation between a thing and 
 a person. He next proceeds to give the derivative 
 laws of utility somewhat in the following manner : 
 — That separate portions of the same pleasure- 
 giving object have very different degrees of utility, 
 and that in general for each person only a limited 
 number of such portions has utility ; any addition 
 beyond this limit is useless, but the point of use- 
 lessness is only reached after the utility has gone 
 through all the stages or degrees of intensity. 
 Hence he draws the practical conclusion that each 
 person should so distribute his resources as to 
 render the final increments of each pleasure-giving 
 commodity of equal utility for him. 
 
 In the next place Gossen deals with labour, 
 starting from the proposition that the utility of 
 any product must be estimated after deduction
 
 xxxviii Preface. 
 
 of the pains of labour required to produce it. He 
 describes the variation of the pain of labour much 
 as I have done, exhibiting it graphically, and in- 
 ferring that we must carry on labour to the point 
 at which the utility of the product equals the pain 
 of production. In treating the theory of exchange 
 he shows how barter gives rise to an mimense 
 increase of utility, and he infers that exchange will 
 proceed up to the point at which the utilities of the 
 portions next to be given and received are equal. 
 A complicated geometrical representation of the 
 theory of exchange is given. The theory of rent 
 is investigated in a most general manner, and the 
 work concludes with somewhat vague social specu- 
 lations, which, in Professor Adamson's opinion, are 
 of inferior merit compared with the earlier portions 
 of the treatise. 
 
 From this statement it is quite apparent that 
 Gossen has completely anticipated me as regards 
 the general principles and method of the theory 
 of Economics. So far as I can gather, his treat- 
 ment of the fundamental theory is even more 
 general and thorough than what I was able to 
 scheme out. In discussing the book, I lie under 
 the serious difficulty of not being able to read it ; 
 but, judging from what Professor Adamson has 
 written or read to me, and from an examination
 
 Preface. xxxix 
 
 of the diagrams and symbolic parts of the work, 
 I shoukl infer that Gosseii lias been unfortunate 
 in the development of his theory. Instead of 
 dealing, as Cournot and myself have done, with 
 undetermined functions, and introducing the least 
 possible amount of assumption, Gossen assumed, 
 for the sake of simplicity, that economic functions 
 follow a linear law, so that his curves of utility are 
 generally taken as straight lines. This assumption 
 enables him to work out a great quantity of precise 
 formulas and tabular results, which fill many pages 
 of the book. But, inasmuch as the functions of 
 economic science are seldom or never really linear, 
 and usually diverge very far from the straight line, 
 I think that the symbolic and geometric illustra- 
 tions and developments introduced by Gossen must 
 for the most part be put down among the many 
 products of misplaced ingenuity. I may add, in my 
 own behalf, that he does not seem really to reach the 
 equations of exchange as established in this book ; 
 that the theory of capital and interest is wanting ; 
 and that there is a total absence of any resemblance 
 between the working out of the matter, except such 
 as arises from a common basis of truth. 
 
 The coincidence, however, between the essential 
 ideas of Gossen's system and my own is so striking, 
 that I desire to state distinctly, in the first place,
 
 xl Preface. 
 
 that I never saw nor so much as heard any hint 
 of the existence of Gossen's book before August 
 1878, and to explain, in the second place, how 
 it was that I did not do so. My unfortunate want 
 of linguistic power has prevented me, in spite of 
 many attempts, from ever becoming familiar enough 
 with German to read a German book. I once 
 managed to spell out with assistance part of the 
 logical lecture notes of Kant ; but that is my sole 
 achievement in German literature. Now this work 
 of Gossen has remained unknown even to most 
 of the great readers of Germany. Professor Adam- 
 son remarks that the work seems to have attracted 
 no attention in Germany. The eminent and learned 
 economist of Amsterdam, Professor N. G. Pierson, 
 writes to me, ' Gossen's book is totally unknown 
 to me. Reseller does not mention it in his very 
 laborious History of Political Economy in Germany. 
 I never saw it quoted ; but I will try to get it. It 
 is very curious that such a remarkable work has 
 remained totally unknown even to a man like 
 Professor Roscher, who has read everything.' Mr. 
 Cliffe Leslie, also, who has made the German 
 Economists his special study, informs me that he 
 was quite unaware of the existence of the book p. 
 
 • P A copy of Gossen's book will be found in the Library of the 
 British Museum (Press mark 8408, cc). It was not acquired by
 
 Preface. xli 
 
 Under such circumstances it would have been far 
 more probable that I should discover the theory 
 of pleasure and pain, than that I should discoA^er 
 Gossen's book, and I have carefully pointed out, both 
 in the first edition and in this, certain passages of 
 Bentham, Senior, Jennings, and other authors from 
 which my system was, more or less, consciously de- 
 veloped. I cannot claim to be totally indifferent to 
 the rights of priority ; and from the year 1862, when 
 my theory was first published in brief outline, I have 
 often pleased myself with the thought that it was 
 at once a novel and an important theory. From 
 what I have now stated in this preface it is evident 
 that novelty can no longer be attributed to the 
 leading features of the theory. Much is clearly 
 due to Dupuit, and of the rest a great share must 
 be assigned to Gossen. Regret may easily be 
 swallowed up in satisfaction if I succeed eventually 
 in making that understood and valued which has 
 been so sadly neglected. 
 
 Almost nothing is known to me concerning 
 Gossen ; it is uncertain whether he is living or not. 
 On the title-page he describes himself as Koniglich 
 preussischem Regierungs- Assessor ausser Dienst, 
 which may be translated ' Royal Prussian Govern- 
 that institution until May 24, 1865, as shown by the date stamped 
 upon the copy.
 
 xlii Preface. 
 
 ment Assessor, retired ; ' but the tone of his re- 
 marks here and there seems to. indicate that he 
 was a disappointed if not an injured man. The 
 reception of his one work can have lent no relief 
 to these feelings ; rather it must much have deep- 
 ened them. The book seems to have contained 
 his one cherished theory; for I can find under 
 the name of Gossen no trace of anj'- other pub- 
 lication or scientific memoir whatever. The history 
 of these forgotten works is, indeed, a strange and 
 discouraging one ; but the day must come when 
 the eyes of those who cannot see will be opened. 
 Then will due honour be given to all who like 
 Cournot and Gossen have laboured in a thankless 
 field of human knowledge, and have met with 
 the neglect or ridicule they might well have 
 expected. Not indeed that such men do really 
 work for the sake of honour; they bring forth 
 a theory as the tree brings forth its fruit. 
 
 It remains for me to refer to the mathematico- 
 economic writings of M. Leon Walras, the Rector 
 of the Academy of Lausanne. It is curious that 
 Lausanne, already distinguished by the early work of 
 Isnard (1781), should recently have furnished such 
 important additions to the science as the Memoirs 
 of Walras. For important they are, not only 
 because they complete and prove that which was
 
 Preface. xliii 
 
 before published elsewhere in the works described 
 above, but because they contain a third or fourth 
 independent discovery of the principles of the 
 theory. If we are to trace out 'the filiation of 
 ideas ' by which M. Walras was led to his theory, 
 we should naturally look back to the work of his 
 father, Auguste Walras, published at Paris in 1831, 
 and entitled ' De la Nature de la Richesse, et de 
 I'origine de la Valeur/ In this work we find, it is 
 true, no distinct recognition of the mathematical 
 method, but the analysis of value is often acute and 
 philosophic. The principal point of the work more- 
 over is true, that value depends upon rarety — ' La 
 valeur,' says Auguste Walras, ' derive de la rarete.' 
 Now it is precisely upon this idea of the degree of 
 rarety of commodities that Leon Walras bases his 
 system. The fact that some four or more indepen- 
 dent writers such as Dupuit, Gossen, Walras, and 
 myself, should in such different ways have reached 
 substantially the same views of the fundamental 
 ideas of economic science, cannot but lend great 
 probability, not to say approximate certainty, to 
 those views. I am glad to hear that M. Walras 
 intends to bring out a new edition of his Mathe- 
 matico-Economic Memoirs, to which the attention 
 of my readers is invited. The titles of his publi- 
 cations will be found in the Appendix I.
 
 xliv Preface. 
 
 The works of Von Thtinen and of several other 
 German economists contain mathematical investi- 
 gations of much interest and importance. A con- 
 siderable number of such works will be found noted 
 in the list, which, however, is especially defective 
 as regards German literature. I regret that I am 
 not able to treat this branch of the subject in an 
 adequate manner. 
 
 My bibliographical list shows that in recent 
 3^ears, that is to say since the year 1873, there has 
 been a great increase in the number of mathe- 
 matico-economic writings. The names of Fontan- 
 eau, Walras, Avigdor, Lefevre, Petersen, Boccardo, 
 recur time after time. In such periodicals as the 
 Journal des Actuaires Fran^ais, or the National- 
 Oekonomisk Tidsskrift — a journal so creditable to 
 the energy and talent of the Danish Economic 
 School — the mathematical theory of Economics is 
 treated as one of established interest and truth, with 
 which readers would naturally be acquainted. In 
 England we have absolutely no periodical in which 
 such discussions could be conducted. The reader 
 will not fail to remark that it is into the hands 
 of French, Italian, Danish, or Dutch writers that 
 this most important subject is rapidly passing. 
 They will develop that science which only excites 
 ridicule and incredulity among the followers of
 
 Preface. xlv 
 
 Mill and Ricardo. There are just a few English 
 mathematicians, such as Fleeming Jenkin, George 
 Darwin, Alfred Marshall, or H. D. Macleod, and one 
 or two Americans lilve Professor Simon Newcomb, 
 who venture to write upon the obnoxious subject 
 of mathematico-economic science. I ought to add, 
 however, that at Cambridge (England) the mathe- 
 matical treatment of Economics is becoming gra- 
 dually recognised owing to the former influence of 
 Mr. Alfred Marshall, now the principal of University 
 College, Bristol, whose ingenious mathematico- 
 economic problems, expounded moi^e geometrico^ 
 have just been privately printed at Cambridge. 
 
 If we overlook Hutcheson, who did not expressly 
 write on Economics, the earliest mathematico- 
 economic author seems to be the Italian Ceva, 
 whose works have just been brought to notice in 
 the Giornale degli Economisti (see 1878, Nicolini). 
 Ceva wrote in the early part of the 18th century, 
 but I have as yet no further information about 
 him. The next author in the list is the celebrated 
 Beccaria, who printed a very small, but distinctly 
 mathematical, tract on Taxation as early as 1765. 
 Italians were thus first in the field. The earliest 
 English work of the kind yet discovered is an 
 anonymous ' Essay on the Theory of Money,' pub- 
 lished in London in 1771, five years before the era
 
 xlvi Preface. 
 
 of the 'Wealth of Nations.' Though crude and 
 absurd in some parts, it is not devoid of interest 
 and ability, and contains a distinct and partially 
 valid attempt to establish a mathematical theory 
 of currency. This remarkable Essay is, so far as I 
 know, wholly forgotten and almost lost in England. 
 Neither MacCulloch nor any other English econo- 
 mist known to me, mentions the work. I discovered 
 its existence a few months ago by accidentally 
 finding a copy on a bookseller's stall. But it 
 shames an Englishman to learn that English works 
 thus unknown in their own country are known 
 abroad, and I owe to Professor Luigi Cossa, of the 
 University of Pavia, the information that the Essay 
 was written by Major -General Henry Lloyd, an 
 author of some merit in other branches of litera- 
 ture. Signer Cossa's excellent ' Guide alia Studio 
 di Economia Politica,' a concise but judiciously 
 written text-book, is well qualified to open our 
 eyes as to the insular narrowness of our economic 
 learning. It is a book of a kind much needed 
 by our students of Economics, and I wish that it 
 could be published in an English dress. 
 
 From this bibliographical survey emerges the 
 wholly unexpected result, that the mathematical 
 treatment of Economics is coeval with the science 
 itself. The notion tliat there is any novelty or
 
 Preface. xlvii 
 
 originality in the application of mathematical 
 methods or symhols must he dismissed altogether. 
 While there have been political economists there 
 has always been a certain number who with vari- 
 ous success have struck into the unpopular but 
 right path. The unfortunate and discouraging 
 aspect of the matter is the complete oblivion into 
 which this part of the literature of Economics has 
 always fallen, oblivion so complete that each 
 mathematico-economic writer has been obliged to 
 begin almost de novo. It is with the purpose of 
 preventing for the future as far as I can such 
 ignorance of previous exertions, that I have spent 
 so much pains upon this list of books. 
 
 I should add that in arranging the list I have 
 followed, very imperfectly, the excellent example 
 set by Professor Mansfield Merriman, of the Sheffield 
 Scientific School of Yale College, in his ' List of 
 Writings relating to the Method of Least Squares <i.' 
 Such bibliographies are of immense utility, and 
 I hope that the time is nearly come when each 
 student of a special branch of science or literature 
 will feel bound to work out its bibliography, unless, 
 of course, the task shall have been already accom- 
 plished. The reader will see that, in Appendix II, 
 
 1 'Transactions of the Connecticut Academy,* 1877, vol. iv. 
 pp. 151-232.
 
 xlviii Preface. 
 
 I have taken the liberty of working out also a 
 part of the bibliography of my own writings. 
 
 Looking now to the eventual results of the 
 theory, I must beg the reader to bear in mind that 
 this book was never put forward as containing 
 a systematic view of Economics. It treats only 
 of the theory, and is but an elementary sketch of 
 elementary principles. The working out of a com- 
 plete system based on these lines must be a matter 
 of time and labour, and I know not when, if ever, 
 I shall be able to attempt it. In the last chapter, 
 I have, however, indicated the manner in which 
 the theory of wages will be affected. This chapter 
 is reprinted almost as it was wi-itten in 1871 ; since 
 then the wage-fund theory has been abandoned 
 by most English Economists, owing to the attacks 
 of Mr. Cliffe Leslie, Mr. Shadwell, Professor Cairnes, 
 Professor Francis Walker, and some others. Quite 
 recently more extensive reading and more careful 
 cogitation have led to a certain change in my ideas 
 concerning the superstructure of Economics — in 
 this wise — 
 
 Firstly, I am convinced that the doctrine of 
 wages, which I adopted in 1871, under the impres- 
 sion that it was somewhat novel, is not really novel 
 at all, except to those whose view is bounded by the 
 maze of the Ricardian Economics. The true doc-
 
 Preface. xlix 
 
 trine may be more or less clearly traced through the 
 writings of a succession of great French Economists, 
 from Condillac, Bandeau, and Le Trosne, through 
 J.-B. Say, Destutt de Tracy, Storch, and others, down 
 to Bastiat and Courcelle-Seneuil. The conclusion 
 to which I am ever more clearly coming is that the 
 only hope of attaining a true s^^stem of Economics 
 is to fling aside, once and for ever, the mazy and 
 preposterous assumptions of the Ricardian School. 
 Our English Economists have been living in a fool's 
 paradise. The truth is with the French School, 
 and the sooner we recognise the fact, the better 
 it will be for all the world, except perhaps the few 
 Avriters who are too far committed to the old 
 erroneous doctrines to allow of renunciation. 
 
 Although, as I have said, the true theory of w^ages 
 is not new as regards the French School, it is new, 
 or at any rate re-newed, as regards our English 
 Schools of Economics. One of the first to treat 
 the subject from the right point of view was Mr. 
 Cliffe Leslie, in an article first published in Fraser's 
 Magazine for July 1868, and subsequently reprinted 
 in a collection of Essays^. Some years afterwards 
 Mr. J. L. Shadwell independently worked out the 
 
 r ' Land Systems ami Industrial Economy of Ireland, England, 
 and Continental Countries.' London, 1870. Appendix, pp. 
 357-379. 
 
 d
 
 1 Preface. 
 
 same theory of wages which he has fully expounded 
 in his admirable ' System of Political Economy s.' 
 In Hearn's Plutology, however, as pointed out in 
 the text of this book (pp. 296-7), we find the same 
 general idea that wages are the share of the pro- 
 duce which the laws of supply and demand enable 
 the labourer to secure. It is probable that like 
 ideas might be traced in other works were this 
 the place to attempt a history of the subject. 
 
 Secondly, I feel sure that when, casting ourselves 
 fi-ee from the Wage-Fund Theory, The Cost of Pro- 
 duction doctrine of Value, the Natural Rate of 
 Wages, and other misleading or false Ricardian 
 doctrines, we begin to trace out clearly and simply 
 the results of a correct theory, it will not be diffi- 
 cult to arrive at a true doctrine of wages. This 
 will probably be reached somewhat in the following 
 
 I way — We must regard labour, land, knowledge, and 
 capital as conjoint conditions of the whole produce, 
 not as causes each of a certain portion of the pro- 
 duce. Thus in an elementary state of society, 
 when each labourer owns all the three or four 
 requisites of production, there would really be no 
 such thing as wages, rent, or interest at all. Distri- 
 bution does not arise even in idea, and the produce 
 
 ' is simply the aggregate effect of the aggregate con- 
 
 a London, 1877, Triibner.
 
 Preface. li 
 
 ditions. It is only when separate owners of the 
 elements of i^rodiiction join their properties, and 
 traffic with each other, that distribution begins, and 
 then it is entirely subject to the principles of A^alue 
 and the laws of suj^ply and demand. Each labourer 
 must be regarded, like each landowner and each 
 capitalist, as bringing into the common stock one 
 part of the component elements, bargaining for the 
 best share of the produce which the conditions 
 of the market allow him to claim successfully. In 
 theory the labourer has a monopoly of labour 
 of each particular kind, as much as the landowner 
 of land, and the capitalist of other requisite articles. 
 Property is only another name for monopoly. But 
 when different persons own property of exactly the 
 same kind, they become subject to the important 
 Law of Indifference, as I have called it (pp. 98-101), 
 namely, that in the same open market, at an}' one 
 moment, there cannot be two prices for the same 
 kind of article. Thus monoj^oly is limited hy com- 
 petition, and no owner, whether of labour, land, or 
 capital, can, theoretically speaking, obtain a larger 
 share of produce for it than what other owners of ex- 
 actly the same kind of property are willing to accept. 
 So far there may seem to be nothing novel in this 
 view ; it is hardly more than will be found stated 
 in a good many economic works. But as soon as 
 
 d 2
 
 lii Preface. 
 
 we begin to follow out this simj^le view, the conse- 
 quences are rather startling. We are forced, for 
 instance, to admit that rates of wages are governed 
 by the same formal laws as rents. This view is not 
 new to the readers of Storch, who in the third book 
 of his excellent ' Cours d'Economie Politique ' has 
 a chapter * ' De la Rente des talens et des qualites 
 morales.' But it is a very new doctrine to one 
 whose economic horizon is formed by Mill and 
 Fawcett, Ricardo and Adam Smith. Even Storch 
 has not followed out the doctrine thoroughly ; for 
 he applies the idea of rent only to cases of eminent 
 talent. It must be evident, however, that talent 
 and capacity of all kinds are only a question of 
 degree, so that, according to the Law of Continuity, 
 the same principle must apply to all labourers. 
 
 A still more startling result is that, so far as cost 
 of production regulates the values of commodities, 
 wages must enter into the calculation on exactly 
 the same footing as rent. Now it is a prime point 
 of the Ricardian doctrines that rent does not enter 
 into cost of production. As J. S. Mill says ^, ' Rent, 
 therefore, forms no part of the cost of production 
 which determines the value of agricultural produce.' 
 
 t Chapter V, vol. T, p. 304. 
 
 " ' Principles of Political Economy,' Book III, Chapter V, Section 
 2, Paragraph 3.
 
 Preface. liii 
 
 And again v, ' Rent is not an element in the cost of 
 production of the commodity which yiekls it ; except 
 in the cases/ &c. Rent in fact is represented as the 
 cft'ect not the cause of high value ; wages on the 
 contrary are treated as the cause, not the effect. 
 But if rent and wages he really phenomena sub- 
 ject to the same formal laws this opposite rela- 
 tion to value must involve error. The way out of 
 the difficulty is furnished by the second sentence 
 of the paragraph from which the last quotation was 
 taken. Mill goes on to say : 'But when land 
 capable of yielding rent in agriculture is applied 
 to some other purpose, the rent Avhich it would 
 have yielded is an element in the cost of production 
 of the commodity which it is employed to produce.' 
 Here Mill edges in as an exceptional case that 
 which proves to be the rule, reminding one of other 
 exceptional cases described as ' Some peculiar 
 cases of value' (see p. 214 below), which I have 
 shown to include almost all commodities. 
 
 Now Mill allows that when land capable of 
 yielding rent in agriculture is applied to some 
 other purpose, the rent which would have been 
 produced in agriculture is an element in the cost 
 of production of other commodities. But wherefore 
 
 ^ 'Principles of Political Economy,' Book III, Chapter VI, 
 Section 1, Article 9.
 
 ]iv Preface. 
 
 this distinction between agriculture and other 
 branches of industry? Why does not the same 
 principle apply between two different modes of 
 agricultural employment ? If land which has been 
 yielding £2 per acre rent as pasture be ploughed 
 up and used for raising wheat, must not the £2 per 
 acre be debited against the expenses of the produc- 
 tion of wheat ? Suppose that somebody introduced 
 the beetroot culture into England with a view to 
 making sugar; this new branch of industry could 
 not be said to pay unless it yielded, besides all 
 other expenses, the full rents of the lands turned 
 from other kinds of culture But if this be con- 
 ceded, the same principle must apply generally; 
 a potatoe-field should pay as well as a clover-field, 
 and a clover-field as a turnip-field; and so on. 
 The market prices of the produce must adjust 
 themselves so that this shall in the long run be 
 possible. The rotation of crops, no doubt, intro- 
 duces complication into the matter, but does not 
 modify the general reasoning. The principle which 
 emerges is that each portion of land should he 
 applied to that cidture or use which yields the largest 
 total of utility, as measured hy the value of the pro- 
 duce ; if otherwise applied there will be loss. Thus 
 the rent of land is determined by the excess of 
 produce in the most profitable employment.
 
 Preface. Iv 
 
 But when the matter is fully thought out, it will 
 be seen that exactly the same principle applies 
 to wages. A man who can earn six shillings a day 
 in one employment will not turn to another kind 
 of work unless he expects to get six shillings a day 
 or more from it. There is no such thing as absolute 
 cost of labour ; it is all matter of comparison. 
 Every one gets the most which he can for his 
 exertions; some can get little or nothing, because 
 they have not sufficient strength, knowledge, nor 
 ingenuity; others get much, because they have, 
 comparatively s|)eaking, a monopoly of certain 
 powers. Each seeks the work in which his peculiar 
 faculties are most productive of utility, as measured 
 by what other people are willing to pay for the 
 produce. Thus wages are clearly the effect not 
 the cause of the value of the produce. But when 
 labour is turned from one employment to another, 
 the wages it would otherwise have yielded must be 
 debited to the expenses of the new product. Thus 
 the parallelism between the theories of rent and 
 wages is seen to be perfect in theory, however 
 different it may appear to be in the details of appli- 
 cation. Precisely the same view may be applied, 
 mutatis mutandis, to the rent yielded by fixed 
 capital, and to the interest of free capital. In the 
 last case, the Law of Indifference peculiarly applies,
 
 Ivi Freface. 
 
 because free capital, loanable for a certain interval, 
 is equally available for all branches of industry; 
 hence, at any moment and place, the interest of 
 such capital must be the same in all branches of 
 trade. 
 
 I ought to say that Mill, as pointed out to me 
 by Professor Adamson, has a remarkable section 
 at the end of Chapter V, of Book III, of the 
 'Principles,' in which he explains that all in- 
 equalities, artificial or natural, give rise to extra 
 gains of the nature of Rent. This section is a 
 very satisftictory one inasmuch as it tends to sup- 
 port the view on which I am now insisting, a 
 view, however, which Avlien properly followed out 
 will overthrow many of the principal doctrines 
 of the Ricardo-Mill Economics. Those who have 
 studied Mill's philosophic character as long and 
 minutely as I have done, will not for a moment 
 suppose that the occurrence of this section in Mill's 
 book tends to establish its consistency with other 
 portions of the same treatise. 
 
 But of course I cannot follow out the discussion 
 of this matter in a mere pireface. The results to 
 be expected are partly indicated in my Primer 
 of Political Economy, but in that little treatise 
 my remarks upon the Origin of Rent (p. 94), 
 as originally printed in the first edition, were
 
 Preface,. Ivii 
 
 erroneous, and the section altogether needs to be 
 rewritten. When at length a true system of 
 Economics comes to be established, it will be 
 seen that that able but wrong-headed man, David 
 Ricardo, shunted the car of Economic science on 
 to a wrong line, a line, however, on which it 
 was further urged towards confusion by his equally 
 able and wrong-headed admirer John Stuart Mill. 
 There were Economists, such as Malthus and Senior, 
 who had a far better comprehension of the true 
 doctrines (though not free from the Ricardian 
 errors), but they were driven out of the field by 
 the unity and influence of the Ricardo-Mill school. 
 It will be a work of labour to pick up the frag- 
 ments of a shattered science and to start anew, 
 but it is a work from which they must not shrink 
 who wish to see any advance of Economic Science. 
 
 The ' Chestnuts, 
 Hampstead Heath, N.W. 
 May, 1879.
 
 C O N T E N T S. 
 
 CHAPTER I. 
 
 INTEODUCTION. 
 
 Introduction ....... 
 
 Mathematical Character of the Science 
 
 Confusion between Mathematical and Exact Sciences 
 
 Capability of Exact Measurement 
 
 Measurement of Feeling and Motives . 
 
 Logical Method of Economics .... 
 
 Relation of Economics to Ethics 
 
 PAGE 
 1 
 
 3 
 
 6 
 
 8 
 
 13 
 
 18 
 
 25 
 
 CHAPTER II. 
 
 THEORY OF PLEASUBE AND PAIN. 
 
 Pleasure and Pain as Quantities 
 Pain the Negative of Pleasure 
 Anticipated Feeling . 
 Uncertainty of Future Events 
 
 30 
 34 
 36 
 
 38
 
 Ix 
 
 Contents. 
 
 CHAPTER III. 
 
 THEOEY OF UTILITY. 
 
 Definition of Terms ..... 
 
 The Laws of Human Want 
 
 Utility is not an Intrinsic Quality 
 
 Law of the Variation of Utility . 
 
 Total Utility and Degree of Utility 
 
 Variation of the Final Degree of Utility 
 
 Disutility and Discommodity 
 
 Distribution of Commodity in different Uses 
 
 Theory of Dimensions of Economic Quantities 
 
 Actual, Prospective, and Potential Utility . 
 
 Distribution of a Commodity in time . 
 
 PAGE 
 
 40 
 42 
 47 
 49 
 53 
 56 
 62 
 63 
 66 
 74 
 77 
 
 CHAPTER IV. 
 
 THEORY OF EXCHANGE. 
 
 Importance of Exchange in Economics 
 Ambiguity of the term Value 
 Value expresses Ratio of Exchange 
 Popular use of the term Value 
 Dimension of Value . 
 Definition of Market . 
 Definition of Trading Body 
 The Law of Indifference 
 The Theory of Exchange . 
 
 81 
 82 
 84 
 85 
 90 
 91 
 95 
 98 
 103
 
 Contents. 
 
 Ixi 
 
 Symbolic Statement of the Theory 
 
 Analogy to the Theory of the Lever 
 
 Impediments to Exchange . 
 
 Illustrations of the Theory of Exchange 
 
 Problems in the Theory of Exchange 
 
 Complex Cases of the Theory 
 
 Competition in Exchange . 
 
 Failure of the Equations of Exchange 
 
 Negative and Zero Value . 
 
 Equivalence of Commodities 
 
 Acquired Utility of Commodities 
 
 The Gain by Exchange 
 
 Numerical Determination of the Laws of Utility 
 
 Opinions as to the Variation of Price 
 
 Variation of the Price of Corn 
 
 The Origin of Value . 
 
 PAGE 
 
 106 
 110 
 115 
 117 
 121 
 124 
 127 
 128 
 137 
 145 
 149 
 153 
 158 
 160 
 165 
 174 
 
 CHAPTER V. 
 
 THEORY OF LABOUE. 
 
 Definition of Labour . 
 
 Quantitative Notions of Labour . 
 
 Symbolic Statement of the Theory 
 
 Dimensions of Labour 
 
 Balance between Need and Labour 
 
 Distribution of Labour 
 
 Belation of the Theoi-ies of Labour and Exchange 
 
 181 
 184 
 189 
 193 
 194 
 198 
 201
 
 Ixii 
 
 Contents. 
 
 
 PAGE 
 
 Kelations of Economic Quantities 
 
 . 205 
 
 Various Cases of the Theory .... 
 
 . 209 
 
 Joint Production 
 
 . 214 
 
 Over-production ...... 
 
 . 219 
 
 Limits to the Intensity of Labour 
 
 . 221 
 
 CHAPTER VI. 
 
 
 THEORY OF RENT. 
 
 Accepted Opinions concerning Rent 
 Symbolic Statement of the Theory 
 Illustrations of the Theory 
 
 228 
 233 
 238 
 
 CHAPTER VII. 
 
 THEORY OF CAPITAL. 
 
 The Function of Capital 
 Capital is concerned with Time . 
 Quantitative Notions concerning Capital 
 Expression for Amount of Investment 
 Dimensions of Capital, Credit, and Debit 
 Effect of the Duration of "Work . 
 Illustrations of the Investment of Capital 
 Fixed and Circulating Capital 
 Free and lavested Capital . 
 Uniformity of the Rate of Interest 
 General Expression for the Rate of Interest 
 Dimension of Interest 
 
 241 
 243 
 249 
 252 
 253 
 255 
 258 
 262 
 263 
 264 
 266 
 268
 
 Contents. Ixiii 
 
 PAGE 
 
 Peacock on the Dimenslong of Interest . . . .271 
 
 Tendency of Profits to a Minimum 274 
 
 Advantage of Capital to Industry . . . . .277 
 Are Articles in the Consumers' hands Capital ? . . . 280 
 
 CHAPTER VIII. 
 
 CONCLUDING REMARKS. 
 
 The Doctrine of Population . . . . . .288 
 
 Relation of "Wages and Profit . . . . . .289 
 
 Professor Hearn's Views . . . . . . .296 
 
 The Noxious Influence of Authority ..... 298 
 
 APPENDIX I. 
 List of Mathematico-Economic Writings .... 301 
 
 APPENDIX IT. 
 
 List of the Author's Economic Writings . . . .311
 
 THE 
 
 THEORY OF POLITICAL ECONOMY. 
 
 CHAPTER I. 
 
 INTRODUCTION. 
 
 The science of Political Economy rests upon a 
 few notions of an apparently simple character. 
 Utility, wealth, value, commodity, labour, land, 
 capital, are the elements of the subject ; and who- 
 ever has a thorough comprehension of their nature 
 must possess or be soon able to acquire a know- 
 ledge of the whole science. As almost every eco- 
 nomical writer has remarked, it is in treating the 
 simple elements that we require the most care and 
 precision, since the least error of conception must 
 vitiate all our deductions. Accordingly, I have 
 devoted the following pages to an investigation 
 of the conditions and relations of the above-named 
 notions. 
 
 Repeated reflection and inquiry have led me to 
 the somewhat novel opinion, that value depends 
 
 B
 
 2 Tlie Theory of Political Economy. 
 
 entirely upon utility. Prevailing opinions make 
 labour rather than utility the origin of value ; 
 and there are even those who distinctly assert 
 that labour is the cause of value. I show, on the 
 contrary, that we have only to trace out carefully 
 the natural laws of the variation of utility, as 
 depending upon the quantity of commodity in our 
 possession, in order to arrive at a satisfactory 
 theory of exchange, of which the ordinary laws of 
 sujjply and demand are a necessary consequence. 
 This theory is in harmony with facts ; and, when- 
 ever there is any apparent reason for the belief 
 that labour is the cause of value, we obtain an 
 exj)lanation of the reason. Labour is found often 
 to determine value, but only in an indirect manner, 
 by varying the degree of utility of the commodity 
 through an increase or limitation of the supply. 
 
 These views are not put forward in a hasty or 
 ill-considered manner. All the chief points of the 
 theory were sketched out seventeen years ago ; 
 but they were then published only in the form of 
 a brief paper communicated to the Statistical or 
 Economic Section of the British Association at the 
 Cambridge Meeting, which took place in the year 
 1862. A still briefer abstract of that paper was 
 inserted in the Report of the Meeting '\ and the 
 paper itself was not printed until June 1866 b. 
 
 <^ 'Reports of Sections/ p. 158. 
 
 ^ 'Journal of the Statistical Society,' vol. xxix. p. 282.
 
 Introduction. 3 
 
 Since writing that paper, I have, over and over 
 again, questioned the truth of my own notions, but 
 without ever finding any reason to doubt their sub- 
 stantial correctness. 
 
 Mathematical Character of the Science. 
 
 It is clear that Economics, if it is to be a science 
 at all, must be a mathematical science. There 
 exists much prejudice against attempts to intro- 
 duce the methods and language of mathematics 
 into any branch of the moral sciences. Many 
 persons seem to think that the physical sciences 
 form the proper sphere of mathematical method, 
 and that the moral sciences demand some other 
 method, — I know not what. My theory of Econo- 
 mics, however, is purely mathematical in character. 
 Nay, believing that the quantities with which Ave 
 deal must be subject to continuous variation, I do 
 not hesitate to use the appropriate branch of 
 mathematical science, involving though it does the 
 fearless consideration of infinitely small quantities. 
 The tlieory consists in applying the differential 
 calculus to the familiar notions of wealth, utility, 
 value, demand, supply, capital, interest, labour, 
 and all the other quantitative notions belonging 
 to the daily operations of industry. As the com- 
 plete theory of almost every other science involves 
 
 B 2
 
 4 27^.6 Theory of Political Economy. 
 
 the use of that calculus, so we cannot have a true 
 theory of Economics without its aid. 
 
 To me it seems that our science must he mathe- 
 matical simply because it deals ivith quantities. 
 Wherever the things treated are capable of being 
 greater or less, there the laws and relations must 
 be mathematical in nature. The ordinary laws of 
 supply and demand treat entirely of quantities of 
 commodity demanded or supplied, and express the 
 manner in which the quantities vary in connection 
 with the price. In consequence of this fact the 
 laws are mathematical. Economists cannot alter 
 their nature by denying them the name ; they 
 might as well try to alter red light by calling it 
 blue. Whether the mathematical laws of Econo- 
 mics are stated in words, or in the usual symbols, 
 ^, y> 2, p, q, etc., is an accident, or a matter of mere 
 convenience. If we had no regard to trouble and 
 prolixity, the most complicated mathematical pro- 
 blems might be stated in ordinary language, and 
 their solution might be traced out by words. In 
 fact, some distinguished mathematicians have 
 shown a liking for getting rid of their symbols, 
 and expressing their arguments and results in 
 language as nearly as possible approximating to 
 that in common use. In his ' Sj^steme du Monde,' 
 Laplace attempted to describe the truths of physi- 
 cal astronomy in common language ; and Thomson 
 and Tait interweave their great ' Treatise on
 
 Introduction. 5 
 
 Natural Philosophy' with an interpretation in 
 ordinary words, supposed to be within the com- 
 l^rehension of general readers c. 
 
 These attempts, however distinguished and inge- 
 nious their authors, soon disclose the inherent 
 defects of the grammar and dictionary for ex- 
 pressing complicated relations. The symbols of 
 mathematical books are not different in nature from 
 language ; they form a perfected system of lan- 
 guage, adapted to the notions and relations which 
 we need to express. They do not constitute the 
 mode of reasoning they embody; they merely 
 facilitate its exhibition and comprehension. If, 
 then, in Economics, we have to deal with quantities 
 and complicated relations of quantities, we must 
 reason mathematically; we do not render the 
 science less mathematical by avoiding the sym- 
 bols of algebra, — we merely refuse to employ, in 
 a very imperfect science, much needing every 
 kind of assistance, that apparatus of appro- 
 priate signs which is found indispensable in other 
 sciences. 
 
 c The large type or non-symbolic portion of the Treatise has 
 been reprinted in a separate volume, under the title ' Elements 
 of Natural Philosophy, by Professors Sir W. Thomson and P. Gr. 
 Tait. Part I. Oxford, Clarendon Press, 1873.' But the authors 
 appear to me inaccurate in describing this work, in the preface, as 
 non-mathematical. It is comparatively non-symbolic, but equally 
 mathematical with the complete Treatise.
 
 6 The Theory of Political Economy. 
 
 Confusion hetiveen Mathematical and Exact 
 Sciences. 
 
 Many persons entertain a prejudice against mathe- 
 matical language, arising out of a confusion between 
 the ideas of a mathematical science and an exact 
 science. They think that we must not pretend to 
 calculate unless we have the precise data which 
 will enable us to obtain a precise answer to our 
 calculations ; but, in reality, there is no such thing 
 as an exact science, except in a comparative sense. 
 Astronomy is more exact than other sciences, be- 
 cause the position of a planet or star admits of 
 close measurement ; but, if we examine the methods 
 of physical astronomy, we find that they are all 
 approximate. Every solution involves hypotheses 
 which are not really true : as, for instance, that 
 the earth is a smooth, homogeneous spheroid. 
 Even the apparently simpler problems in statics 
 or dynamics are only hypothetical approximations 
 to the truth ^. 
 
 We can calculate the effect of a crow-bar, provided 
 it be perfectly inflexible and liave a perfectly hard 
 fulcrum, — which is never the case e. The data are 
 
 d This subject of the approximate character of quantitative 
 science is pursued, at some length, in my ' Principles of Science,' 
 chapter xxi, on ' The Theory of Approximation/ and elsewhere in 
 the same work. 
 
 e Thomson and Tait's ' Treatise on Natural Philosophy,' vol. i. 
 p. 337.
 
 Introduction. 7 
 
 almost wholly deficient for the complete solution 
 of any one i^roblem in natural science. Had 
 physicists waited until their data were perfectly 
 precise before they brought in the aid of mathe- 
 matics, we should have still been in the age of 
 science which terminated at the time of Galileo. 
 
 When we examine the less precise physical 
 sciences, we find that physicists are, of all men, 
 most bold in developing their mathematical theories 
 in advance of their data. Let any one who doubts 
 this examine Airy's ' Theory of the Tides,' as given 
 in the Encyclopsedia Metropolitana ; he will there 
 find a wonderfully complex mathematical theory 
 which is confessed by its author to be incapable of 
 exact or even approximate application, because the 
 results of the various and often unknown contours 
 of the seas do not admit of numerical verification. 
 In this and many other cases we have mathe- 
 matical theory without the data requisite for 
 precise calculation. 
 
 The greater or less accuracy attainable in a 
 mathematical science is a matter of accident, and 
 does not affect the fundamental character of the 
 science. There can be but two classes of sciences 
 — those which are simply logical, and those which, 
 besides being logiccd, are also rnathematiccd. If there 
 be any science which determines merely Avhether a 
 thing be or be not — whether an event will happen, 
 or will not happen — it must be a purely logical
 
 8 The Theory of Political Economy. 
 
 science ; but if the thing may be greater or less, 
 or the event may happen sooner or later, nearer 
 or farther, then quantitative notions enter, and the 
 science must be mathematical in nature, by what- 
 ever name we call it. 
 
 Capability of Exact Measurement. 
 
 Many will object, no doubt, that the notions 
 which we treat in this science are incapable of any 
 measurement. We cannot weigh, nor gauge, nor 
 test the feelings of the mind ; there is no unit of 
 labour, or suffering, or enjoyment. It might thus 
 seem as if a mathematical theory of Economics 
 would be necessarily deprived for ever of numerical 
 data. 
 
 I answer, in the first place, that nothing is less 
 warranted in science than an uninquiring and un- 
 hoping spirit. In matters of this kind, those who 
 despair are almost invariably those who have never 
 tried to succeed. A man might be despondent had 
 he spent a lifetime on a difficult task without a 
 gleam of encouragement ; but the popular opinions 
 on the extension of mathematical theory tend to 
 deter any man from attempting tasks which, how- 
 ever difficult, ought, some day, to be achieved. 
 
 If we trace the history of other sciences, we 
 gather no lessons of discouragement. In the 
 case of almost everything which is now exactly
 
 Introduction. 9 
 
 measured, we can go back to the age when the 
 vaguest notions prevailed. Previous to the time 
 of Pascal, who would have thought of measuring 
 douU and belief f Wlio could have conceived that 
 the investigation of petty games of chance would 
 have led to the creation of perhaps the most sub- 
 lime branch of mathematical science — the theory 
 of probabilities ? There are sciences which, even 
 within the memory of men now living, have be- 
 come exactly quantitative. While Quesnay and 
 Bandeau and Le Trosne and Condillac were found- 
 ing Political Economy in France, and Adam Smith 
 in England, electricity was a vague phenomenon, 
 which was known, indeed, to be capable of be- 
 coming greater or less, but was not measured nor 
 calculated : it is within the last forty or fifty years 
 that a mathematical theory of electricity, founded 
 on exact data, has been established. We now enjoy 
 precise quantitative notions concerning heat, and 
 can measure the temperature of a body to less 
 than j^ part of a degree Centigrade. Compare 
 this precision with that of the earliest makers of 
 thermometers, the Academicians del Cimento, who 
 used to graduate their instruments by placing them 
 in the sun's rays to obtain a point of fixed tem- 
 perature f 
 
 f See ' Principles of Science,' chapter xiii, on ' Tlie Exact Measure- 
 ment of Phenomena,' 3rd Ed., p. 270.
 
 10 The Theory of Political Economy. 
 
 De Morgan excellently saidg, 'As to some mag- 
 nitudes, the clear idea of measurement comes soon : 
 in the case of length, for example. But let us 
 take a more difficult one, and trace the steps by 
 which we acquire and fix the idea : say weight. 
 
 What weight is, we need not know We 
 
 know it as a magnitude before we give it a name : 
 any child can discover the more that there is in 
 a bullet, and the less that there is in a cork of 
 twice its size. Had it not been for the simple 
 contrivance of the balance, which we are well 
 assured (how, it matters not here) enables us to 
 poise equal weights against one another, that is, to 
 detect equality and inequality, and thence to as- 
 certain how many times the greater contains the 
 less, w^e might not to this day have had much 
 clearer ideas on the subject of weight, as a mag- 
 nitude, than we have on those of talent, prudence, 
 or self-denial, looked at in the same light. All who 
 are ever so little of geometers will remember the 
 time when their notions of an angle, as a magni- 
 tude, were as vague as, perhaj)s more so than, 
 those of a moral quality ; and they will also re- 
 member the steps by which this vagueness became 
 clearness and precision.' 
 
 Now there can be no doubt that j)leasure, pain, 
 labour, utility, value, Avealth, money, capital, &c. 
 
 s 'Formal Logic,' p. 175.
 
 Introduction. 11 
 
 are all notions admitting of quantity: nay, the 
 whole of our actions in industry and trade certainly 
 depend upon comparing quantities of advantage or 
 disadvantage. Even the theories of moralists have 
 recognised the quantitative character of the subject. 
 Bentham's ' Introduction to the Principles of Morals 
 and Legislation ' is thoroughly mathematical in the 
 character of the method. He tells us ^^ to estimate 
 the tendency of an action thus : ' Sum up all the 
 values of all the pleasures on the one side, and 
 those of all the pains on the other. The balance, 
 if it be on the side of pleasure, will give the good 
 tendency of the act upon the whole, with respect 
 to the interests of that individual person ; if on the 
 side of pain, the bad tendency of it upon the whole.' 
 The mathematical character of Bentham's treat- 
 ment of moral science is also well exemplified in 
 his remarkable tract entitled *A Table of the 
 Springs of Action,' printed in 1817, as in p. 3, 
 and elsewhere. 
 
 ' But where,' the reader will perhaps ask, ' are 
 your numerical data for estimating pleasures and 
 pains in Political Economy ? ' I answer, that my 
 numerical data are more abundant and precise 
 than those possessed by any other science, but that 
 we have not yet known how to employ them. The 
 very abundance of our data is perplexing. There is 
 
 h Chapter iv, on the ' Value of a lot of Pleasure or Pain, How 
 to be measured,' section v, 5.
 
 12 Tha Theory of Political Econo7ny. 
 
 not a clerk nor book-keeper in the country who is 
 not engaged in recording numerical facts for the 
 economist. The private-account books, the great 
 ledgers of merchants and bankers and public offices, 
 the share lists, price lists, bank returns, monetary 
 intelligence, Custom-house and other Government 
 returns, are all full of the kind of numerical data 
 required to render Economics an exact mathe- 
 matical science. Thousands of folio volumes of 
 statistical, parliamentary, or other publications 
 await the labour of the investigator. It is partly 
 the very extent and complexity of the informa- 
 tion which deters us from its proper use. But it 
 is chiefly a want of method and completeness in 
 this vast mass of information which prevents our 
 employing it in the scientific investigation of the 
 natural laws of Economics. 
 
 I hesitate to say that men will ever have the 
 means of measuring directly the feelings of the 
 human heart. A unit of pleasure or of pain is 
 difficult even to conceive ; but it is the amount of 
 these feelings which is continually prompting us to 
 buying and selling, borrowing and lending, labour- 
 ing and resting, producing and consuming ; and it 
 is from the quantitative ejfects of the feelings that vje 
 must estimate their comjKtrative amounts. We can 
 no more know nor measure gravity in its own 
 nature than we can measure a feeling ; but, just as 
 we measure gravity by its effects in the motion
 
 Introduction. 13 
 
 of a pendulum, so we may estimate the equality 
 or inequality of feelings by the decisions of the 
 human mind. The will is our pendulum, and its 
 oscillations are minutely registered in the price 
 lists of the markets. I know not Avhen we shall 
 have a perfect system of statistics, but the want 
 of it is the only insuperable obstacle in the way 
 of making Economics an exact science. In the 
 absence of complete statistics, the science will not 
 be less mathematical, though it will be immensely 
 less useful than if it were, comparatively speaking, 
 exact. A correct theory is the first step towards 
 improvement, by showing what we need and what 
 we might accomplish. 
 
 Measurement of Feeling and Motives. 
 
 Many readers may, even after reading the pre- 
 ceding remarks, consider it quite impossible to 
 create such a calculus as is here contemplated, 
 because Ave have no means of defining and mea- 
 suring quantities of feeling, like we can measure 
 a mile, or a right angle, or any other physical 
 quantity. I have granted that we can hardly form 
 the conception of a unit of pleasure or pain, so 
 that the numerical expression of quantities of 
 feeling seems to be out of the question. But we 
 only employ units of measurement in other thiugs 
 to facilitate the comparison of quantities; and if 
 we can compare the quantities directly, we do not 
 
 /
 
 14 The Theory of Political Economy. 
 
 need the units. Now the mind of an individual 
 is the balance which makes its own comparisons, 
 and is the final judge of quantities of feeling. 
 As Mr. Bain saj^s^ ' It is only an identical proposi- 
 tion to affirm that the greatest of two pleasures, 
 or what appears such, sways the resulting action ; 
 for it is tliis resulting action that alone deter- 
 mines which is the greater.' 
 
 Pleasures, in short, are, for the time being, as 
 the mind estimates them ; so that we cannot make 
 a choice, or manifest the will in any way, without 
 indicating thereby an excess of pleasure in some 
 direction. It is true that the mind often hesitates 
 and is perplexed in making a choice of great 
 importance : this indicates either varying estimates 
 of the motives, or a feeling of incapacity to grasp 
 the quantities concerned. I should not think of 
 claiming for the mind any accurate power of 
 measuring and adding and subtracting feelings, 
 so as to get an exact balance. We can seldom 
 or never affirm that one pleasure is an exact 
 multiple of another ; but the reader who carefully 
 criticises the following theory will find that it 
 seldom involves the comparison of quantities of 
 feeling differing much in amount. The theory turns 
 upon those critical points where pleasures are 
 nearly, if not quite, equal. I never attempt to 
 estimate the whole pleasure gained by purchasing 
 
 i ' The Emotions and the Will,' 1st Ed., p. 447.
 
 Introduction. 15 
 
 a commodity; the theory merely expresses that, 
 when a man has purchased enough, he would de- 
 rive equal pleasure from the possession of a small 
 quantity more as he Avould from the money price 
 of it. Similarly, the whole amount of pleasure that 
 a man gains by a day's labour hardly enters into 
 the question ; it is when a man is doubtful whether 
 to increase his hours of labour or not, that we 
 discover an equality between the pain of that ex- 
 tension and the pleasure of the increase of pos- 
 sessions derived from it. 
 
 The reader will find, again, that there is never, 
 in any single instance, an attempt made to com- 
 pare the amount of feeling in one mind with that 
 in another. I see no means by which such com- 
 parison can be accomplished. The susceptibility 
 of one mind may, for what we know, be a thousand 
 times greater than that of another. But, provided 
 that the susceptibility was different in a like ratio 
 in all directions, we should never be able to dis- 
 cover the difference. Every mind is thus in- 
 scrutable to every other mind, and no common 
 denominator of feeling seems to be possible. But 
 even if we could compare the feelings of different 
 minds, we should not need to do so ; for one mind 
 only affects another indirectly. Every event in the 
 outward world is represented in the mind by a 
 corresponding motive, and it is by the balance of 
 these that the will is swayed. But the motive in
 
 16 The Theory of Political Economy. 
 
 one mind is weighed only against other motives 
 in the same mind, never against the motives in 
 other minds. Each person is to other persons 
 a portion of the outward world — the non-ego as 
 the metaphysicians call it. Thus motives in the 
 mind of A may give rise to phenomena which 
 may he represented by motives in the mind of 
 B ; but between A and B there is a gulf Hence 
 the weighing of motives must always be confined 
 to the bosom of the individual. 
 
 I must here point out that, though the theory 
 presumes to investigate the condition of a mind, 
 and bases upon this investigation the whole of 
 Economics, practically it is an aggregate of indi- 
 viduals which will be treated. The general forms 
 of the laws of Economics are the same in the case 
 of individuals and nations ; and, in reality, it is a 
 law operating in the case of multitudes of indi- 
 viduals which gives rise to the aggregate repre- 
 sented in the transactions of a nation. Practically, 
 however, it is quite impossible to detect the opera- 
 tion of general laws of this kind in the actions of 
 one or a few individuals. The motives and condi- 
 tions are so numerous and complicated, that -the 
 resulting actions have the appearance of caprice, 
 and are beyond the analytic powers of science. 
 With every increase in the price of such a com- 
 modity as sugar, we ought, theoretically speaking, 
 to find every person reducing his consumption by
 
 Introduction. 17 
 
 a small amount, and according to some regular 
 law. In realit}^ many persons would make no 
 change at all; a few, probably, would go to the 
 extent of dispensing with tlie use of sugar alto- 
 gether so long as its cost continued to be excessive. 
 It would be by examining the average consump- 
 tion of sugar in a large population that we might 
 detect a continuous variation, connected with the 
 variation of price by a constant law. It would not, 
 of necessit}'', happen that the law would be exactly 
 the same hi the case of aggregates and individuals, 
 unless all those individuals were of the same 
 character and position as regards wealth and 
 habits ; but there would be a more or less regular 
 law to w^hich the same kind of forniidtie would 
 apply. The use of an average, or, what is the 
 same, an aggregate result, depends upon the high 
 probability that accidental and disturbing causes 
 will operate, in the long run, as often in one direc- 
 tion as the other, so as to neutralise each other. 
 Provided that we have a sufficient number of 
 independent cases, we may then detect the effect 
 of any tendency, however slight. Accordingly, ques- 
 tions which appear, and perhaps are, quite indeter- 
 minate as regards individuals, may be capable of 
 exact investigation and solution in regard to great 
 masses and wide averages ^. 
 
 ^ Concerning the meaning and employment of Averages, see 
 ' Principles of Science,' cbaptcr xvi, on ' The Method of Means.' 
 
 C
 
 18 Tlie Theory of Political Economy. 
 
 Logical Method of Economics. 
 
 The logical method of Economics as a branch 
 of the social sciences is a subject on which much 
 might be written, and on which very diverse 
 opinions are held at the present day (1879). In 
 this place I can only make a few brief remarks. 
 I think that John Stuart Mill is substantially 
 correct in considering our science to be a case of 
 what he calls i the Physical or Concrete Deductive 
 Method ; he considers that we may start from 
 some obvious psychological law, as for instance, 
 that a greater gain is preferred to a smaller one, 
 and we may then reason downwards, and predict 
 the phenomena which will be produced in society 
 by such a law. The causes in action in any com- 
 munity are, indeed, so complicated that we shall 
 seldom be able to discover the undisturbed effects 
 of any one law, but, so far as we can analyse the 
 statistical phenomena observed, we obtain a verifi- 
 cation of our reasoning. This view of the matter 
 is almost identical with that adopted by the late 
 Professor Cairnes in his Lectures on ' The Character 
 and Logical Method of Political Economy ni.' 
 
 The principal objection to be urged against this 
 treatment of the subject, is that Mill has described 
 the Concrete Deductive Method as if it were one 
 
 1 ' System of Logic,' book vi. chap. ix. section 3. 
 m Second Edition (Macmillan), 1875.
 
 Introduction. 19 
 
 of many inductive methods. In my Elementary 
 Lessons in Logic (p. 258), I proposed to call the 
 method the Complete Method, as implying that it 
 combines observation, deduction, and induction in 
 the most complete and perfect way. But I sub- 
 sequently arrived at the conclusion that this so- 
 called Deductive Method is no special method at 
 all, but simply induction itself in its essential 
 form. As I have fully explained^, Induction is 
 an inverse operation, the inverse of Deduction, and 
 can only be performed by the use of deduction. 
 Possessing certain facts of observation, we frame 
 an hypothesis as to the laws governing those 
 facts ; we reason from the hypothesis deductively 
 to the results to be expected ; and we then ex- 
 amine these results in connection with the facts in 
 question; coincidence confirms the whole reason- 
 ing ; conflict obliges us either to seek for disturbing 
 causes, or else to abandon our hypothesis. In this 
 procedure there is nothing peculiar ; when properly 
 understood it is found to be the method of all the 
 inductive sciences. 
 
 The science of Economics, however, is in some 
 degree peculiar, owing to the fact, pointed out by 
 J. S. Mill and Cairnes, that its ultimate laws are 
 known to us immediately by intuition, or, at any 
 rate they are furnished to us ready made by other 
 mental or physical sciences. That every person 
 
 " * Principles of Science,' chapters vii, ix, xii, etc. 
 C 2
 
 20 The Theory of Political Economy. 
 
 will choose the greater apparent good ; that human 
 wants are more or less quickly satiated ; that 
 prolonged labour becomes more and more painful, 
 are a few of the simple inductions on which we 
 can proceed to reason deductively with great con- 
 fidence. From these axioms we can deduce the 
 laws of supply and demand, the laws of that 
 difficult conception, value, and all the intricate 
 results of commerce, so far as data are available. 
 The final agreement of our inferences with a 
 posteriori observations ratifies our method. But 
 unfortunately this verification is often the least 
 satisfactory part of the process, because, as J. S. 
 Mill has fully explained, the circumstances of a 
 nation are infinitely complicated, and we seldom 
 get two or more instances which are comparable. 
 To fulfil the conditions of inductive inquiry, we 
 ought to be able to observe the effects of a cause 
 coming singly into action, while all other causes 
 remain unaltered. Entirely to prove the good 
 effects of Free Trade in England, for example, we 
 ought to have the nation unaltered in every cir- 
 cumstance except the abolition of burdens and 
 restrictions on trade «. But it is obvious that while 
 Free Trade was being introduced into England, 
 many other causes of prosperity were also coming 
 into action — the progress of invention, the con- 
 struction of railways, the profuse consumption of 
 
 " ' Piiiicijjles of Science/ chapter xix, on ' Expeiinieut.'
 
 Introduction. 
 
 21 
 
 coal, the extension of the colonies, etc., etc. 
 Although, then, the heneficent results of Free 
 Trade are great and unquestionable, they could 
 liardly be proved to exist a i^steriori ; they are to 
 be believed because deductive reasoning from pre- 
 mises of almost certain truth, leads us confidently 
 to expect such results, and there is nothing in 
 experience which in the least conflicts Avith our , 
 expectations. In spite of occasional revulsions, due ; 
 to periodical fluctuations depending on physical 
 causes, the immense prosperity of the country since 
 the adoption of Free Trade, confirms our antici- 
 pations as far as, under complex circumstances, 
 facts are capable of doing so. It will thus be seen 
 that Political Economy tends to be more deductive 
 than many of the physical sciences, in which closely 
 approximate verification is often possible ; but, even 
 so far as the science is inductive, it involves the 
 use of deductive reasoning, as already explained. 
 
 Within the last year or two, much discussion has 
 been raised concerning the Philosophical Method 
 of Political Economy, by Mr. T. E. Cliffe Leslie's 
 interesting Essay on that subject P, as also by the 
 recent address of Dr.' Ingram at the Dublin Meeting 
 of the British Association*!. I quite concur with 
 these able and eminent economists so far as to 
 
 < 
 
 P ' Hermathena,' No. iv, Dublin, 1876, p. 1. 
 1 ' Statistical Journal,' January, 1879, vol. xli. p. 602. Also reprint 
 by Longmans, 1878.
 
 22 The Theory of Political Economy. 
 
 allow that historical investigation is of great import- 
 ance in Social Science. But, instead of converting 
 our present science of economics into an historical 
 science, utterly destroying it in the process, I would 
 perfect and develope what we already possess, and 
 at the same time erect a new branch of social 
 science on an historical foundation. This new 
 branch of science, on which many learned men, 
 such as Richard Jones, de Laveleye, Lavergne, 
 Cliffe Leslie, Sir Henry Maine, Thorold Rogers, have 
 already laboured, is doubtless a portion of what 
 Herbert Spencer calls Sociology, the Science of the 
 Evolution of Social Relations. Political Economy 
 is in a chaotic state at present, because there is 
 need of subdividing a too extensive sphere of 
 knowledge. Quesnay, Sir James Steuart, Bandeau, 
 Le Trosne, and Condillac first differentiated Econo- 
 mics sufficiently to lead it to be regarded as a 
 distinct science; it has since been loaded with 
 great accretions due to the progress of investigation. 
 It is only by subdivision, by recognising a branch 
 of Economic Sociology, together possibly with two 
 or three other branches of statistical, j ural, or social 
 science, that we can rescue our science from its 
 confused state. I have already endeavoured to 
 shew the need of this step in a lecture delivered 
 at the University College, in October, 1876r, and 
 
 r ' Fortnightly Review,' December 1876 ; ' The Future of Political 
 Economy.'
 
 Introduction. 23 
 
 I shall perhaps have a future opportunity of en- 
 larging more upon the subject. 
 
 To return, however, to the topic of the present 
 work, the theory here given may be described as 
 the mecha7iics of utility and self-interest. Oversights 
 may have been committed in tracing out its de- 
 tails, but in its main features this theory must be 
 the true one. Its method is as sure and demon- 
 strative as that of kinematics or statics, nay, 
 almost as self-evident as are the elements of Euclid, 
 when the real meaning of the formulae is fully 
 seized. 
 
 I do not hesitate to say, too, that Economics 
 might be gradually erected into an exact science, 
 if only commercial statistics were far more com- 
 plete and accurate than they are at present, so 
 that the formulae could be endowed with exact 
 meaning by the aid of numerical data. These data 
 Avould consist chiefly in accurate accounts of the 
 quantities of goods possessed and consumed by the 
 community, and the prices at which they are ex- 
 changed. There is no reason whatever why we 
 should not have those statistics, except the cost 
 and trouble of collecting them, and the unwilling- 
 ness of persons to afford information. The quanti- 
 ties themselves to be measured and registered are 
 most concrete and precise. In a few cases we 
 already have information approximating to com- 
 pleteness, as when a commodity like tea, sugar.
 
 24 The Theory of Political Economy, 
 
 coffee, or tobacco is wholly imported. But when 
 articles are untaxed, and partly produced within 
 the countr}'-, we have yet the vaguest notions of 
 the quantities consumed. Some slight success is 
 now, at last, attending the ejfforts to gather agri- 
 cultural statistics; and the great need felt by 
 men engaged in the cotton and other trades to 
 obtain accurate accounts of stocks, imports, and 
 consumption, will probably lead to the publication 
 of far more complete information than we have 
 hitherto enjoyed. 
 
 The deductive science of Economics must be 
 verified and rendered useful by the purely empi- 
 rical science of Statistics. Theory must be invested 
 with the reality and life of fact. But the difficul- 
 ties of this union are immensely great, and I 
 appreciate them quite as much as does Cairnes 
 in his admirable lectures ' On the Character and 
 Logical Method of Political Economy.' I make 
 hardly any attempt to employ statistics in this 
 work, and thus I do not pretend to any numerical 
 precision. But, before we attempt any investiga- 
 tion of facts, we must have correct theoretical 
 notions ; and of what are here presented, I would 
 say, in the words of Hume, in his 'Essay on Com- 
 merce,' ' If false, let them be rejected : but no one 
 has a right to entertain a prejudice against them 
 merely because they are out of the common road.'
 
 Introduction. 25 
 
 Relation of Economics to Ethics. 
 
 I Avish to say a, few words, in this place, upon 
 the rchition of Economics to Moral Science. The 
 theory Avhich follows is entirely based on a calculus 
 of pleasure and pain ; and the object of Economics 
 is to maximise happiness by purchasing pleasure, 
 as it were, at the loAvest cost of pain. The language 
 emploj'ed may be open to misapprehension, and it 
 may seem as if pleasures and pains of a gross kind 
 were treated as the all-sufficient motives to guide 
 the mind of man. I have no hesitation in accepting 
 the Utilitarian theory of morals which does uphold 
 the effect upon the happiness of mankind as the 
 criterion of what is right and wrong. But I have 
 never felt that there is anything in that theory to 
 prevent our putting the widest and highest inter- 
 pretation upon the terms used. 
 
 Jeremy Bentham put forAvard the Utilitarian 
 theory in the most uncompromising manner. Ac- 
 cording to him, whatever is of interest or import- 
 ance to us must be the cause of pleasure or of 
 pain ; and Avhen the terms are used with a suffi- 
 ciently wide meaning, pleasure and pain include 
 all the forces Avhicli drive us to action. They are 
 explicitly or implicitly the matter, of all our cal- 
 culations, and form the ultimate quantities to be 
 treated in all the moral sciences. The words of 
 Bentham on this subject may require some ex- 
 planation and qualification, but they are too grand
 
 26 The llieory of Political Economy. 
 
 and too full of truth to be omitted. ' Nature/ he 
 says s, ' has placed mankind under the governance 
 of two sovereign masters — pai^i and j)^easure. It 
 is for them alone to point out what we ought to 
 do, as well as to determine what we shall do. On 
 the one hand the standard of right and wrong, 
 on the other the chain of causes and effects, are 
 fastened to their throne. Thej govern us in all 
 we do, in all we say, in all we think : every effort 
 we can make to throw off our subjection will serve 
 but to demonstrate and confirm it. In Avords a 
 man may pretend to abjure their empire ; but, in 
 reality, he will remain subject to it all the while. 
 The jorinciiole of utility recognises this subjection, 
 and assumes it for the foundation of that system, 
 the object of which is to rear the fabric of felicity 
 by the hands of reason and of law. Systems 
 which attempt to question it, deal in sounds 
 instead of sense, in caprice instead of reason, in 
 darkness instead of light.' 
 
 In connection with this j)assage we may take 
 that of Paley, who says, with his usual clear 
 brevity*, 'I hold that pleasures differ in nothing 
 but in continuance and intensity.' 
 
 The acceptance or non-acceptance of the basis 
 of the Utilitarian doctrine depends, in my mind, 
 
 8 ' An Introduction to the Principles of Morals and Legislation,' 
 by Jeremy Bentham. Edition of 1823, vol. i. p. 1. 
 
 t ' Principles of Moral and Political Philosophy,' book i. chap. 6.
 
 ItitrodactLO)i. 27 
 
 on the exact interpretation of the language used. 
 As it seems to me, the feelings of which a man 
 is capable are of various grades. He is always 
 subject to mere physical pleasure or pain, neces- 
 sarily arising from his bodily wants and suscepti- 
 bilities. He is capable also of mental and moral 
 feelings of several degrees of elevation. A higher 
 motive may rightly overbalance all considerations 
 belonging even to the next lower range of feelings ; 
 but so long as the higher motive does not inter- 
 vene, it is surely both desirable and right that 
 the lower motives should be balanced against each 
 other. Starting with the lowest stage — it is a 
 man's duty, as it is his natural inclination, to 
 earn sufficient food and whatever else may best 
 satisfy his proper and moderate desires. If the 
 claims of a family or of friends fall upon him, it 
 may become desirable that he should deny his 
 own desires and even his physical needs their 
 full customary gratification. But the claims of a 
 family are only a step to a higher grade of duties 
 
 The safety of a nation, the welfare of great 
 populations, may happen to depend upon his exer- 
 tions, if he be a soldier or a statesman : claims 
 of a very strong kind may now be overbalanced 
 by claims of a still stronger kind. Nor should I 
 venture to say that, at any point, we have reached 
 the highest rank — the supreme motives which 
 should guide the mind. The statesman may
 
 28 Tlie Theory of Political Ecijno]nij. 
 
 discover a conflict between motives; a measure 
 may promise, as it would seem, the greatest good 
 to great numbers, and yet there may be motives of 
 uprightness and honour that may liinder his pro- 
 moting the measure. How such difficult questions 
 may be rightly determined it is not my purpose 
 to inquire here. 
 
 The utilitarian theory holds, that all forces 
 influencing the mind of man are pleasures and 
 pains; and Paley went so far as to say, that 
 all pleasures and pains are of one kind only. 
 Mr. Bain has carried out this view to its complete 
 extent, saying ^S ' No amount of complication is 
 ever able to disguise the general fact, that our 
 voluntary activity is moved by only two great 
 classes of stimulants ; either a pleasure or a pain, 
 present or remote, must lurk in every situation 
 that drives us into action.' The question certainly 
 appears to turn upon the language used. Call any 
 motive which attracts us to a certain course of 
 conduct, pleasure ; and call any motive which 
 deters us from that conduct, jmin ; and it becomes 
 impossible to deny that all actions are governed 
 by pleasure and pain. But it then becomes indis- 
 pensable to admit that a single higher pleasure 
 will sometimes neutralise a vast extent and con- 
 tinuance of lower pains. It seems hardly possible 
 to admit Paley's statement, except with an inter- 
 
 " ' The Emotions and the Will,' 1st Ed. p. 460.
 
 Introduction. 29 
 
 pretation that would probably reverse his intended 
 meaning. ^lotives and feelings are certainly of the 
 same kind to the extent that we are able to weigh 
 them against each other ; but they are, neverthe- 
 less, almost incomparable in power and authority. 
 
 My present purpose is accomplished in pointing- 
 out this hierarchy of feeling, and assigning a proper 
 place to the pleasures and pains with which the 
 Economist deals. It is the lowest rank of feelings 
 which we here treat. The calculus of utility aims 
 at supplying the ordinary wants of man at the 
 least cost of labour. Each labourer, in the absence 
 of other motives, is supposed to devote his energy 
 to the accumulation of wealth. A higher calculus 
 of moral right and wrong would be needed to show 
 how he may best employ that wealth for the good 
 of others as well as himself. But when that higher 
 calculus gives no prohibition, we need the lower 
 calculus to gain us the utmost good in matters of 
 moral indifference. There is no rule of morals to 
 forbid our making two blades of grass grow instead 
 of one, if, by the wise expenditure of labour, we 
 can do so. And we may certainly sa}', with Francis 
 Bacon, ' while philosophers are disputing whether 
 virtue or pleasure be the proper aim of life, do 
 you provide yourself with the instruments of 
 either.'
 
 CHAPTER II. 
 
 THEORY OF PLEASURE AND PAIN. 
 
 Pleasure and Pain as Quantities. 
 
 Proceeding to consider how pleasure and pain 
 can be estimated as magnitudes, we must un- 
 doubtedly accept what Bentham has laid down 
 upon this subject. 'To a person,' he says'\ 'con- 
 sidered hy himself, the value of a pleasure or pain, 
 considered hy itself, Avill be greater or less according 
 to the four following circumstances : — 
 
 (1) Its intensity. 
 
 (2) Its duration. 
 
 (3) Its certainty or uncertainty. 
 
 (4) Its propinquity or remoteness. 
 
 ^ ' An Introduction to the Principles of Morals and Legislation, 
 2nd Ed., 1823, vol. i. p. 49. The earliest writer, w\\o, so far as I 
 know, has treated Pleasure and Pain in a definitely quantitative 
 manner, is Francis Hutcheson, in his 'Essay on the Nature and 
 Conduct of the Passions and Affections/ 1728, pp. 34-43, 126, etc.
 
 Theory of Pleasure and Pain. 31 
 
 These are the circumstances which are to be 
 considered in estimating a pleasure or a pain 
 considered each of them by itself.' 
 
 Bentham^ goes on to consider three other cir- 
 cumstances which relate to the ultimate and 
 complete result of any act or feeling ; these 
 ai'e — 
 
 (5) Fecundity, or the chance a feeling has of 
 
 being followed by feelings of the same 
 kind ; that is, pleasures, if it be a pleasure ; 
 pains, if it be a pain. 
 
 (6) Purity, or the chance it has of not being 
 
 followed by feelings of an opposite kind. 
 And 
 
 (7) Extent, or the number of persons to whom 
 
 it extends, and who are affected by it. 
 These three last circumstances are of high im- 
 portance as regards the theory of morals ; but 
 they will not enter into the more simple and 
 restricted problem which we attempt to solve in 
 Economics. 
 
 A feeling, Avhether of pleasure or of pain, must 
 be regarded as having two dimensions, or modes 
 of varying in regard to quantity. Every feeling 
 must last some time, and it may last a longer 
 or shorter time ; while it lasts, it may be more 
 or less acute and intense. If in two cases the 
 duration of feeling is the same, that case will 
 
 b Introduction, p. 50.
 
 32 The Theory of Political Economy. 
 
 produce the greater quantity which is the more 
 intense ; or we may say that, with the same dura- 
 tion, the quantity will be proportional to the 
 intensity. On the other hand, if the intensity of 
 a feeling were to remain constant, the quantity of 
 feelino: would increase with its duration. Two 
 days of the same degree of happiness are to be 
 twice as much desired as one day ; two days of 
 suffering are to be twice as much feared. If the 
 intensity ever continued fixed, the whole quantity 
 would be found by multiplyiug the number of 
 units of intensity into the number of units of 
 duration. Pleasure and pain, then, are quantities 
 possessing two dimensions, just as superficies 
 possesses the two dimensions of length and 
 breadth. 
 
 In almost every case, however, the intensity of 
 feeling will change from moment to moment. 
 Incessant variation characterises our states of 
 mind, and this is the source of the main difficul- 
 ties of the subject. Nevertheless, if these varia- 
 tions can be traced out at all, or any approach to 
 method and law can be detected, it will be possible 
 to form a conception of the resulting quantity of 
 feeling. We may ijnagine that the intensity changes 
 at the end of every minute, but remains constant in 
 tlie intervals. The quantity during each minute may 
 l)e represented, as in Fig. I, by a rectangle whose 
 base is supposed to correspond to the duration of
 
 Theory of Pleasure and Pain. 
 
 33 
 
 a minute, and whose height is proportional to the 
 intensity of the feeling during the minute in 
 
 Bg.L 
 
 question. Along the line ox we measure time, and 
 along parallels to the perpendicular line oij we 
 measure intensity. Each of the rectangles between 
 pm and qn represents the feeling of one minute. 
 The aggregate quantity of feeling generated during 
 tlie time mn will then be represented by the 
 aggregate area of the rectangles between pm and 
 qn. In this case the intensity of the feeling is 
 supposed to be gradually declining. 
 
 But it is an artificial assumption that the in- 
 tensity would vary by sudden steps and at regular 
 intervals. The error thus introduced will not be 
 great if the intervals of time are very short, and 
 will be less the shorter the intervals are made. 
 To avoid all error, we must imagine the intervals 
 of time to be infinitely short ; that is, we must 
 treat the intensity as varying continuously. Thus 
 tlie proper representation of the variation of feeling 
 
 D
 
 34 
 
 The Theo7'y of Political Economy. 
 
 is found in a curve of more or less complex 
 character. In Fig. II the height of each point of 
 
 Fiq.E 
 
 the curve pq, above the horizontal line ox, indicates 
 the intensity of feeling in a moment of time ; and 
 the whole quantity of feeling generated in the time 
 mn is measured by the area bounded by the lines 
 jpm, qn, mn, and pq. The feeling belonging to any 
 other time, ma, will be measured by the space 
 mabp cut off by the perpendicular line ah. 
 
 Pain the Negative of Pleasure. 
 
 It will be readily conceded that pain is the 
 opposite of pleasure ; so that to decrease pain is 
 to increase pleasure ; to add pain is to decrease 
 pleasure. Thus we may treat pleasure and pain 
 as positive and negative quantities are treated in 
 algebra. The algebraic sum of a series of pleasures 
 and pains will be obtained by adding the pleasures 
 together and the pains together, and then striking
 
 Theory of Pleasure and Pain. 35 
 
 the balance by subtracting the smaller amount 
 from the greater. Our object will always be to 
 maximise the resulting sum in the direction of 
 pleasure, which we may fairly call the positive 
 direction. This object we shall accomplish by ac- 
 cepting everything, and undertaking every action 
 of which the resulting pleasure exceeds the pain 
 which is undergone ; we must avoid every object 
 or action which leaves a balance in the other 
 direction. 
 
 The most important parts of the theory will turn 
 upon the exact equality, without regard to sign, of 
 the pleasure derived from the possession of an 
 object, and the pain encountered in its acquisition. 
 I am glad, therefore, to quote the following pas- 
 sage from Mr. Bahi's treatise on 'The Emotions 
 and the Will c,' in which he exactly expresses the 
 opposition of pleasure and pain : — ' When pain is 
 followed by pleasure, there is a tendency in the one, 
 more or less, to neutralise the other. When the 
 pleasure exactly assuages the pain, we say that 
 tlie two are equivalent, or equal in amount, although 
 of opposite nature, like hot and cold, positive and 
 negative ; and when two different kinds of pleasure 
 have the power of satiating the same amount of 
 pain, there is fair ground for pronouncing them 
 of equal emotional power. Just as acids are pro- 
 nounced equivalent when in amount sufficient to 
 
 « First Edition, p. 30. 
 D 2
 
 36 The Theory of Political Economy. 
 
 neutralise the same portion of alkali, and as heat 
 is estimated bj the quantity of snow melted by it, 
 so pleasures are fairly compared as to their total 
 efficacy on the mind, by the amount of pain that 
 they are capable of submerging. In this sense there 
 may be an effective estimate of degree.' 
 
 Anticipated Feeling. 
 
 Bentham has stated ^\ that one of the main ele- 
 ments in estimating the force of a pleasure or pain 
 is its propinquity or remoteness. It is certain that 
 a very large part of what we experience in life 
 depends not on the actual circumstances of the 
 moment so much as on the anticipation of future 
 events. As Mr. Bain says ^, ' The foretaste of 
 i:)leasure is pleasure begun : every actual delight 
 casts before it a corresponding ideal.' Every one 
 must have felt that the enjoyment actually expe- 
 rienced at any moment is but limited in amount, 
 and usually fails to answer to the anticipations 
 which have been formed. 'Man never is but 
 always to be blest ' is a correct description of our 
 ordinary state of mind ; and there is little doubt 
 that, in minds of much intelligence and foresight, 
 the greatest force of feeling and motive arises from 
 the anticipation of a long-continued future. 
 
 ^ See above, p. 30. 
 
 « ' The Emotions and the AVill/ First Edition, p. 74.
 
 Theory of Pleasure and Pain. 37 
 
 Now, between the actual ainoiiiit of feeling antici- 
 pated and that which is felt there must be some 
 natural relation, very varial)lc no doubt according 
 to circumstances, the intellectual standing of the 
 race, or the character of the individual ; and yet 
 subject to some general laws of variation. The 
 intensity of present anticipated feeling must, to 
 use a mathematical expression, be some fmiciion 
 of the future actual feeling and of the intervening 
 time, and it must increase as we approach the 
 moment of realisation. The change, again, must 
 be less rapid the further we are from the moment, 
 and more rapid as we come nearer to it. An event 
 which is to happen a year hence affects us on the 
 average about as much one day as another; but 
 an event of importance, which is to take place three 
 days hence, will probably affect us on each of the 
 intervening days more acutely than the last. 
 
 This po\^'er of anticipation must have a large 
 influence in Economics; for upon it is based all 
 accumulation of stocks of commodity to be con- 
 sumed at a future time. That class or race of men 
 who have the most foresight will work most for 
 the future. The untutored savage, like the child, 
 is wholly occupied with the pleasures and the 
 troubles of the moment ; the morrow is dimly felt ; 
 the limit of his horizon is but a few days off. The 
 wants of a future 3^ear, or of a lifetime, are wholly 
 unforeseen. But, in a state of civilisation, a vague
 
 38 The Theory of Political Economy. 
 
 though powerful feeling of the future is the main 
 incentive to industry and saving. The cares of the 
 moment are but ripples on the tide of achievement 
 and hope. We may safely call that man happy 
 who, however lowly his position and limited his 
 possessions, can always hope for more than he has, 
 and can feel that every moment of exertion tends 
 to realise his aspirations. He, on the contrary, who 
 seizes the enjoyment of the passing moment with- 
 out regard to coming times, must discover sooner 
 or later, that his stock of pleasure is on the wane, 
 and that even hope begins to fail. 
 
 Uncertainty of Future Events. 
 
 In admitting the force of anticipated feeling, we 
 are compelled to take account of the uncertainty 
 of all future events. We ought never to estimate 
 the value of that which may or may not happen 
 as if it would certainly happen. When it is as 
 likely as not that I shall receive £100, the chance 
 is worth but £50, because if, for a great many times 
 in succession, I purchase the chance at this rate, 
 I shall almost certainly neither lose nor gain. The 
 test of correct estimation of probabilities is that 
 the calculations agree with fact on the average. 
 If we apply this rule to all future interests, we 
 must reduce our estimate of any feeling in the ratio 
 of the numbers expressing the probability of its 
 occurrence. If the probability is only one in ten
 
 Theory of Pleasure and Pain, 39 
 
 that I shall have a certain day of pleasure, I ought 
 to anticipate the pleasure with one-tenth of the 
 force which would belong to it if certain. In select- 
 ing a course of action which depends on uncertain 
 events, as, in fact, does everything in life, I should 
 multiply the quantity of feeling attaching to every 
 future event by the fraction denoting its proba- 
 bility. A great casualty, which is very unlikely 
 to happen, may not be so important as a slight 
 casualty which is nearly sure to happen. Almost 
 unconsciously we make calculations of this kind 
 more or less accurately in all the ordinary affairs 
 of life ; and in systems of life, fire, marine or other 
 insurance, we carry out the calculations to great 
 perfection. In all industry directed to future pur- 
 poses, we must take similar account of our want 
 of knowledge of what is to be.
 
 CHAPTER III. 
 
 T H E 11 Y OF UTILITY 
 
 Definition of Terms. 
 
 Pleasure and pain are undoubtedly the ultimate 
 objects of the Calculus of Economics. To satisfy 
 our wants to the utmost with the least effort — to 
 procure the greatest amount of what is desirable 
 at the expense of the least that is undesirable 
 - — in other words, to maximise pleasure, is the 
 problem of Economics. But it is convenient to 
 transfer our attention as soon as possible to the 
 physical objects or actions which are the source 
 to us of pleasures and pains. A very large part 
 of the labour of any community is spent upon the 
 production of the ordinary necessaries and conve- 
 niences of life, such as food, clothing, buildings, 
 utensils, furniture, ornaments, &c. ; and the aggre- 
 gate of these things, therefore, is the immediate 
 object of our attention.
 
 Theonj of Utility. 41 
 
 It is desirable to introduce at once, and to define, 
 some terms which facilitate the expression of the 
 Principles of Economics. By a commodity we shall ^ 
 understand any object, substance, action or service, 
 which can afford pleasure or ward off pain. The 
 name >vas originally abstract, and denoted the 
 quality of anything by which it was capable of 
 serving- man. Having acquired, by a common 
 process of confusion, a concrete signification, it 
 will be well to retain the word entirely for that 
 signification, and employ the term utility to denote ^J 
 the abstract quality whereby an object serves our 
 purposes, and becomes entitled to rank as a com- 
 modity. Whatever can i)roduce pleasure or pre- 
 vent pain may possess utility. J.-B. Say has 
 correctl}^ and briefly defined utility as ' la faculte 
 qu'ont les choses de pouvoir servir a I'homme, de 
 quelque maniere que ce soit.' The food which 
 prevents the pangs of hunger, the clothes which 
 fend off the cold of winter, possess incontestable 
 utility; but we must beware of restricting the 
 meaning of the word by any moral considerations. 
 An3'thing which an individual is found to desire 
 and to labour for must be assumed to possess for 
 him utility. In the science of Economics we treat 
 men not as they ought to l)e, but as they 
 are. Bentham, in establishing the foundations of 
 Moral Science in his great ' Introduction to the 
 Principles of Morals and Legislation' (p. 3), thus
 
 42 The Theory of Political Economy. 
 
 comprehensively defines the term in question : — 
 * By utility is meant that property in any object, 
 whereby it tends to produce benefit, advantage, 
 pleasure, good, or happiness (all this, in the present 
 case, comes to the same thing), . or (what comes 
 again to the same thing) to prevent the happening 
 of mischief, pain, evil, or unhappiness to the party 
 whose interest is considered/ 
 
 This perfectly expresses the meaning of the word 
 in Economics, provided that the will or inclination 
 of the person immediately concerned is taken as 
 the sole criterion, for the time, of what is or is not 
 useful. 
 
 The Laivs of Human Want. 
 
 Economics must be founded upon a full and 
 accurate investigation of the conditions of utility; 
 and, to understand this element, we must neces- 
 sarily examine the wants and desires of man. We, 
 first of all, need a theory of the consumption of 
 wealth. J. S. Mill, indeed, has given an opinion 
 inconsistent with this. ' Political Economy,' he 
 saysf, 'has nothing to do with the consumption 
 of wealth, further than as the consideration of it 
 is inseparable from that of production, or from 
 that of distribution. We know not of any laws 
 of the consumption of wealth, as the subject of a 
 
 f ' Essays on some unsettled Questions of Political Economy,' 
 p. 132.
 
 Theory of Utility. 43 
 
 distinct science; they can be no other than the 
 laws of human enjoyment.' 
 
 But it is surely obvious that Economics does 
 rest upon the laws of human enjoyment ; and that, 
 if those laws are developed by no other science, 
 they must be developed by economists. We labour 
 to produce with the sole object of consuming, and 
 the kinds and amounts of goods produced must be 
 determined with regard to what we want to con- 
 sume. Every manufacturer knows and feels hoAv 
 closely he must anticipate the tastes and needs 
 of his customers : his whole success depends upon 
 it; and, in like manner, the theory of Economics 
 must begin with a correct theory of consumption. 
 Many economists have had a clear perception of 
 this truth. Lord Lauderdale distinctly states &, 
 that ' the great and important step tow^ards ascer- 
 taining the causes of the direction wdiich industry 
 takes in nations .... seems to be the discovery of 
 what dictates the proportion of demand for the 
 various articles which are produced.' Senior, in his 
 admirable treatise, has also recognised this truth, 
 and pointed out what he calls the Laiu of Variety 
 in human requirements. The necessaries of life 
 are so few^ and simple, that a man is soon satisfied 
 in regard to these, and desires to extend his range 
 of enjoyment. His first object is to vary his food ; 
 
 e ' Inquiry into the Nature and Origin of Public AVealth,' Second 
 Edition, 1819, p. 306.
 
 44 The Theory of Political Economy. 
 
 but there soon arises the desire of variety and 
 elegance in dress ; and to this succeeds the desire 
 to build, to ornament, and to furnish — tastes 
 which, where they exist, are absolutely insatiable, 
 and seem to increase with every improvement in 
 civilisation ii. 
 
 Many French economists also have observed that 
 human wants are the ultimate subject-matter of 
 Economics ; Bastiat, for instance, in his ' Harmonies 
 of Political Economy,' says i, ' Wants, Efforts, Satis- 
 faction — this is the circle of Political Economy.' 
 
 In still later years, Courcelle-Seneuil actually 
 commenced his treatise with a definition of tvant 
 — 'Le besoin economique est un desir qui a pour 
 but la possession et la jouissance d'un objet 
 materiel i\' And I conceive that he has given the 
 best possible statement of the problem of Econo- 
 mics when he expresses its object as ' a satisfaire 
 nos besoins avec la moindre somme de travail 
 possible 1.' 
 
 Professor Hearn also begins his excellent treatise, 
 entitled 'Plutology, or the Theory of Efforts to 
 supply Human Wants,' with a chapter in Avhich he 
 
 '' 'Encyclopaedia Metropolitana,' art. Political Economy, p. 133. 
 Fifth Edition of Eepriiit, p. 11. 
 
 i ' Harmonies of Political Economy,' translated by P. J. Stirling, 
 1860, p. 65. 
 
 ^ 'Traits Th^orique et Pratique d'Economie Politique,' par J. 
 G. Courcelle-Seneuil, 2mc ed., Parip, 1867, torn. i. p. 25. 
 
 1 Jh. p. 33.
 
 Theory of Utility. 45 
 
 considers the nature of the wants impelling man to 
 exertion. 
 
 The writer, however, who seems to me to have 
 reached the deepest comprehension of the founda- 
 tions of Economics, is T. E. Banfield. His course 
 of Lectures delivered in the University of Cam- 
 bridge in 1844, and published under the title of 
 'The Organization of Labour,' is highly interest- 
 ing, though not always correct. In the following 
 passage "^ he profoundly points out that the 
 scientific basis of Economics is in a theory of con- 
 sumption : I need make no excuse for quoting this 
 passage at full length. 
 
 'The lower wants man experiences in common 
 with brutes. The cravings of hunger and thirst, 
 the effects of heat and cold, of drought and damp, 
 he feels with more acuteness than the rest of the 
 animal world. His sufferings are doubtless sharp- 
 ened by the consciousness that he has no right to 
 be subject to such inflictions. Experience, however, 
 shows that privations of various kinds affect men 
 differently in degree according to the circumstances 
 in which they are placed. For some men the priva- 
 tion of certain enjoyments is intolerable, whose 
 loss is not even felt by others. Some, again, 
 sacrifice all that others hold dear for the grati- 
 fication of longings and aspirations that are 
 incomprehensible to their neighbours. Upon this 
 
 ™ Second Edition, p. H.
 
 46 The Theory of Political Econoiny. 
 
 complex foundation of low wants and high aspira- 
 tions the Political Economist has to build the 
 theory of production and consumption. 
 
 ' An examination of the nature and intensity 
 
 of man's wants shows that this connection between 
 
 i them gives to Political Economy its scientific basis. 
 
 The first proposition of the theory of consumption 
 
 is, that the satisfaction of every lower ivant in the 
 
 scale creates a desire of a higher character. If the 
 
 higher desire existed previous to the satisfaction 
 
 i of the primary want, it becomes more intense 
 
 I when the latter is removed. The removal of a 
 
 primary want commonly awakens the sense of more 
 
 than one secondary privation : thus a full supply 
 
 of ordinary food not only excites to delicacy in 
 
 I eating, but awakens attention to clothing. The 
 
 highest grade in the scale of wants, that of pleasure 
 
 derived from the beauties of nature and art, is 
 
 usually confined to men who are exempted from 
 
 all the lower privations. Thus the demand for, and 
 
 the consumption of, objects of refined enjoyment 
 
 has its lever in the facility with which the primary 
 
 wants are satisfied. This, therefore, is the key to 
 
 I the true theory of value. Without relative values 
 
 I in the objects to the acquirement of which we 
 
 I direct our power, there would be no foundation 
 
 for Political Economy as a science.'
 
 Theory of Utility. 47 
 
 Utility is not an Intrinsic Quality. 
 
 My princij^al work now lies in tracing out the 
 exact nature and conditions of utility. It seems 
 strange indeed that economists have not bestowed 
 more minute attention on a subject which doubtless 
 furnishes the true key to the problem of Economics. 
 
 In the first place, utility, though a quality of 
 things, is no inherent quality. It is better described 
 as a circumstance of things arising out of their 
 relation to man's requirements. As Senior most 
 accurately says, 'Utility denotes no intrinsic quality 
 in the things which we call useful ; it merely ex- 
 presses their relations to the pains and pleasures 
 of mankind.' We can never, therefore, say abso- 
 lutely that some objects have utility and others 
 have not. The ore lying in the mine, the diamond 
 escaping the eye of the searcher, the wheat lying 
 unreaped, the fruit ungathered for want of con- 
 sumers, have no utility at all. The most wdiole- 
 some and necessary kinds of food are useless unless 
 there are hands to collect and mouths to eat them 
 sooner or later. Nor, when we consider the matter 
 closely, can we say that all portions of the same 
 commodity possess equal utility. Water, for in- 
 stance, may be roughly described as the most 
 useful of all substances. A quart of water per 
 day has the high utility of saving a person from 
 dying in a most distressing manner. Several gallons
 
 48 The Theory of Political Economy. 
 
 a day may possess much utility for such purposes 
 as cooking and washing; but after an adequate 
 supply is secured for these uses, any additional 
 quantity is a matter of comparative indifference. 
 All that we can say, then, is, that water, up to 
 a certain quantity, is indispensable ; that further 
 quantities will have various degrees of utility ; but 
 that beyond a certain quantity the utility sinks 
 gradually to zero; it may even become negative, 
 that is to say, further supplies of the same sub- 
 stance may become inconvenient and hurtful. 
 
 Exactly the same considerations apply more or 
 less clearly to every other article. A pound of 
 bread per day supplied to a person saves him from 
 starvation, and has the highest conceivable utility. 
 A second pound per day has also no slight utility : 
 it keeps him in a state of comparative plenty, 
 though it be not altogether indispensable. A third 
 pound would begin to be superfluous. It is clear, 
 then, that utility is not propoi'tional to commodity : 
 the very same articles vary in utility according as 
 we already possess more or less of the same article. 
 The like may be said of other things. One suit of 
 clothes per annum is necessary, a second conveni- 
 ent, a third desirable, a fourth not unacceptable ; 
 but we, sooner or later, reach a point at which 
 further supplies are not desired with any per- 
 ceptible force, unless it be for subsequent use.
 
 Theory of Utility. 49 
 
 Law of the Variation of Utility, 
 
 Let us now investigate tliis subject a little more 
 closely. Utility must be considered as measuredl 
 by, or even as actually identical with, the addition I 
 made to a person's happiness. It is a convenient « 
 name for the aggregate of the favourable balance 
 of feeling produced — the sum of the pleasure 
 created and the pain prevented. We must now 
 carefully discriminate between the total utility 
 arising from any commodity and the utility at- 
 taching to any particular portion of it. Thus the 
 total utility of the food we eat consists in main- 
 taining life, and may be considered as infinitely 
 great ; but if we were to sul)tract a tenth part 
 from what we eat daily, our loss would be but 
 slight. We should certainly not lose a tenth part 
 of the whole utility of food to us. It might be 
 doubtful whether we should suffer any harm at all. 
 
 Let us imagine the whole quantity of food which 
 a person consumes on an average during twenty- 
 four hours to be divided into ten equal parts. If 
 his food be reduced by the last part, he will suffer 
 but little ; if a second tenth part be deficient, he 
 will feel the want distinctly ; the subtraction of 
 the third tenth part will be decidedly injurious ; 
 with every subsequent subtraction of a tenth part 
 his sufferings will be more and more serious, until 
 at length he will ])e upon the verge of starvation. 
 
 E
 
 50 
 
 The Theory of Political Economy. 
 
 Now, if we call each of the tenth parts an incre- 
 ment, the meaning of these facts is, that each in- 
 crement of food is less necessary, or possesses less 
 utility, than the previous one. To explain this 
 variation of utility, we may make use of space- 
 representations, which I have found convenient 
 in illustrating the laws of Economics in my College 
 lectures during fifteen years past. 
 
 Let the line occ be used as a measure of the 
 quantity of food, and let it be divided into ten 
 equal parts to correspond to the ten portions of 
 food mentioned above. Upon these equal lines are 
 constructed rectangles, and the area of each rect- 
 angle may l)e assumed to represent the utility of 
 
 / 
 
 p p 
 
 T 
 
 m^m 
 
 VI VII Vlll 
 
 the increment of food corresponding to its base. 
 Thus the utility of the last increment is small, 
 being proportional to the small rectangle on x. 
 As we approach towards o, each increment bears 
 a larger rectangle, that standing upon iii being 
 the largest complete rectangle. The utility of the
 
 Theory of Utility. 51 
 
 next increment, n, is undefined, as also that of i, 
 since these portions of food would be indispen- 
 sable to life, and their utility, therefore, infinitely 
 great. 
 
 We can now form a clear notion of the utility 
 of the whole food, or of any part of it ; for we have 
 only to add together the i)roper rectangles. The 
 utility of the first half of the food will be the sum 
 of the rectangles standing on the line oa ; that of 
 the second half will be represented by the sum 
 of the smaller rectangles betAveen a and h. The 
 total utility of the food will be the whole sum of 
 the rectangles, and will be infinitely great. 
 
 The comparative utility of the several portions 
 is, however, the most important point. Utility 
 may be treated ^^ as a quantity of two dimensions^ 
 one dimension consisting in the quantity of the 
 commodity, and another in the intensity of the 
 effect produced upon the consumer. Now, the 
 quantity of the commodity is measured on the 
 horizontal line ox, and the intensity of utility will 
 be measured by the length of the upright lines, 
 or ordinates. The intensity of utility of the third 
 increment is measured either by pq, or i^q, and its 
 utility is the product of the units in pji multiplied 
 by those in pg-. 
 
 But the division of the food into ten equal parts 
 
 " The theory of dimensions of utility is fully stated in a subse- 
 quent section. 
 
 E 2
 
 52 The Theory of Political Economy. 
 
 is an arbitrary supposition. If we had taken 
 twenty or a hundred or more equal parts, the same 
 general principle would hold true, namely, that 
 each small portion would be less useful and neces- 
 sary than the last. The law may be considered to 
 hold true theoretically, however small the incre- 
 ments are made ; and in this way we shall at last 
 reach a figure which is undistinguishable from a 
 continuous curve. The notion of infinitely small 
 quantities of food may seem absurd as regards the 
 consumption of one individual ; but, when we con- 
 sider the consumption of a nation as a whole, the 
 consumption may well be conceived to increase 
 or diminish by quantities which are, practically 
 speaking, infinitely small compared with the whole 
 consumption. The laws which we are about to 
 trace out are to be conceived as theoretically true 
 of the individual; they can only be practically 
 verified as regards the aggregate transactions, pro- 
 ductions and consumptions of a large body of 
 people. But the laws of the aggregate depend of 
 course upon the laws applying to individual cases. 
 
 The law of the variation of the degree of utility 
 of food may thus be represented by a continuous 
 curve "phq (Fig. IV), and the perpendicular height 
 of each point of the curve above the line ox, re- 
 presents the degree of utility of the commodity 
 when a certain amount has been consumed. 
 
 TJius, when the quantity oa has been consumed.
 
 Theory of Utility. 
 
 53 
 
 the degree of utility corresponds to the length of 
 the line ah ; for if we take a very little more food, 
 ad, its utility will be the product of ad and ah 
 
 B^.W 
 
 very nearly, and more nearly the less is the magni- 
 tude of ad. The degree of utility is thus properly 
 measured by the height of a very narrow rectangle 
 corresponding to a very small quantity of food, 
 which theoretically ought to be infinitely small. 
 
 Total Utility and Degree of Utility. 
 
 We are now in a position to appreciate perfectly 
 the difference between the total utility of any com- 
 modity and the degree of utility of the commodity 
 at any point. These are, in fact, quantities of alto- 
 gether different kinds, the first being represented 
 by an area, and the second by a line. We must 
 consider how we may express these notions in 
 appropriate mathematical language. 
 
 Let X signify, as is usual in mathematical books, 
 the quantity which varies independently, — in this
 
 54 The Theory of Political Economy. 
 
 case the quantity of commodity. Let u denote the 
 ivhole utility proceeding from the consumption of x. 
 Then u will be, as mathematicians say, a functio 
 of X ; that is, it will vary in some continuous and 
 regular, but probably unknown, manner, when x is 
 made to vary. Our great object at present, how- 
 ever, is to express the degi-ee of utility. 
 
 Mathematicians employ the sign a prefixed to 
 a sign of quantity, such as x, to signify that a 
 quantity of the same nature as x, but small in pro- 
 portion to X, is taken into consideration. Thus a x 
 means a small portion of x, and x+ a £c is there- 
 fore a quantity a little greater thaii x. Now, when 
 a? is a quantity of commodity, the utility of £c + ax 
 will be more than that of ic as a general rule. Let 
 the whole utility of x + a a? be denoted by tt + a u ; 
 then it is obvious that the increment of utility a u 
 belongs to the increment of commodity ax; and 
 if, for the sake of argument, we suppose the degree 
 of utility uniform over the whole of a x, which is 
 nearly true owing to its smallness, Ave shall find 
 the corresponding degree of utility by dividing a w 
 by ax. 
 
 We find these considerations fully illustrated by 
 Fig. IV, in which oa represents x, and ah is the degree 
 of utility at the point a. Now, if we increase x by 
 the small quantity aa\ or ax, the utility is in- 
 creased by the small rectangle ahUaJ, or au; and, 
 since a rectangle is the product of its sides, we
 
 Theory of Uiditij. 55 
 
 find that the length of the line ah, the degree of 
 utility, is represented by the fraction ^^. 
 
 As already explained, however, the utility of a 
 commodity may be considered to vary with perfect 
 continuity, so that we commit a small error in 
 assuming it to be uniform over the whole incre- 
 ment A a*. To avoid this we must imagine acc to 
 be reduced to an infinitely small size, ^u de- 
 creasing- with it. The smaller the quantities are 
 the more nearly we shall have a correct expres- 
 sion for ah, the degree of utility at the point a. Thus 
 
 the limit of this fraction ^-^, or, as it is commonly 
 
 AiC 
 
 (jiXb 
 
 expressed, — , is the degree of utility con'esponding 
 
 to the quantity of commodity x. The degree of 
 utility is, in mathematical language, the differential 
 coefficient of u considered as a function of x, and 
 will itself be another function of x. 
 
 We shall seldom need to consider the degree of 
 utility except as regards the last increment which 
 has been consumed or, which comes to the same 
 thing, the next increment which is about to be con- 
 sumed. I shall therefore commonly use the expres- 
 sion ^?ia/ degree of utility, as meaning the degree of 
 utility of the last addition, or the next possible 
 addition of a very small, or infinitely small, quantity 
 to, the existing stock. In ordinary circumstances,
 
 56 The Theory of Political Economy. 
 
 too, the final degree of utility Avill not be great 
 compared with what it might be. Only in famine 
 or other extreme circumstances do we ap];)roach 
 the higher degrees of utility. Accordingly, we can 
 often treat the lower portions of the curves of 
 variation (2^l>q, Fig. IV) which concern ordinary 
 commercial transactions, while we leave out of 
 sight the jDortions beyond p or q. It is also evident 
 that we may know the degree of utility at any 
 point while ignorant of the total utility, that is, 
 the area of the whole cuiwe. To be able to esti- 
 mate the total enjoyment of a person would be 
 an interesting thing, but it would not be really so 
 important as to be able to estimate the additions 
 and subtractions to his enjoyment, which circum- 
 stances occasion. In the same way a very wealthy 
 person may be quite unable to form any accurate 
 statement of his aggregate wealth ; but he may 
 nevertheless have exact accounts of income and 
 expenditure, that is, of additions and subtractions. 
 
 Variation of the Final Degree of Utility. 
 
 The final degree of utility is that function upon 
 which the Theory of Economics will be found to 
 turn. Economists, generally speaking, have failed 
 to discriminate between this function and the total 
 utility, and from tliis confusion has arisen much 
 perplexity. Many commodities which are most
 
 Theo7^y of Utility. 57 
 
 useful to us are esteemed and desired but little. 
 We cannot live without water, and 3^et in ordinary 
 circumstances we set no value on it. Why is this ? 
 Simply because m'c usually have so much of it that 
 its final degree of utility is reduced nearly to zero. 
 We enjoy, every da}^ the almost infinite utility of 
 water, but then we do not need to consume more 
 than we liave. Let the supply run short by 
 drought, and we begin to feel the higher degrees 
 of utility, of which we think but little at other 
 times. 
 
 The variation of the function expressing the 
 final degree of utility is the all-important point 
 in economic problems. We may state as a general 
 law, that the degree of utility varies with the quantity 
 of commodity, and idtimately decreases as that quan- 
 tity increases. No commodity can be named which 
 we continue to desire with the same force, whatever 
 be the quantit}'^ already in use or possession. All 
 our appetites are capable of satisfaction or satiety 
 sooner or later, in fact, both these words mean, 
 etymologicall}^, that we have had enough, so that 
 more is of no use to us. It does not follow, 
 indeed, that the degree of utility will ahva3^s sink 
 to zero. This may be the case Avith some things, 
 especially the simple animal requirements, such 
 as food, water, air, &c. But the more refined and 
 intellectual our needs become, the less are they 
 capable of satiety. To the desire for articles of
 
 58 The Theory of Political Economy. 
 
 taste, science, or curiosity, when once excited, there 
 is hardly a limit. 
 
 This great principle of the ultimate decrease of 
 the final degree of utility of any commodity is im- 
 plied in the writings of many economists, though 
 seldom distinctly stated. It is the real law which 
 lies at the basis of Senior's so-called 'Law of 
 Variety.' Indeed, Senior incidentally states the 
 law itself. He says : ' It is obvious that our desires 
 do not aim so much at quantity as at diversity. 
 Not only are there limits to the pleasure which 
 commodities of any given class can afford, but the 
 pleasure diminishes in a rapidly increasing ratio 
 long before those limits are reached. Two articles 
 of the same kind will seldom afford twice the 
 pleasure of one, and still less will ten give five 
 times the pleasure of two. In proportion, there- 
 fore, as any article is abundant, the number of 
 those who are provided with it, and do not wish, 
 or wish but little, to increase their provision, is 
 likely to be great ; and, so far as they are con- 
 cerned, the additional supply loses all, or nearly 
 all, its utility. And, in proportion to its scarcity, 
 the number of those who are in want of it, and the 
 degree in which they want it, are likely to be in- 
 creased ; and its utility, or, in other words, the 
 pleasure w^iich the possession of a given quantity 
 of it will afford, increases proportionally ».' 
 
 " 'Encyclopaedia Metropolitana,' p. 133. Reprint, p. 12.
 
 Theory of Utility.. 59 
 
 Baiificlcl's ' Law of the Subordination of Wants ' 
 also rests upon the same basis. It cannot be said, 
 ■with accuracy, that the satisfaction of a lower 
 want creates a higher Avant ; it merely permits the 
 higher want to manifest itself. We distribute our 
 labour and possessions in such a way as to satisfy 
 the more pressing wants first. If food runs short, 
 the all-absorbing question is, how to obtain more, 
 because, at the moment, more pleasure or pain 
 depends upon food than upon any other commodity. 
 But, when food is moderately abundant, its final 
 degree of utility falls very Ioav, and w^ants of a 
 more complex and less satiable nature become com- 
 pai'atively prominent. 
 
 The writer, hoAvever, who appears to me to 
 have most clearly appreciated the nature and 
 importance of the law of utility, is Richard Jen- 
 nings, who, in 1855, published a small book called 
 the 'Natural Elements of Political Economy p.' 
 This Avork treats of the physical groundAvork of 
 Economics, shoAving its dependence on physiological 
 laAvs. It displays great insight into the real basis 
 of Economics ; yet I am not aAA^are that economists 
 have bestowed the slightest attention on Jennings' 
 views q. I giA^e, therefore, a full extract from his 
 
 P London : Longmans. 
 
 a Cairnes is, however, an exception. See his work on ' The 
 Character and Logical Method of Political Economy.' London, 
 1857, p. 81. Second Edition (Macmillan), 1875, pp. 56, 110, 
 224 App. B.
 
 y 
 
 GO The Theory of Political Economy. 
 
 remarks on the nature of utility. It will be seen 
 that the law, as I state it, is no novelty, and 
 that careful deduction from principles in our 
 possession is alone needed to give us a correct 
 Theory of Economics, 
 
 ' To turn from the relative effect of commodities, 
 in reducing sensations, to those which are abso- 
 lute, or dependent only on the quantity of each 
 commodity, it is but too well known to every con- 
 dition of men, that the degree of each sensation 
 which is produced, is by no means commensurate 
 with the quantity of the commodity applied to the 
 
 senses These effects require to be closely 
 
 observed, because they are the foundation of the 
 changes of money price, which valuable objects 
 command in times of varied scarcity and abun- 
 dance ; we shall therefore here direct our attention 
 to them for the purpose of ascertaining the nature 
 of the law according to which the sensations that 
 attend on consumption vary in degree with changes 
 in the quantity of the commodity consumed. 
 
 ' We may gaze upon an object until we can no 
 longer discern it, listen until we can no longer 
 hear, smell initil the sense of odour is exhausted, 
 taste until the object becomes nauseous, and touch 
 until it becomes painful ; we may consume food 
 until we are fully satisfied, and use stimulants 
 until more would cause pain. On the other hand, 
 the same object offered to the special senses for
 
 Theonj of Utility. 61 
 
 a moderate duration of time, and the same food 
 or stimulants consumed when we are exhausted 
 or weary, may convey much gratification. If the 
 whole quantity of the commodity consumed during 
 the interval of these two states of sensation, the 
 state of satiety and the state of inanition, be con- 
 ceived to be divided into a number of equal parts, 
 each marked with its proper degrees of sensation, 
 the question to be determined will be, what rela- 
 tion does the difference in the degrees of the 
 sensation bear to the difference in the quantities 
 of the commodity? 
 
 * First, with respect to all commodities, our feel- 
 ' ino;s show tliat the dejyrees of satisfaction do not 
 proceed pari passu with the quantities consumed ; 
 they do not advance equally with each instalment 
 of the commodity offered to the senses, and then 
 suddenly stop ; but dhninish gradually, until they 
 ultimately disappear, arid further instalments can 
 produce no further satisfaction. In this progres- 
 sive scale the increments of sensation resulting 
 from equal increments of the commodity are 
 obviously less and less at each step, — each degree 
 of sensation is less than the preceding degree. 
 Placing ourselves at that middle point of sensa- 
 tion, the juste milieu^ the aurea mediocritas, the 
 apKTTov fjLerpov of sages, wliicli is the most usual 
 status of the mass of mankind, and which, there- 
 fore, is the best position that can be chosen for
 
 62 The Theory of Political Economy. 
 
 measuring deviations from the usual amount, we 
 may say that the law which expresses the rela- 
 tion of degrees of sensation to quantities of com- 
 modities is of this character : if the average or 
 temperate quantity of commodities be increased, 
 the satisfaction derived is increased in a less 
 degree, and ultimately ceases to be increased at 
 all; if the average or temperate quantity be 
 diminished, the loss of more and more satisfaction 
 will continually ensue, and the detriment thence 
 arising will ultimately become exceedingly great ^\' 
 
 Disutility and Discommodity. 
 
 A few Avords will suffice to suggest tiiat as 
 utility corresponds to the production of pleasure, 
 or, at least, a favourable alteration in the balance 
 of pleasure and pain, so negative utility will 
 consist in the production of pain, or the unfavour- 
 able alteration of the balance. In reality we must 
 be almost as often concerned with the one as with 
 the other; nevertheless, economists have not em- 
 ployed any distinct technical terms to express that 
 j)roduction of pain, which accompanies so many 
 actions of life. They have fixed their attention on 
 the more agreeable aspect of the matter. It will 
 b.e allowable, however, to appropriate the good- 
 
 >• pp. 96-99.
 
 Theory of UtUliy. 03 
 
 English word discommodity, to signify any sub- 
 stance or action which is the opposite of com- 
 modity, that is to say, anytldng ivliich ive desire to 
 get rid of, like ashes or sewage. Discommodity 
 is, indeed, properly an abstract form signifying 
 inconvenience, or disadvantage ; but, as the noun 
 commodities has been used in the English language 
 for four hundred years at least as a concrete term s, 
 so we may now convert discommodity into a con- 
 crete term, and speak of discommodities as sub- 
 stances or things, which possess the quality of 
 causing inconvenience or harm. For the abstract 
 notion, the opposite or negative of utility, we may 
 invent the term disutility, which will mean some- 
 thing different from inutility, or the absence of ' 
 utility. It is obvious that utility passes through 
 inutility before changing into disutility, these 
 notions being related as + , o and — . 
 
 Distribution of Commodity in different Uses. 
 
 The principles of utility may be illustrated by 
 considering the mode in which we distribute a com- 
 modity when it is capable of several uses. There 
 are articles which may be employed for many dis- 
 tinct purposes : thus, barley may be used either to 
 
 8 It is used precisely in its present economical sense in the re- 
 markable Processe of the Libelle of English Policie, probably written 
 in the 15th century, and printed in Hakluyt's voyages.
 
 64 The Theory of Political Economy. 
 
 make beer, spirits, bread, or to feed cattle ; sugar 
 may be used to eat, or for producing alcohol; 
 timber may be used in construction, or as fuel; 
 iron and other metals may be applied to many 
 different purposes. Imagine, then, a community in 
 the possession of a certain stock of barley; what 
 principles will regulate their mode of consuming 
 it. Or, as we have not yet reached the subject of 
 exchange, imagine an isolated family, or even an 
 individual, possessing an adequate stock, and using 
 some in one way and some in another. The theory 
 of utility gives, theoretically speaking, a complete 
 solution of the question. 
 
 Let s be the whole stock of some commodity, 
 and let it be capable of two distinct uses. Then 
 Ave may represent the two quantities appropriated 
 to these uses by x^ and y^, it being a condition 
 that a-i + ?/i — s. The person may be conceived as 
 successively expending small quantities of the 
 commodity; now it is the inevitable tendency of 
 human nature to choose that course which appears 
 to offer the greatest advantage at the moment. 
 Hence, when the person remains satisfied with the 
 distribution he has made, it follows that no alter- 
 ation would yield him more pleasure ; which 
 amounts to saying that an increment of commo- 
 dity would yield exactly as much utility in one 
 use as in another. Let az/i, au-z, be the incre- 
 ments of utility, which might arise respectively
 
 Theory of Utility. 65 
 
 from consuming- an increment of commodity in 
 the two different Avays. When the distribution 
 is completed, we ought to have /\Ux-- ^u.,; or at 
 the limit we have the equation 
 
 dx dy 
 which is true wdien x, y are respectively equal to 
 ^i> Vi- We must, in other words, have the faial 
 degrees of utility in the two uses equal. 
 
 The same reasoning which applies to uses of the 
 same commodity will evidently apply to any two 
 uses, and hence to all uses simultaneously, so that 
 we obtain a series of equations less numerous by a 
 unit than the number of ways of using the com- 
 modity. The general result is that commodity, if 
 consumed by a perfectly wise being, must be con- 
 sumed with a maximum production of utility. 
 
 We should often find these equations to fail. 
 Even when x is equal to —^ of the stock, its degree 
 of utility might still exceed the utility attaching to 
 the remaining -^ part in either of the other uses. 
 This would mean that it was preferable to give the 
 whole commodity to the first use. Such a case 
 might perhaps be said to be not the exception but 
 the rule ; for, whenever a commodity is capable of 
 only one use, the circumstance is theoretically re- 
 presented by saying, that the final degree of utility 
 in this employment always exceeds that in any 
 other employment.
 
 66 The Theory of Political Economy. 
 
 Under peculiar circumstances great changes may 
 take place in the consumption of a commodity. In 
 a time of scarcity the utility of barley as food might 
 rise so high as to exceed altogether its utility, even 
 as regards the smallest quantity, in producing 
 alcoholic liquors ; its consumption in the latter 
 way would then cease. In a besieged town the 
 employment of articles becomes revolutionised. 
 Things of great utility in other respects are ruth- 
 lessly applied to strange purposes. In Paris a vast 
 stock of horses were eaten, not so much because 
 they were useless in other ways, as because they 
 were needed more strongly as food. A certain 
 stock of horses had, indeed, to be retained as a 
 necessary aid to locomotion, so that the equation of 
 the degrees of utility never wholly failed. 
 
 Theory of Dimensions of Economic Quantities. 
 
 In the recent progress of physical science, it has 
 been found requisite to use notation for the purpose 
 of displaying clearly the natures and relations of 
 the various kinds of quantities concerned. Each 
 different sort of quantity is, of course, expressed in 
 terms of its own appropriate unit — length in terms 
 of yards, or metres ; surface, or area, in terms of 
 square yards or square metres ; time in terms of 
 seconds, days, or years ; and so forth. But the 
 more complicated quantities are evidently related
 
 Theory of Utility. 67 
 
 to the simpler ones. Surface is measured by the 
 square yard, that is to say, the unit of length is 
 involved tA^ice over, and if by L we denote one 
 dimension of length, then the dimensions of surface 
 are LL, or XI The dimensions of cubic capacity 
 are in like manner LLL, or L^. 
 
 In these cases the dimensions all enter positively, 
 because the number of units in the cubical body, 
 for instance, is found by multiplying the numbers 
 of units in its length, breadth and depth. In other 
 cases a dimension enters negatively. Thus denoting 
 time by T, it is easy to see that the dimensions of 
 velocity will be L divided by T, or LT~^, because 
 the number of units in the velocity of a body is 
 found by dividing the units of length passed over 
 by the units of time occupied in passing. In ex- 
 pressing the dimensions of thermal and electric 
 quantities, fractional exponents often become ne- 
 cessar}', and the subject assumes the form of a 
 theory of considerable complexity. The reader to 
 whom this branch of science is new will find a 
 section briefly describing it in my Principles of 
 Science, 3rd ed. p. 325, or he may refer to the works 
 there mentioned *. 
 
 Now, if such a theory of dimensions is requisite 
 
 I J. D. Everett's ' Illustrations of the Centimetre-gramme- 
 secoud System of Units,' 1875; Fleeming Jenkin's 'Text-book of 
 Electricity and Magnetism,' 1873; Clerk Maxwell's 'Theory of 
 Heat,' or the commencement of his great Treatise on Electricity, 
 vol. I. p. 2. 
 
 F 2
 
 68 The Theory of Political Economy. 
 
 in dealing with the precise ideas of physical mag- 
 nitudes, it seems to be still more desirable as 
 regards the quantities with which we are con- 
 cerned in Economics. One of the first and most 
 ij difficult steps in a science is to conceive clearly 
 I the nature of the magnitudes about which we 
 ' are arguing. Heat was long the subject of dis- 
 cussion and experiment before physicists formed 
 any definite idea how its quantity could be mea- 
 sured and connected with other physical quan- 
 tities. Yet, until that w^as done, it could not be 
 considered the subject of an exact science. For 
 one or two centuries economists have been wrang- 
 ling about wealth, demand and supply, value, pro- 
 \ duction, capital, interest, and the like ; but hardly 
 any one could say exactly what were the natures of 
 the quantities in question. Believing that it is in 
 j forming these primary ideas that Ave require to 
 exercise the greatest care, I have thought it well 
 worth the trouble and space to enter fully into a 
 discussion of the dimensions of economic quantities. 
 /' Beginning with the easiest and simplest ideas, 
 \ the dimensio7is of commodity regarded merely as a 
 I physical quantity will be the dimensions of mass. 
 It is true that commodities are measured in various 
 ways, — thread by length, carpet by length, corn 
 and liquids by cubic measure, eggs by number, 
 metals and most other goods by weight. But it 
 is obvious that, though the carpet be sold by 

 
 Theorij of Utility. 69 
 
 length, the breadth and the weight of the cloth 
 are equally taken into account in fixing the terms 
 of sale. There will generally be a tacit reference 
 to weight, and through weight to mass of materials 
 in all measurement of commodity. Even if this be 
 not always the case, we may, for the sake of sim- 
 plifying our symbols in the first treatment of the 
 subject, assume that it is so. We need hardly 
 recede to any ultimate analysis of the physical 
 conditions of the commodity, but may take it to be 
 measured by mass, symbolised by M, the sign 
 usually employed in physical science to denote this 
 dimension. 
 
 A little consideration Avill show, however, that 
 we have really little to do with absolute quantities 
 of commodity. One hundred sacks of corn regarded 
 merely by themselves can have no important mean- 
 ing for the economist. Whether the quantity is 
 large or small, enough or too much, depends in the 
 first place upon the number of consumers for whom 
 it is intended, and, in the second place, upon the 
 time for which it is to last them. We may per- 
 haps throw out of view number of consumers in 
 this theory, by supposing that we are always deal- 
 ing with the single average individual, the unit of 
 which population is made up. Still, we cannot 
 similarly get rid of the element of time. Quantity 
 of supply must necessarily be estimated by the 
 number of units of commodity divided by the
 
 70 The Theory of Political Economy, 
 
 number of units in the time over which it is to 
 be expended. Thus it will involve M positively 
 and T negatively, and its dimensions will be re- 
 presented by MT~\ Thus in reality supply should 
 be taken to mean not supply absolutely, but rate of 
 supp)ly. 
 
 ,, Consumption of commodity must have the same 
 i , dimensions. For goods must be consumed in time ; 
 any action or effect endures a greater or less time, 
 and commodity which will be abundant for a less 
 time, may be scanty for a greater time. To say 
 that a town consumes fifty million gallons of water 
 is unmeaning per se. Before we can form any 
 judgment about the statement, we must know 
 whether it is consumed in a day, or a week, or a 
 month. 
 
 Following out, this course of thought we shall 
 
 j arrive at the conclusion that time enters into all 
 
 II economic questions. We live in time, and think 
 and act in time; we are in fact altogether the 
 creatures of time. Accordingly i t is ra te of supply, 
 
 u rate of production , rate o f consump tion, per unit 
 of time that we shall be really treating ; but it 
 does not follow that T~^ enters into all the dimen- 
 
 jjions with which we deal. 
 
 As was fully explained in Chapter II, the ulti- 
 mate quantities which we treat in Economics are 
 Pleasures and Pains, and our most difficult task 
 will be to express their dimensions correctly. In
 
 Theory of Utility. 71 
 
 the first place, pleasure and pain must be regarded 
 as measured upon the same scale, and as having, 
 therefore, the same dimensions, being quantities of 
 the same kind, which can be added and subtracted ; 
 they differ only in sign or direction. Noav, the only 
 dimension belonging properly to feeling, seems iojio^^i-- 
 be intensity, and this intensity must be independent/ 
 both of time, and of the quantity of commodityv-'^ 
 enjoyed. The intensity of feeling must mean, theni ^ Ijy 
 I the instantaneous state produced by an elementary or\ ^H^ 
 [infinitesimal quantity of commodity co7isumed. *^ 
 
 Intensity of feeling, however, is only another 
 name for degree of utility, which represents the 
 favourable effect produced upon the human frame 
 by the consumption of commodity, that is by an, 
 elementary or infinitesimal quantity of commodity.) 
 Putting U to indicate this dimension, we must 
 remember that U will not represent even the full 
 dimensions of the instantaneous state of pleasure 
 or pain, much less the continued state which 
 extends over a certain duration of time. The; 
 instantaneous state depends upon the sufficiency 
 or insufficiency of supply of commodity. To enjoy 
 a highly pleasurable condition, a person must want 
 a good deal of commodity, and must be well sup- 
 plied with it. Now, this supply is, as already ex- 
 plained, rate of supply, so that we must multiply 
 U by MT~^ in order to arrive at the real instan- 
 taneous state of feeling. The kind of quantity
 
 72 The Theory of Political Economy. 
 
 thus symbolised by MUT'^ must be interpreted 
 as meaning so much commodity producing a cer- 
 tain amount of pleasitixihle effect per imit of time. 
 But this quantity will not be quantity of utility 
 itself. It will only be that quantity which, when 
 multiplied by time, will produce quantity of utility. 
 Pleasure, as was stated at the outset, has the 
 dimensions intensity and* duration. It is then this 
 intcMsity which is symbolised by MUT"^, and we 
 must multiply this last symbol by T in order to 
 obtain the dimensions of utility or quantity of 
 pleasure produced. But in making this multi- 
 plication, MUT-^T, reduces to MU, which must 
 therefore be taken to denote the dimensions of 
 quantity of utility. 
 
 We here meet with an explanation of the fact, 
 so long perplexing to me, that the element of time 
 does not appear throughout the diagrams and pro- 
 blems of this theory relating to utility and ex- 
 change. All goes on in time, and time is a neces- 
 sary element of the question ; yet it does not 
 explicitly appear. Recurring to our diagrams, that 
 for instance on p. 50, it is obvious that the dimen- 
 sion U, or degree of utility, is measured upon the 
 perpendicular axis oy. The horizontal axis must, 
 therefore, be that upon which rate of supply of 
 commodity or MT~^ is measured, strictly speaking. 
 If now we introduce the duration of the utility, Ave 
 should apparently need a third axis, perpendicular
 
 Theory of Utility. 73 
 
 to the plane of the page, upon whicli to denote it. 
 But were we to introduce this third dimension, we 
 shoukl obtain a solid figure, representing a quantity 
 truly of three dimensions. This would be erroneous, 
 because the third dimension T enters negatively 
 into the quantity represented by the horizontal 
 axis. Thus time eliminates itself, and we arrive 
 at a quantity of two dimensions correctly repre- 
 sented by a curvilinear area, one dimension of 
 which corresponds to each of the factors in MU. 
 
 This result is at first sight paradoxical ; but the 
 difficulty is exactly analogous to that which occurs 
 in the question of interest, and Avhich led so pro- 
 found a mathematician as Dean Peacock into a 
 blunder, as Avill be shown in the Chapter upon 
 Capital. Interest of money is proportional to the 
 length of time for which the principal is lent, and 
 also to the amount of money lent and the rate of 
 interest. But this rate of interest involves time 
 negatively, so that time is ultimately eliminated, 
 and interest emerges with the same dimensions as 
 the principal sum. In the case of utility we begin 
 Avith a certain absolute stock of commodity, M. 
 In expending it we must spread it over more 
 or less time, so that it is really rate of supply 
 which is to be considered ; but it is this rate 
 3IT~^, not simply M, which influences the final 
 degi'ce of utility, U, at which it is consumed. If 
 the same commodity be made to last a longer time,
 
 74 The Theory of Political Economy. 
 
 the degree of utility will be higher, because the 
 necessity of the consumer will be less satisfied. 
 Thus the absolute amount of utility produced will 
 as a general rule be greater as the time of expen- 
 diture is greater; but this will also be the case 
 with the quantity symbolised by MU, because the 
 quantity U will under those circumstances be 
 greater, while M remains constant. 
 
 To clear up the matter still further if possible, I 
 will recapitulate the results we have arrived at. 
 
 M means absolute amount of commodity. cuytCLoJJuJfy sl;. 
 
 MT~^ means amount of commodity applied, so 
 much per unit of time. 
 
 Z7 means the resulting pleasurable effect of any 
 increment of that supply an infinitesimal quantity '^,,^^^^ 
 supplied per unit of time. 
 
 MUT~^ means therefore so much pleasurable 
 effect produced per unit of commodity per unit 
 of time. v[f^'" •0''/ 
 
 MUT~^T, or MU, means therefore so much 
 absolute pleasurable effect produced by commodity 
 in an unspecified duration of time. 
 
 Actual, Prospective, and Potential Utility. 
 
 The difficulties of Economics are mainly the 
 difficulties of conceiving clearly and fully the con- 
 ditions of utility. Even at the risk of being tire- 
 some, I will therefore point out more minutely
 
 Theory of Utility. 75 
 
 how various are the senses in which a thing may 
 be said to have utility. 
 
 It is quite usual, and perhaps correct, to call iron 
 or water or timber a useful substance ; but we 
 may mean by these words at least three distinct 
 facts. We may mean that a particular piece of 
 iron is at the present moment actually useful to 
 some person ; or that, although not actually useful, 
 it is expected to be useful at a future time ; or we 
 may only mean that it would be useful if it Avere 
 in the possession of some person needing it. The 
 iron rails of a railway, the iron which composes 
 the Britannia Bridge, or an ocean steamer, is 
 actually useful; the iron lying in a merchant's 
 store is not useful at present, though it is expected 
 soon to be so ; but there is a vast quantity of iron 
 existing in the bowels of the earth, which has all 
 the physical properties of iron, and might be useful 
 if extracted, though it never will be. These are 
 instances of actual, j)rosi')ective, and j^otential utility. 
 
 It will be apparent that j'^otential utility does not 
 really enter into the science of Economics, and 
 when I speak of utility simply, I do not mean to 
 include potential utility. It is a question of phys- 
 ical science whether a substance possesses qualities 
 which might make it suitable to our needs if it 
 were within our reach. Only when there arises 
 some degree of probability, however slight, that 
 a particular object will be needed, does it acquire
 
 76 The Theory of Political Ecomony. 
 
 prospective utility, capable of rendering it a de- 
 sirable possession. As Condillac correctly re- 
 marks " — ' On diroit que les choses ne commencent 
 a exister pour eux, qu'au moment oil ils ont un 
 interet a savoir qu'elles existent.' But a very large 
 part in industry, and the science of industry, be- 
 longs to prospective utility. We can at any one 
 moment use only a very small fraction of what we 
 possess. By far the greater part of what we hold 
 might be allowed to perish at any moment, without 
 harm, if we could have it re-created with equal 
 ease at a future moment, when need of it arises. 
 
 We might also distinguish, as is customary with 
 French economists, between direct and indirect 
 utility. Direct utility attaches to a thing like food, 
 which we can actually apply to satisfy our wants. 
 But things which have no direct utility may be the 
 means of procuring us such by exchange, and they 
 may therefore be said to have indirect utility ^. To 
 the latter form of utility I have elsewhere applied 
 the name acquired utility i. This distinction is not 
 the same as that which is made in the Theory of 
 Capital between mediate and immediate utility, the 
 former being that of any implement, machine, or 
 other means of procuring commodities possessing 
 
 u Condillac, ' Le Commerce et le Gouvernement,' Seconde Partie, 
 Introduction. (Euvres Completes. Paris, 1803. Tom vii. p. 2. 
 x'Garnier, ' Traite d'Economie Politique,' 5nie ed. p. 11. 
 y See Chapter IV.
 
 Theory of Utilitij. 77 
 
 immediate and direct utility — that is, the power of 
 satisfying want''. 
 
 Distribution of a Commodity in time. 
 
 We have seen that, when a commodity is capable 
 of being used for different purposes, definite prin- 
 ciples regulate its application to those purposes. 
 A similar question arises when a stock of com- 
 modity is in hand, and must be expended over 
 a certain interval of time more or less definite. 
 The science of Economics must point out the mode 
 of consuming it to the greatest advantage — that 
 is, with a maximum result of utility. If we reckon 
 all future pleasures and pains as if they were pre- 
 sent, the solution will be the same as in the case of 
 different uses. If a commodity has to be distri- 
 buted over n days' use, and v^, v.^, &c. be the final 
 degrees of utility on each day's consumption, then 
 we ought clearly to have 
 
 v-^ = v.^ = v^= . . . =v„. 
 
 It may, however, be uncertain during how many 
 days we may require the stock to last. The com- 
 modity might be of a perishable nature, so that 
 if we were to keep some of it for ten days, it might 
 become unserviceable, and its utility be sacrificed. 
 Assuming that we can estimate more or less 
 exactly the probability of its remaining good, let 
 j^i' i^2' Pi ' • • Pio be these probabilities. Then, on 
 
 =s See Chapter VII.
 
 78 The Theory of Political Economy. 
 
 the principle (p. 38) tliat a future pleasure or pain 
 must be reduced in proportion to its want of cer- 
 tainty, we have the equations 
 
 The general result is, that as the probability is less, 
 the commodity assigned to each day is less, so that 
 V, its final degree of utility, will be greater. 
 
 So far we have taken no account of the varying 
 influence of an event according to its propinquity 
 or remoteness. The distribution of commodity 
 described is that which should be made and would 
 be made by a being of perfect good sense and fore- 
 sight. To secure a maximum of benefit in life, 
 all future events, all future pleasures or pains, 
 should act upon us with the same force as if they 
 Avere present, allowance being made for their un- 
 certainty. The factor expressing the effect of 
 remoteness should, in short, always be unity, so 
 that time should have no influence. But no 
 human mind is constituted in this perfect way : 
 a future feeling is always less influential than 
 a present one. To take this fact into account, let 
 5'n 9'2' 9'3> &c. be the undetermined fractions which 
 express the ratios of the present pleasures or pains 
 to those future ones from whose anticipation they 
 arise. Having a stock of commodity in hand, our 
 tendency will be to distribute it so that the follow- 
 ing equations will hold true — 
 
 Vl p, qi = V2P2q2 = '^3P'3qS= ' • • = %iPnqn-
 
 Theory of Utility. 79 
 
 It will be an obvious consequence of these equa- 
 tions that less commodity Avill be assigned to 
 future days in some proportion to the intervening 
 time. 
 
 An illustrative problem, involving questions of 
 prospective utility and probability, is found in the 
 case of a vessel at sea, which is insufficiently vic- 
 tualled for the probable length of the voyage to the 
 nearest port. The actual length of the voyage 
 depends on the winds, and must be uncertain; 
 but we may suppose that it will almost certainly 
 last ten days or more, but not more than thirty 
 days. It is apparent that if the food were divided 
 into thirty equal parts, partial famine and suffering 
 would be certainly endured for the first ten days, 
 to ward off later evils which may not be encoun- 
 tered. To consume one-tenth part of the food on 
 each of the first ten days would be still worse, as 
 almost certainly entailing starvation on the follow- 
 ing days. To determine the most beneficial distri- 
 bution of the food, we should require to know the 
 probability of each day between the tenth and 
 thirtieth days forming part of the voyage, and also 
 the law of variation of the degree of utility of food. 
 The whole stock ought then to be divided into 
 thirty portions, allotted to each of the thirty days, 
 and of such magnitudes that the final degrees of 
 utility multiplied by the probabilities may be 
 equal. Thus, let v^, v^, Vg, &c. be the final degrees
 
 80 The Theory of Political Economy. 
 
 of utility of the first, second, third, and other days 
 supplied, and p-^, jp.2, ^3, &c. the probabilities that 
 the days in question will form part of the voyage ; 
 then we ought to have 
 
 If these equations did not hold true, it would be 
 beneficial to transfer a small portion from one lot 
 to some other lot. As the voyage is supposed cer- 
 tainly to last the first ten days, we have 
 
 Pi=P2^ ' ' • =2ho = '^ ; 
 hence we must have 
 
 v^ = v.2= . . . =Vio; 
 
 that is to say, the allotments to the first ten days 
 should be equal. They should afterwards decrease 
 according to some regular law ; for, as the proba- 
 bility decreases, the final degree of utility should 
 increase in inverse proportion.
 
 CHAPTER IV. 
 
 THEORY OP EXCHANGE, 
 
 Irnporta7ice of Exchange in Economics. 
 
 Exchange is so important a process in the 
 maximising of utility and the saving of labour, 
 that some economists have regarded their science 
 as treating of this operation alone. Utility arises 
 from commodities being brought in suitable quan- 
 tities and at the proper times into the possession 
 of persons needing them ; and it is by exchange, 
 more than any other means, that this is effected. 
 Trade is not indeed the only method of econo- 
 mising : a single individual may gain in utility by 
 a proper consumption of the stock in his possession. 
 The best employment of labour and capital by 
 a single person is also a question disconnected from 
 that of exchange, and vdiich must yet be treated 
 in the science. But, with these exceptions, I am 
 
 G
 
 82 The Theory of Political Economy. 
 
 perfectly willing to agree with the high importance 
 attributed to exchange. 
 
 It is impossible to have a correct idea of the 
 science of Economics without a perfect comprehen- 
 sion of the Theory of Exchange ; and I find it both 
 possible and desirable to consider this subject be- 
 fore introducing any notions concerning labour or 
 the jDroduction of commodities. In these words 
 of J. S. Mill I thoroughly concur : ' Almost every 
 speculation respecting the economical interests of 
 a society thus constituted, implies some theory of 
 Value: the smallest error on that subject infects 
 with corresponding error all our other conclusions ; 
 and anything vague or misty in our conception of 
 it, creates confusion and uncertainty in everything 
 else/ But when he proceeds to say, 'Happily, 
 there is nothing in the laws of Value which re- 
 mains for the present or any future writer to clear 
 up; the theory of the subject is complete''^ — he 
 utters that which it would be rash to say of any 
 of the sciences. 
 
 Ambiguity of the term Value. 
 
 I must, in the first place, point out the thoroughly 
 ambiguous and unscientific character of the term 
 vahw. Adam Smith noticed the extreme difference 
 of meaning between value i7i use and value in 
 
 * ' Principles of Political Economy,' book iii. chap. 1. § 1.
 
 Theory of Exchange. 83 
 
 exchange ; and it is usual for writers on Economics 
 to caution their readers against the confusion of 
 thought to which they are liable. But I do not 
 believe that either writers or readers can avoid 
 the confusion so long as they use the word. In 
 spite of the most acute feeling of the danger, 
 I often detect myself using the word improperly ; 
 nor do I think tliat the best authors escape the 
 danger. 
 
 Let us turn to Mill's definition of Exchange 
 Value ^\ and we see at once the misleading power of 
 the term. He tells us — ' Value is a relative term. 
 The value of a thing means the quantity of some 
 other thing, or of things in general, which it 
 exchanges for.' Now, if there is any fact certain 
 about exchange value, it is, that it means not an 
 object at all, but a circumstance of an object. 
 Value implies, in fact, a relation ; but if so, it 
 cannot jiossibly be some other thing. A student of 
 Economics has no hope of ever being clear and 
 correct in his ideas of the science if he thinks of 
 value as at all a thi7ig or an object, or even as 
 anything which lies in a thing or object. Persons 
 are thus led to sj^eak of such a nonentity as 
 intrinsic value. There are, doubtless, qualities 
 inherent in such a substance as gold or iron which 
 influence its value ; but the word Value, so far as 
 it can be correctly used, merely expresses the 
 
 ^ ' Principles of Political Economy,' book iii. chap. 6. 
 G 2
 
 84 The Theory of Political Economy. 
 
 circumstance of its exchanging in a certain ratio for 
 some other substance. 
 
 Value expresses Ratio of Exchange. 
 
 If a ton of pig-iron exchanges in a market for an 
 ounce of standard gold, neither the iron is value, 
 nor the gold ; nor is there value in the iron nor in 
 the gold. The notion of value is concerned only in 
 the fact or circumstance of one exchanging for the 
 other. Thus it is scientifically incorrect to say 
 that the value of the ton of iron is the ounce of 
 gold : we thus convert value into a concrete thing ; 
 and it is, of course, equally incorrect to say that 
 the value of the ounce of gold is the ton of iron. 
 The more correct and safe expression is, that the 
 value of the ton of iron is equal to the value of the 
 ounce of gold, or that their values are as one to 
 one. 
 
 Value in exchange expresses nothing but a 
 ratio, and the term should not be used in any other 
 sense. To speak simply of the value of an ounce 
 of gold is as absurd as to speak of the ratio of the 
 numher seventeen. What is the ratio of the number 
 seventeen ? The question admits no answer, for 
 there must be another number named in order to 
 make a ratio ; and the ratio will differ according to 
 the number suggested. What is the value of iron 
 compared with that of gold? — is an intelligible
 
 Theory of Exchange. 85 
 
 question. Tlie answer consists in stating the ratio 
 of the quantities exchanged. 
 
 Popular use of the term Value. 
 
 In the popular use of the word vahie no less 
 than three distinct though connected meanings 
 seem to be confused together. These may be 
 described as 
 
 (1) Value in use ; 
 
 (2) Esteem, or urgency of desire; 
 
 (3) Ratio of exchange. 
 
 Adam Smith, in the familiar passage already 
 referred to, distinguished between the first and the 
 third meanings. He said ^ ' The word value, it is 
 to be observed, has two different meanings, and 
 sometimes expresses the power of purchasing other 
 goods which the possession of that object conveys. 
 The one may be called " value in use ; " the other 
 " value in exchange." The things which have the 
 greatest value in use have frequently little or no 
 value in exchange; and, on the contrary, those 
 which have the greatest value in exchange have 
 frequently little or no value in use. Nothing is 
 more useful than water : but it will purchase 
 scarce anything; scarce anything can be had in 
 exchange for it. A diamond, on the contrary, has 
 scarce any value in use ; but a very great quantity 
 
 c ' "Wealth of Nations,' book i. chap. 4, near the end.
 
 86 Tlic Theory of Political Economy. 
 
 of otlier goods may frequently be had in exchange 
 for it.' 
 
 It is sufficiently plain that, when Smith speaks 
 of water as being highly useful and yet devoid 
 of purchasing power, he means ivater in abundance, 
 that is to say, water so abundantly supplied that it 
 has exerted its full useful effect, or its total utility. 
 Water, v/hen it becomes very scarce, as in a dry 
 desert, acquires exceedingly great purchasing 
 power. Thus Smith evidently means by value in 
 use, the total utility of a substance of vjhich the degree 
 of utility has sunk very loiv, because the ivant of such 
 substance has been well nigh satisfied. By purchas- 
 ing power he clearly means the ratio of exchange for 
 other commodities. But here he fails to point out 
 that the quantity of goods received in exchange 
 depends just as much upon the nature of the goods 
 received, as on the nature of those given for them. 
 In exchange for a diamond we can get a great 
 quantity of iron, or corn, or paving stones, or other 
 commodity of which there is abundance; but we 
 can get very few rubies, sapphires, or other 
 precious stones. Silver is of high purchasing 
 powTr compared with zinc, or lead, or iron, but of 
 small purchasing power compared with gold, 
 platinum, or iridium. Yet we might well say in 
 any case that diamond and silver are things of high 
 value. Thus I am led to think that the word 
 value is often used in reality to mean intensity of
 
 Theory of Exchange. 87 
 
 desire or esteem for a thing. A silver ornament is 
 a beantiful object apart from all ideas of traffic ; 
 it may thns be valued or esteemed simply because 
 it suits the taste and fancy of its owner, and is the 
 only one possessed. Even Robinson Crusoe must 
 have looked upon each of his possessions with vary- 
 ing esteem and desire for more, although he was 
 incapable of exchanging with any other person. 
 Now, in this sense value seems to be identical with 
 the final degree of utility of a commodity, as 
 defined in a previous page (p. 53) ; it is measured 
 by the intensity of the pleasure or benefit which 
 would be obtained from a new increment of the 
 same commodity. No doubt there is a close 
 connection between value in this meaning, and 
 value as ratio of exchange. Nothing can have 
 a high purchasing power unless it be highly 
 esteemed in itself; but it may be highly esteemed 
 apart from all comparison with other things ; and, 
 though highly esteemed, it may have a low 
 purchasing power, because those things against 
 which it is measured, are still more esteemed. 
 
 Thus I come to the conclusion that, in the use 
 of the word value, three distinct meanings are 
 habitually confused together, and require to be 
 thus distinguished — 
 
 (1) Value in use = total utility; 
 
 (2) Esteem = final degree of utility ; 
 
 (3) Purchasing poAver = ratio of exchange.
 
 88 The Theory of Political Economy. 
 
 It is not to be expected that we could profitably 
 discuss such matters as economical doctrines, while 
 the fundamental ideas of the subject are thus 
 jumbled up together in one ambiguous word. The 
 only thorough remedy consists in substituting for 
 the dangerous name value that one of three stated 
 meanings which is intended in each case. In this 
 work, therefore, I shall discontinue the use of the 
 word value altogether, and when, as will be most 
 often the case, in the remainder of the book, I need 
 to refer to the third meaning, often called by 
 economists exchayige or excliangeahle value, I shall 
 substitute the wholly unequivocal expression Ratio 
 of Exchange, specifying at the same time what are 
 the two articles exchanged. When we speak of the 
 ratio of exchange of pig-iron and gold, there can be 
 no possible doubt that we intend to refer to the 
 ratio of the number of units of the one commodity 
 to the number of units of the other commodity for 
 which it exchanges, the units being arbitrary 
 concrete magnitudes, but the ratio an abstract 
 number. 
 
 When I proposed, in the first edition of this 
 book, to use Ratio of Exchange instead of the word 
 value, the expression had been so little, if at all, 
 employed by English economists, that it amounted 
 to an innovation. J. S. Mill, indeed, in his chapters 
 on Value, speaks once and again of things exchang- 
 ing for each other 'in the ratio of their cost of
 
 Theory of Exchange. 89 
 
 production ; ' but lie always omits to say distinctly 
 that exchange value is itself a matter of ratio. As 
 to Ricardo, Malthus, Adam Smith, and other great 
 English economists, although they usually dis- 
 course at some length upon the meanings of the 
 Avord value, I am not aware that they ever 
 explicitly apply the name ratio to exchange or 
 exchangeable value. Yet ratio is unquestionably 
 the correct scientific term, and the only term 
 which is strictly and entirely correct. 
 
 It is interesting, therefore, to find that, although 
 overlooked by English economists, the expression 
 had been used by two or more of the truly 
 scientific French economists, namely Le Trosne 
 and Condillac. Le Trosne carefully defines value 
 in the following terms ^^ — ' La valeur consiste dans 
 le rapport d'echange qui se trouve entre telle chose 
 et telle autre, entre telle mesure d'une production 
 et telle mesure des autres.' Condillac apparently 
 adopts the words of Le Trosne, saying © of value, 
 ' Qu'elle consiste dans le rapport d'echange entre 
 telle chose et telle autre.' Such economical works 
 as those of Baudeau, Le Trosne, and Condillac w^re 
 almost w^holly unknown to English readers until 
 attention was drawn to them by Mr. H. D. Macleod 
 
 d ' De I'lnt^ret Social,' 1777, chap. 1. § 4. 
 
 *^ 'Le Commerce et le Gouvernenicnt,' 1776 ; ' (Euvres Completes 
 de Comlillac,' 1803, Tom. 6"»c, p. 20.
 
 90 Tlie Theory of Political Economy. 
 
 and Professor Adamson ; but I shall endeavour for 
 the future to make proper use of them. 
 
 Dimension of Value. 
 
 There is no difficulty in seeing that, when we 
 use the word Value in the sense of ratio of 
 exchange, its dimension will be simply zero. 
 Value will be expressed, like angular magnitude 
 and other ratios in general, by abstract number. 
 Angular magnitude is measured by the ratio of 
 a line to a line, the ratio of the arc subtended 
 by the angle to the radius of the circle. So value 
 in this sense is a ratio of the quantity of one 
 commodity to the quantity of some other com- 
 modity exchanged for it. If we compare the 
 commodities simply as physical quantities, we have 
 the dimensions M divided by M, or MM \ or M°. 
 Exactly the same result would be obtained if, 
 instead of taking the mere physical quantities, we 
 were to compare their utilities, for we should then 
 have MU divided by MU or M°U°, which, as it really 
 means unity, is identical in meaning with M°. 
 
 When we use the word value in the sense of 
 esteem, or m-gency of desire, the feeling with which 
 Oliver Twist must have regarded a few more 
 mouthfuls when he ' asked for more,' the meaning 
 of the word, as already explained, is identical with 
 degree of utility, of which the dimension is U. 
 
 fl
 
 Thcoru of Exchange. 91 
 
 Lastly, the value in use of Adam Smith or the total 
 utility, is the integral of U d M, and has the dimen- 
 sions MU. We may thus tabulate our results 
 concerning the ambiguous uses of the word value — 
 
 Popular Expression of Meaning. 
 
 Scientific Expression. 
 
 Dimensions, 
 
 (1) Value in use 
 
 Total Utility 
 
 . . MU. 
 
 (2) Esteem, or Urgency 
 
 
 
 of Desire for more 
 
 Final Degree of Utility 
 
 . . U. 
 
 (3) rurchasing Power 
 
 Ratio of Exchange 
 
 . . M°. 
 
 Dejinition of Marhei. 
 
 Before proceeding to the Theory of Exchange, it 
 will be desirable to place beyond doubt the mean- 
 ings of two other terms which I shall frequently 
 employ. 
 
 By a Market I shall mean much what conmiercial 
 men use it to express. Originally a market was 
 a public place in a town where provisions and 
 other objects were exposed for sale ; but the word 
 has been generalised, so as to mean any body 
 of persons who are in intimate business relations 
 and carry on extensive transactions in any commo- 
 dity. A great city may contain as many markets 
 as there are important branches of trade, and these 
 markets may or may not be localised. The central 
 point of a market is the public exchange, — mart 
 or auction rooms, where the traders agree to 
 meet and transact business. In London, the Stock 
 Market, the Corn Market, the Coal Market, the
 
 92 The Theory of Political Economy. 
 
 Sugar Market, and many others, are distinctly 
 localised ; in Manchester, the Cotton Market, the 
 Cotton Waste Market, and others. But this dis- 
 tinction of locality is not necessary. The traders 
 may be spread over a whole town, or region of 
 country, and yet make a market, if they are, by 
 means of fairs, meetings, published price lists, the 
 post office, or otherwise, in close communication 
 with each other. Thus, the common expression 
 Money Market denotes no locality : it is applied to 
 the aggregate of those bankers, capitalists, and 
 other traders wdio lend or borrow money, and who 
 constantly exchange information concerning the 
 course of business f. 
 
 In Economics we may usefully adopt this term 
 with a clear and well-defined meaning. By a 
 market I shall mean two or more persons dealing 
 in two or more commodities, whose stocks of those 
 commodities and intentions of exchanging are 
 known to all. It is also essential that the ratio 
 of exchange between any two persons should be 
 
 f T find that Cournot has long since defined the economical use 
 of the word market, with admirable brevity and precision, but 
 exactly to the same effect as the text above. He incidentally says in a 
 footnote (' R^cherches sur les Principes Math^matiques de la Theorie 
 des Eichesses/ Paris, 1838, p. 55), ' On sait que les ^conomistes en- 
 tendent par marche, non pas un lieu d^termin^ ou se consomment 
 les achats et les ventes, mais tout un territoire dont les parties sont 
 unies par des rapports de libre commerce, en sorte que les prix s'y 
 nivellent avcc facility et promptitude.'
 
 Theory of Exchange. 93 
 
 known to all the others. It is only so far as this 
 commiinitj of knowledge extends that the market 
 extends. Any persons who are not acquainted at 
 the moment with the prevailing ratio of exchange, 
 or whose stocks are not available for want of com- 
 munication, must not be considered part of the 
 market. Secret or unknown stocks of a commo- 
 dity must also be considered beyond reach of 
 a market so long as they remain secret and un- 
 known. Every individual must be considered as 
 exchanging from a pure regard to his own require- 
 ments or private interests, and there must be 
 perfectly free competition, so that any one will 
 exchange with any one else for the slightest appa- 
 rent advantage. There must be no conspiracies for 
 absorbing and holding supplies to produce un- 
 natural ratios of exchange. Were a conspiracy 
 of farmers to withhold all corn from market, the 
 consumers might be driven, by starvation, to pay 
 prices bearing no proper relation to the existing 
 supplies, and the ordinary conditions of the market 
 "would be thus overthrown. 
 
 The theoretical conception of a perfect market 
 is more or less completely carried out in practice. 
 It is the work of brokers in any extensive market 
 to organise exchange, so that every purchase shall 
 be made with the most thorough acquaintance 
 with the conditions of the trade. Each broker 
 strives to gain the best knowledge of the conditions
 
 94 The Theory of Political Economy. 
 
 ot supply and demand, and the earliest intimation 
 of any change. He is in communication with as 
 many other traders as possible, in order to have 
 the widest range of information, and the greatest 
 chance of making suitable exchanges. It is only 
 thus that a definite market price can be ascertained 
 at every moment, and varied according to the fre- 
 quent news capable of affecting buyers and sellers. 
 By the mediation of a body of brokers a complete 
 consensus is established, and the stock of every 
 seller or the demand of every buyer brought into 
 the market. It is of the very essence of trade to 
 have wide and constant information. A market, 
 then, is theoretically perfect only when all traders 
 have perfect knowledge of the conditions of supply 
 and demand, and the consequent ratio of exchange ; 
 and in such a market, as we shall now see, there 
 can only be one ratio of exchange of one uniform 
 commodity at any moment. 
 
 So essential is a knowledge of the real state 
 of supply and demand to the smooth procedure 
 of trade and the real good of the community, that 
 I conceive it would be quite legitimate to compel 
 the publication of any requisite statistics. Secrecy 
 can only conduce to the profit of speculators who 
 gain from great fluctuations of prices. Speculation 
 is advantageous to the public only so far as it tends 
 to equalise prices ; and it is, therefore, against the 
 public good to allow speculators to foster artifi-
 
 Theory of Exchange. 95 
 
 cially the inequalities of prices by which they 
 profit. Tlie welfare of millions both of consumers 
 and producers depends upon an accurate know- 
 ledge of the stocks of cotton and corn ; and it 
 would, therefore, be no unwarrantable interference 
 with the liberty of the subject to require any infor- 
 mation as to the stocks in hand. In Billingsgate 
 fish market there was long ago a regulation to the 
 effect that salesmen shall fix up in a conspicuous 
 place every morning a statement of the kind and 
 amount of their stocks*. The same principle has 
 long been recognised in the Acts of Parliament 
 concerning the collection of statistics of the quan- 
 tities and prices of corn sold in English market 
 toAvns. More recently similar legislation has taken 
 place as regards the cotton trade, in the Cotton 
 Statistics Act of 1868. Publicity, whenever it can 
 thus be enforced on markets by public authority, 
 tends almost always to the advantage of everybody 
 except perhaps a few speculators and financiers. 
 
 Definition of Trading Body. 
 
 1 find it necessary to adopt some expression for 
 any number of people whose aggregate influence 
 in a market, either in the way of supj^ly or demand, 
 we have to consider. By a trading body I mean, in 
 the most general manner, any body either of buyers 
 
 s Waterston's ' Cyclopaedia of Commerce,' ed. 1846, ]). 466.
 
 96 The Theory of Political Economy. 
 
 or sellers. The trading body ma}^ be a single indi- 
 vidual in one case; it may be the whole inhabitants 
 of a continent in another ; it may be the indivi- 
 duals of a trade diffused through a country in a 
 third. England and North America will be trading 
 bodies if we are considering the corn we receive 
 from America in exchange for iron and other 
 goods. The continent of Europe is a trading body 
 as purchasing coal from England. The farmers 
 of England are a trading body when they sell 
 corn to the millers, and the millers both when they 
 buy corn from the farmers and sell flour to the 
 bakers. 
 
 We must use the expression with this wide 
 meaning, because the principles of exchange are 
 the same in nature, however wide or narrow may 
 be the market considered. Every trading body 
 is either an individual or an aggregate of indivi- 
 duals, and the law, in the case of the aggregate, 
 must depend upon the fulfilment of law in the 
 individuals. We cannot usually observe any pre- 
 cise and continuous variation in the wants and 
 deeds of an individual, because the action of extra- 
 neous motives, or what would seem to be caprice, 
 overwhelms minute tendencies. As I have already 
 remarked (p. 17), a single individual does not vary 
 his consumption of sugar, butter, or eggs from 
 week to week by infinitesimal amounts, according 
 to each small change in the price. He probably
 
 Theory of Exchange. 97 
 
 continues his ordinary consumption until accident 
 directs his attention to a rise in price, and he then, 
 perhaps, discontinues the use of the articles alto- 
 gether for a time. But the aggregate, or what is 
 the same, the average consumption, of a large com- 
 munity will be found to vary continuously or 
 nearly so. The most minute tendencies make 
 themselves apparent in a wide average. Thus, our 
 laws of Economics will be theoretically true in the 
 case of individuals, and practically true in the 
 case of large aggregates; but the general princi- 
 ples will be the same, whatever the extent of the 
 trading' body considered. We shall be justified, 
 then, in using the expression with the utmost 
 generality. 
 
 It should be remarked, however, that the econo- 
 mical laws representing the conduct of large aggre- 
 gates of individuals will never represent exactly 
 the conduct of any one individual. If we could 
 imagine that there were a thousand individuals 
 all exactly alike in regard to their demand for 
 commodities, and their capabilities of supplying 
 them, then the average laws of supply and demand 
 deduced from the conduct of such individuals 
 would agree with the conduct of any one indivi- 
 dual. But a community is composed of persons 
 differing widely in their powers, wants, habits, and 
 possessions. In such circumstances the average 
 laws applying to tliem will come under what I have 
 
 H
 
 98 The Tlieory of Political Economy. 
 
 elsewhere ^^ called the ' Fictitious Mean/ that is to 
 say, they are numerical results which do not 
 pretend to represent the character of any existing 
 thing. But average laws Avould not on this account 
 be less useful, if we could obtain them; for the 
 movements of trade and industry depend upon 
 averages and aggregates, not upon the whims of 
 individuals. 
 
 The Lmo of Indifference. 
 
 When a commodity is perfectly uniform or homo- 
 geneous in quality, any portion may be indif- 
 ferently used in place of an equal portion : hence, 
 in the same market, and at the same moment, all 
 portions must be exchanged at the same ratio. 
 There can be no reason why a person should treat 
 exactly similar things differently, and the slightest 
 excess in what is demanded for one over the other 
 will cause him to take the latter instead of the 
 former. In nicely-balanced exchanges it is a very 
 minute scruple which turns the scale and governs 
 the choice. A minute difference of quality in 
 a commodity may thus give rise to preference, and 
 cause the ratio of exchange to differ. But where 
 no difference exists at all, or where no difference 
 is known to exist, there can be no ground for 
 preference whatever. If, in selling a quantity of 
 
 1» 'Principles of Science,' 1st ed. vol. i. p. 422, 3nl ed. p. 363.
 
 Theory of Exchange. 99 
 
 perfectly equal and uniform barrels of flour, a mer- 
 chant arbitrarily fixed different prices on them, 
 a purchaser would of course select the cheaper 
 ones ; and where there was absolutely no difference 
 in the thing purchased, even an excess of a penny 
 in the price of a thing worth a thousand pounds 
 would be a valid ground of choice. Hence follows 
 what is undoubtedly true, with proper explanations, 
 that in the same open market, at any one moment, 
 there cannot he two ^jrices for the same hind of 
 ajiicle. Such differences as may practically occur 
 arise from extraneous circumstances, such as the 
 defective credit of the purchasers, their imperfect 
 knowledge of the market, and so on. 
 
 The principle above expressed is a general law 
 of the utmost importance in Economics, and I pro- 
 pose to call it The Laiv of Indifference, meaning 
 that, when two objects or commodities are subject 
 to no important difference as regards the purpose 
 in view, they will either of them be taken instead 
 of the other with perfect indifference by a pur- 
 chaser. Every such act of indifferent choice gives 
 rise to an equation of degrees of utility, so that 
 in this principle of indifference we have one of 
 the central pivots of the theory. 
 
 Though the price of the same commodity must 
 be uniform at any one moment, it may vary from 
 moment to moment, and must be conceived as in 
 a state of continual cliange. Theoretically speaking, 
 
 H 2
 
 100 The Theojy of Political Economy. 
 
 it would not usually be possible to buy two por- 
 tions of the same commodity successively at the 
 same ratio of exchange, because, no sooner would 
 the first portion have been bought, than the condi- 
 tions of utility would be altered. When exchanges 
 are made on a large scale, this result will be veri- 
 fied in practice i. If a wealthy person invested 
 £100,000 in the funds in the morning, it is hardly 
 likely that the operation could be repeated in the 
 afternoon at the same price. In any market, if 
 a person goes on buying largely, he will ultimately 
 raise the price against himself. Thus it is apparent 
 that extensive purchases would best be made gra- 
 dually, so as to secure the advantage of a lower 
 price upon the earlier portions. In theory this 
 effect of exchange upon the ratio of exchange must 
 be conceived to exist in some degree, however 
 small may be the purchases made. Strictly speak- 
 ing, the ratio of exchange at any moment is that 
 of dy to dx, of an infinitely small quantity of one 
 commodity to the infinitely small quantity of 
 
 > It is, I believe, verified in the New York Stock Markets, where 
 it is the practice to sell Stocks by auction in successive lots, with- 
 out disclosing the total amount to be put up. "When the amount 
 offered begins to exceed what was expected, then each successive 
 lot brings a less price, and those who bought the earlier lots 
 suffer. But if the amount offered is small, tlie early buyers have 
 the advantage. Such an auction sale only exhibits in miniature 
 what is constantly going on in the markets generally on a large 
 scale,
 
 Theory of Exchange. 101 
 
 another which is given for it. The ratio of ex- i 
 change is really a differential coefficient. The 
 quantity of any article purchased is a function of 
 the price at which it is purchased, and the ratio 
 of exchange expresses the rate at which the quan- 
 tity of the article increases compared with what 
 is given for it. 
 
 We must carefully distinguish, at the same time, | 
 between the Statics and Dynamics of this subject. }■ 
 The real condition of industry is one of perpetual \ 
 motion and change. Commodities are being con-' 
 tinually manufactured and exchanged and con-^ 
 sumed. If we wished to have a complete solution j 
 of the problem in all its natural complexity, wej 
 should have to treat it as a problem of motion — a | 
 problem of dynamics. But it w^ould surely be; 
 absurd to attempt the more difficult question when ;■ 
 the more easy one is yet so imperfectly within our 
 power. It is only as a purely statical problem that ; 
 I can venture to treat the action of exchange. 
 Holders of commodities will be regarded not as 
 continuously passing on these commodities in 
 streams of trade, but as possessing certain fixed 
 amounts which they exchange until they come to 
 equilibrium. 
 
 It is much more easy to determine the point at 
 which a pendulum will come to rest than to cal- 
 culate the velocity at which it will move when 
 displaced from that point of rest. Just so, it is a
 
 102 The Theory of Political Economy. 
 
 far more easy task to lay down the conditions 
 under which trade is completed and interchange 
 ceases, than to attempt to ascertain at what rate 
 trade will go on when equilibrium is not attained. 
 
 The difference will present itself in this form : 
 dynamically we could not treat the ratio of ex- 
 change otherwise than as the ratio of dy and dx, 
 infinitesimal quantities of commodity. Our equa- 
 tions would then be regarded as differential equa- 
 tions, which would have to be integrated. But 
 in the statical view of the question we can sub- 
 stitute the ratio of the finite quantities y and x. 
 Thus, from the self-evident principle, stated on 
 pp. 98-99, that there cannot, in the same market, 
 at the same moment, be two different prices for 
 the same uniform commodity, it follows that the 
 last increments in an act of exchange must he ex- 
 changed in the same ratio as the lohole quantities 
 exchanged. Suppose that two commodities are 
 bartered in the ratio of x for y; then every m*^ 
 part of X is given for the m^^ part of y, and it does 
 not matter for which of the m^^ parts. No part of 
 the commodity can be treated differently to any 
 other part. We may carry this division to an in- 
 definite extent by imagining m to be constantly 
 increased, so that, at the limit, even an infinitely 
 small part of x must be exchanged for an infinitely 
 small part of y, in the same ratio as the whole 
 quantities. This result we may express by stating
 
 Theory of Exchange. 103 
 
 that the increments concerned in the process of 
 exchange must obey the equation 
 
 The use which we shall make of this equation 
 will be seen in the next section. 
 
 The Theory of Exchange. 
 
 The keystone of the whole Theory of Exchange, 
 and of the principal problems of Economics, lies 
 in this projiosition — The ratio of exchange of any 
 tivo commodities will he the reciprocal of the ratio of^ 
 the final degrees of utility of the quantities of com- 
 modity available for consum]}tion after the exchange 
 is completed. When the reader has reflected a little 
 upon the meaning of this proposition, he will see, I 
 think, that it is necessarily true, if the principles of 
 human nature have been correctly represented in 
 previous pages. 
 
 Imagine that there is one trading body possessing 
 only corn, and another possessing only beef. It is 
 certain that, under these circumstances, a portion 
 of the corn may be given in exchange for a por- 
 tion of the beef with a considerable increase of 
 utility. How are we to determine at what point 
 the exchange will cease to be beneficial? This 
 question must involve both the ratio of exchange 
 and the degrees of utility. Suppose, for a moment,
 
 104 The Thtory of Political Economy. 
 
 that the ratio of exchange is approximately that 
 of ten pounds of corn for one pound of beef: then 
 if, to the trading body whicli possesses corn, ten 
 pounds of corn are less useful than one of beef, 
 that body will desire to carry the exchange further. 
 Should the other body possessing beef find one 
 pound less useful than ten pounds of corn, this 
 body will also be desirous to continue the ex- 
 change. Exchange will thus go on until each 
 party has obtained all the benefit that is possible, 
 and loss of utility would result if more were ex- 
 changed. Both parties, then, rest in satisfaction 
 and equilibrium, and the degrees of utility have 
 come to their level, as it were. 
 
 This point of equilibrium will be known by the 
 criterion, that an infinitely small amount of com- 
 modity exchanged in addition, at the same rate, 
 will bring neither gain nor loss of utility. In 
 other words, if increments of commodities be ex- 
 changed at the established ratio, their utilities will 
 be equal for both parties. Thus, if ten pounds of 
 corn were of exactly the same utility as one pound 
 of beef, there would be neither harm nor good in 
 further exchange at this ratio. 
 
 It is hardly possible to represent this theory 
 completely by means of a diagram, but the accom- 
 panying figure may, perhaps, render it clearer. 
 Suppose the line pqr to be a small portion of the 
 i-»K6^^Jburve of utility of one commodity, while the broken
 
 Theory of Exchange. 
 
 105 
 
 line pqr is the like curve of another commodity 
 which has been reversed and superposed on the 
 other. Owing- to this reversal, the quantities of 
 the first commodity are measured along the base 
 
 lYgV: 
 
 line from a towards h, whereas those of the second 
 must be measured in the opposite direction. Let 
 units of both commodities be represented by equal 
 lengths: then the little line da indicates an in- 
 crease of the first commodity, and a decrease of 
 the second. Assume the ratio of exchange to be 
 that of unit for unit, or 1 to 1 : then, by receiving 
 the commodity a a the person will gain the utility 
 ad, and lose the utility dc\ or he will make a net 
 gain of the utility corresponding to the mixtilinear 
 figure cd. He will, therefore, wish to extend the 
 exchange. If he were to go up to the point 6', 
 and were still proceeding, he would, by the next 
 small exchange, receive the utility he, and part 
 with h'f ; or he Avould have a net loss of ef. He 
 would, therefore, have gone too far ; and it is 
 pretty obvious that the point of intersection, q.
 
 106 The Theory of Folitlcal Ecoyioiny. 
 
 defines the place where he would stop with the 
 greatest advantage. It is there that a net gain 
 is converted into a net loss, or rather where, for 
 an infinitely small quantity, there is neither gain 
 nor loss. To represent an infinitely small quantity, 
 or even an exceedingly small quantity, on a dia- 
 gram is, of course, impossible ; but on either side 
 of the line 7nq I have represented the utilities of a 
 small quantity of commodity more or less, and it 
 is apparent that the net gain or loss upon the 
 exchange of these quantities would be trifling. 
 
 Symholic Statement of the Theory. 
 
 To represent this process of reasoning in sym- 
 bols, let AX denote a small increment of corn, 
 and A 2/ a small increment of beef exchanged for 
 it. Now our Law of Indiflference comes into play. 
 As both the corn and the beef are homogeneous 
 commodities, no parts can be exchanged at a dif- 
 ferent ratio from other parts in the same market : 
 hence, if x be the whole quantity of corn given 
 for y, the whole quantity of beef received, a 2/ 
 must have the same ratio to ax ^^ y to x; we 
 have then, 
 
 a y y y 
 
 — ^ = s^, or A y = ^ A a?. 
 
 AX X X 
 
 In a state of equilibrium, the utilities of these 
 increments must be equal in the case of each
 
 Theory of Exchange. 107 
 
 party, in order that neither more nor less exchange 
 would be desirable. Now the increment of beef, 
 
 A 2/, is - times as great as the increment of corn, 
 
 A.r, so that, in order that their utilities shall be 
 
 equal, the degree of utility of beef must be - 
 
 times as great as the degree of utility of corn. 
 Thus we arrive at the principle that the degrees 
 of utility of commodities excha^iged ivill he in the 
 inverse proportion of the magnitudes of the incre- 
 ments exchanged. 
 
 Let us now suppose that the first body, A, ori- 
 ginally possessed the quantity a of corn, and that 
 the second body, B, possessed the quantity b of 
 beef. As the exchange consists in giving x of corn 
 for y of beef, the state of things after exchange will 
 be as follows : — 
 
 A holds ct — x of corn, and y of beef. 
 
 B holds x of corn, and h — y of beef. 
 Let <^i {a — x) denote the final degree of utility of 
 corn to A, and (p^x the corresponding function 
 for B. Also let y^r^y denote A's final degree of 
 utility for beef, and ^2(^-y) B's similar func- 
 tion. Then, as explained on p. 104, A will not 
 be satisfied unless the following equation holds 
 
 true — 
 
 ^1 {a — x).dx = ^iy.dy; 
 
 Qj. (/>! (a-x) ^dy^ 
 yfr^y dx
 
 108 The Theory of Political Economy. 
 
 Hence, substituting for the second member by the 
 equation given on p. 103, we have 
 
 What holds true of A will also hold true of B, 
 mutatis mutandis. He must also derive exactly 
 equal utility from the final increments, otherwise 
 it will be for his interest to exchange either more 
 or less, and he will disturb the conditions of ex- 
 change. Accordingly the following equation must 
 hold true — 
 
 or, substituting as before, 
 
 We arrive, then, at the conclusion, that whenever 
 two commodities are exchanged for each other, and 
 
 more or less can he given or received in infinitely 
 
 small quantities, the quantities exchanged satisfy 
 
 two equations, which may be thus stated in a 
 
 concise form — 
 
 ^1 {a — a?) y ^ cp.^^ 
 
 The two equations are sufficient to determine the 
 results of exchange; for there are only two un- 
 known quantities concerned, namely, x and i/, the 
 quantities given and received. 
 
 A vague notion has existed in the minds of
 
 Theory of Excha7ige. 109 
 
 economical writers, that the conditions of ex- 
 change may he expressed in the form of an 
 equation. Thus, J. S. Mill has saidk; 'Xhe idea 
 of a ratio, as between demand and supply, is out 
 of place, and has no concern in the matter: the 
 proper mathematical analogy is that of an equation. 
 Demand and supply, the quantity demanded and 
 the quantity supplied, Avill be made equal.' Mill 
 here speaks of an equation as only a proper mathe- 
 matical analogy. But if Economics is to be a real 
 science at all, it must not deal merely with analo- 
 gies ; it must reason by real equations like all the 
 other sciences which have reached at all a sys- 
 tematic character. Mill's equation, indeed, is not 
 explicitly the same as any at which we have arrived 
 above. His equation states that the quantity of 
 a commodity given by A is equal to the quantity 
 received by B. This seems at first sight to be 
 a mere truism, for this equality must necessarily 
 exist if any exchange takes place at all. The 
 theory of value, as expounded by Mill, fails to 
 reach the root of the matter, and show how the 
 amount of demand or supply is caused to vary. 
 And Mill does not perceive that, as there must be 
 two parties and two quantities to every exchange, 
 there must be two equations. 
 
 Nevertheless, our theory is perfectly consistent 
 with the laws of supply and demand ; and if we 
 
 ^ ' Principles of Political Econom},' book iii. chap. 2, § 4,
 
 110 The Theory of Political Economy. 
 
 had the functions of utility determined, it would 
 he possible to throw them into a form clearly ex- 
 pressing the equivalence of snpply and demand. 
 We may regard x as the quantity demanded on one 
 side and supplied on the other ; similarly, y is the 
 quantity supplied on the one side and demanded 
 on the other. Now, when we hold the two equa- 
 tions to be simultaneously true, we assume that 
 the X and y of one equation equal those of the 
 other. The laws of supply and demand are thus 
 a result of what seems to me the true theory of 
 value or exchange. 
 
 Analogy to the Theory of the Lever. 
 
 I have heard objections made to the general 
 character of the equations employed in this book. 
 It is remarked that the equations in question con- 
 tinually involve infinitesimal quantities, and 3^et 
 they are not treated as differential equations 
 usually are, that is integrated. There is, indeed, 
 no reason why the process of integration should 
 not be applied when it is required, and I will 
 here show that the equations employed do not 
 differ in general character from those which are 
 really treated in many branches of physical science. 
 Whenever, in fact, we deal with continuously vary- 
 ing quantities, the ultimate equations must lie 
 between infinitesimals. The process of integration,
 
 Theory of Exchange. Ill 
 
 if I understand the matter aright, only ascertains 
 other equations, the truth of wliich follows from 
 the fundamental differential equation. 
 
 The mode in which mechanics is usually treated 
 in elementary works tends to disguise the real 
 foundation of the science which is to be found in 
 the so-called theoiy of virtual velocities. Let us take 
 the description of the lever of the first order as 
 it is given in some of the best modern elementary 
 works, as, for instance, in ^Mr. Magnus' ' Lessons in 
 Elementary Mechanics/ p. 128. We here read as 
 follows : — 
 
 *Let 4-B be a lever turning freely about C, the 
 
 fulcrum, and let P be the force applied at A, and 
 
 W the force exerted, or resistance overcome, or 
 
 weight raised at B. Suppose the lever turned 
 
 through the angle AC A', then the work done by 
 
 P equals P xarc^l^', and Avork done by IF equals 
 
 W X arc BB\ if P and W act perpendicularly to 
 
 the arm. Therefore, by the law of energy, 
 
 A A' AC 
 P xAA'=W X BB', and since -yjtj, = -^777 we have 
 
 PxAC=WxBC, 
 or, P X its arm = W x its arm.' 
 Now, in such a statement as this, we seem to be 
 dealing with plain finite quantities, and there is no 
 apparent difficulty in the matter. In reality the 
 difficulty is only disguised by assuming that P and 
 W act perpendicularly to the arm through finite
 
 112 The Theory of Political Economy. 
 
 arcs. This condition is, indeed, carried out with 
 ai^proximate exactness in the problem of the wheel 
 and axlei, which may be regarded as combining 
 together an infinite series of straight levers, coming 
 successively into operation. In this machine, there- 
 fore, the weights, roughly speaking, always act 
 perpendicularly to arms of invariable length. But, 
 in the generality of cases of the lever, the theory 
 is only true for infinitely small displacements, and 
 no sooner has the lever begun to move through any 
 finite arc AA', than it ceases to be exactly true 
 that the work done by P equals P x arc AA'. Never- 
 theless, the theory is quite correct as applied to the 
 lever considered statically, that is, as in a state 
 of rest and equilibrium, because the finite arcs 
 of displacement, when it really is disj^laced, are 
 exactly proportional to the infinitely small arcs, 
 known as virtual velocities, through which it would 
 be displaced, if instead of being at rest, it suffered 
 an infinitely small displacement. 
 
 It is curious, moreover, that, when we take the 
 theory of the lever treated according to the prin- 
 ciple of virtual velocities, we get equations exactly 
 similar in form to those of the theory of value as 
 established above. The general principle of virtual 
 velocities is to the effect that, if any number of 
 forces be in equilibrium at one or more points of 
 a rigid body, and if this body receive an infinitely 
 
 ' See Magnus' 'Lessons,' § 91.
 
 Theory of Exchange. 113 
 
 small displacement, the algebraic sum of the pro- 
 ducts of each force into its displacement is equal 
 to zero. In the case of a lever of the first order, 
 this amounts to saying that one force multiplied 
 into its displacement will be neutralised by the 
 other force multiplied into its negative displace- 
 ment. But inasmuch as the displacements are 
 exactly proportional to the lengths of the arms 
 of the lever, we obtain as a derivative equation, 
 that the forces multiplied each by its own arm are 
 equal to each other. No doubt in the quotation 
 given above, P >iAC=W x BC is an equation be- 
 tween finite quantities; but the real equation 
 derived immediately from the principle of virtual 
 velocities, is P x AA' = W x BB\ in which P and W 
 are finite, but A A' and BB' are in strictness infi- 
 nitely small displacements. Let us Avrite this 
 
 W AA' 
 equation in the form^-i=^^; then as we also 
 
 , AA' AC 1 ^-^ . 1 W AC 
 
 nave ^-^ = ytp^ we can substitute ; hence -pc _ 7^-^. 
 
 I dwell upon this matter at some length because 
 we here have exactly the forms of the equations of 
 exchange. As we have seen, the original equation 
 
 is of the general form %~ = ~, where (bx and ^ly 
 
 y^y ax ^ ^ 
 
 represent finite expressions for the degrees of 
 utility of the commodities Y and A^, as regards 
 some individual, and dy and dx are infinitesimal 
 
 I
 
 114 The Theory of Political Economy. 
 
 quantities of those commodities exchanged. But 
 these infinitesimals may in this case at least be 
 eliminated, because, in virtue of the Law of In- 
 difference, they ai'e exactly proportional to the 
 whole finite quantities exchanged. Hence for 
 
 V^ we substitute ^. We may write the equations 
 dx X 
 
 so as to make the analogy 
 
 X 
 
 one below the other 
 
 visible — thus 
 
 W 
 P 
 
 AA'_AC 
 BB'~ BC 
 
 (px 
 
 dy 
 dx 
 
 To put this analogy of the theories of exchange 
 and of the lever in the clearest possible light, I give 
 below a diagram, in which the several economic 
 qualities are represented by the parts of the dia- 
 gram to which they correspond or are proportional. 
 
 Fig. F«. 
 
 <px 
 
 dx 
 
 ^:-'' ^2/ 
 
 Now in statical problems no such process as in-
 
 Theory of Exchange. 115 
 
 tegration is applicable. The equation lies actually, 
 between imaginary infinitesimal quantities, and 
 there is no effect to be summed up. Yet there is 
 no statical problem which is not subject to the 
 principle of virtual velocities, and Poisson, in his 
 'Traite de Mecanique,' which commences with 
 statical theorems, asserts explicitly ^^^ 'Dans cet 
 ouvrage, j'emploierai exclusivement la methode 
 des infiniment jyetitsJ 
 
 Impediments to Exchange. 
 
 We have hitherto treated the theory of exchange 
 as if the action of exchange could be carried on 
 without trouble or cost. In reality, the cost of 
 conveyance is almost always of importance, and 
 it is sometimes the principal element in the ques- 
 tion. To the cost of mere transport must be 
 added a variety of charges of brokers, agents, 
 packers, dock, harbour, light dues, &c., together 
 with any customs duties imposed either on the 
 importation or exportation of commodities. All 
 these charges, whether necessary or arbitrary, are 
 so many impediments to commerce, and tend to 
 reduce its advantages. The effect of any one such 
 charge, or of the aggregate of the costs of ex- 
 change, can be represented in our formulae in a 
 very simple manner. 
 
 m Seconde Edition, Paris, 1833, § 12, vol. i. p. 14. 
 I 2
 
 116 TJie Theory of Political Economy. 
 
 . In whatever mode the charges are payable, they 
 may be conceived as paid by the surrender on 
 importation of a certain fraction of the commodity 
 received ; for the amount of the charges will usually 
 be proportional to the quantity of goods, and, if 
 expressed in money, can be considered as turned 
 into commodity. 
 
 Thus, if A gives x in exchange, this is not the 
 quantity received by B ; a part of x is previously 
 subtracted, so that B receives say mx, which is 
 less than x, and the terms of exchange must be 
 adjusted on his part so as to agree with this con- 
 dition. Hence the second equation will be 
 
 y (p^imx) 
 
 mx ^2{^—,y) 
 
 Again, A, though giving x, will not receive the 
 whole of y; but say ny, so that his equation 
 similarly will be 
 
 01 (a — cv) _ 7iy 
 
 The result is, that there is not one ratio of ex- 
 change, but two ratios ; and the more these differ, 
 the less advantage will there be in exchange. It 
 is obvious that A has either to remain satisfied 
 with less of the second commodity than before, or 
 has to give more of his own in i^urchasing it. By 
 an obvious transfer of the factors m and n we may
 
 Theory of Exchange. 117 
 
 state the equations of impeded exchange in the 
 concise form — 
 
 (pi [a — A") __y m. (p^ (mx) 
 n.-^i(ny)~ .v~ ^^{h-y) ' 
 
 Illustrations of the Theory of Exchange. 
 
 As stated above, the Theory of Exchange may 
 seem to be of a somewhat abstract and perplexing 
 character ; but it is not difficult to find practical 
 illustrations which will show how it is verified in 
 the actual working of a great market. The ordinary 
 laws of supply and demand, when properly stated, 
 are the practical manifestation of the theory. Con- 
 siderable discussion has taken place concerning 
 these laws, in consequence of Mr. W. T. Thornton's 
 writings upon the subject in the ' Fortnightly 
 Review,' and in his work on the ' Claims of 
 Labour.' Mill, although he had previously declared 
 the Theory of Value to be complete and perfect 
 (see p. 82), was led by Mr. Thornton's arguments to 
 allow that modification was required. 
 
 For my own part, I think that most of Mr. 
 Thornton's arguments are beside the question. He 
 suggests that there are no regular laws of supply 
 and demand, because he adduces certain cases in 
 which no regular variation can take place. Those 
 cases might be indefinitely multiplied, and yet the 
 laws in question would not be touched. Of course,
 
 118 The Theory of Political Economy. 
 
 laws which assume a continuity of variation are 
 inapplicable where continuous variation is impos- 
 sible. Economists can never be free from diffi- 
 culties unless they will distinguish between a 
 theory and the apiolication of a theory. Because, 
 in retail trade, in English or Dutch auction, or 
 other particular modes of traffic, we cannot at 
 once observe the operation of the laws of supply 
 and demand, it is not in the least to be supposed 
 that those laws are false. In fact, Mr. Thornton 
 seems to allow that, if prospective demand and 
 supply are taken into account, they become sub- 
 stantially true. But, in the actual working of 
 any market, the influence of future events should 
 never be neglected, neither by a merchant nor an 
 economist. 
 
 Though Mr. Thornton's objections are mostly 
 beside the question, his remarks liave served to 
 show that the action of the laws of supply and 
 demand was inadequately explained by previous 
 economists. What constitutes the demand and 
 the supply was not carefully enough investigated. 
 As Mr. Thornton points out, there may be a number 
 of persons willing to buy ; but if their highest offer 
 is ever so little short of the lowest price which the 
 seller is willing to take, their influence is nil. If 
 in an auction there are ten j^eople willing to buy a 
 horse at £20, but not higher, their demand in- 
 stantly ceases when any one person offers £21. I
 
 Theory of Exchange. 119 
 
 am inclined not only to accept such a view, but to 
 carry it further. Any change in the price of an 
 article will be determined not with regard to the 
 large numbers who might or might not buy it at 
 other prices, but by the few who will or will not 
 buy it according as a change is made close to the 
 existing price. 
 
 The theory consists in carrying out this view to 
 the point of asserting, that it is only comparatively 
 insignificant quantities of supply and demand which 
 are at any moment operative on the ratio of ex- 
 change. This is practically verified by what takes 
 place in any very large market — say that of the 
 Consolidated Three Per Cent Annuities. As the 
 whole amount of the English funds is nearly eight 
 hundred millions sterling, the quantity bought or 
 sold by any ordinary purchaser is inconsiderably 
 small in comparison. Even £1,000 worth of stock 
 may be taken as an infinitesimally small incre- 
 ment, because it does not appreciably affect the 
 total existing supply. Now the theory consists in 
 asserting that the market price of the funds is 
 affected from hour to hour not by the enormous 
 amounts which might be bought or sold at ex- 
 treme prices, but by the comparatively insigni- 
 ficant amounts which are being sold or bought at 
 the existing prices. A change of 2:>rice is always 
 occasioned by the overbalancing of the inclinations 
 of those who will or will not sell just about the
 
 120 The Theory of Political Economy. 
 
 point at which prices stand. When Consols are 
 at 93i and business is in a tranquil state, it mat- 
 ters not how many buyers there are at 93, or 
 sellers at 94. They are really off the market. 
 Those only are operative who may be made to 
 buy or sell by a rise or fall of an eighth. The 
 question is, whether the price shall remain at 93f, 
 or rise to 93|, or fall to 93|. This is determined 
 by the sale or purchase of comparatively very 
 small amounts. It is the purchasers who find a 
 little stock more profitable to them than the cor- 
 responding sum of money, who make the price 
 rise by |. When the price of the funds is very 
 steady and the market quiescent, it means that 
 the stocks are distributed among holders in such 
 a way that the exchange of more or less at the 
 prevailing price is a matter of indifference. 
 
 In practice, no market ever long fulfils the 
 theoretical conditions of equilibrium, because, from 
 the various accidents of life and business, there are 
 sure to be people every day compelled to sell, or 
 having sudden inducements to buy. There is 
 nearly always, again, the influence of prospective 
 supply or demand, depending upon the political 
 intelligence of the moment. Speculation compli- 
 cates the action of the laws of supply and demand 
 in a high degree, but does not in the least degree 
 arrest their action or alter their nature. We shall 
 never have a Science of Economics unless we learn
 
 llieory of Exchange. 121 
 
 to discern the operation of law even among the 
 most i3erplexing complications and apparent in- 
 terruptions. 
 
 Problems in the Theory of Exchange. 
 
 We have hitherto considered only one simple 
 case of the Theory of Exchange. In all other 
 cases where the commodities are capable of inde- 
 finite subdivision, the principles will be exactly the 
 same, but the particular conditions may be subject 
 to variation. 
 
 We may, firstly, express the conditions of a great 
 market where vast quantities of some stock are 
 available, so that any one small trader will not 
 appreciably affect the ratio of exchange. This 
 ratio is, then, apj)roximately a fixed number, and 
 each trader exchanges at that ratio just so much 
 as suits him. These circumstances may be repre- 
 sented by supposing A to be a trading body pos- 
 sessing two very large stocks of commodities, a 
 and h. Let C be a person who possesses a com- 
 paratively small quantity c of the second com- 
 modity, and gives a portion of it, y, which is very 
 small compared with h, in exchange for a portion x 
 of a, which is very small compared with a. Then, 
 after exchange, we shall find A in possession of 
 the quantities a — x and h + y, and C in possession 
 of X and c — y. The equations will become
 
 122 The Theory of Political Economy. 
 
 Since a — x and h + y, by supjDOsition, do not appre- 
 ciably differ from a and h, we may substitute the 
 latter quantities, and we have, for the first equa- 
 tion, approximately, 
 
 01 a y 
 ^ = ^ = 7n. 
 Yi 6 ^ 
 
 The ratio of exchange being an approximately fixed 
 ratio determined by the conditions of the trading 
 body A, there is, in reality, only one undetermined 
 quantity, x, the quantity of commodity which C 
 finds it advantageous to purchase by expending 
 part of c. This will now be determined by the 
 equation 
 
 (px a <p2^ 
 
 This equation will represent the condition in 
 regard to any one distinct commodity of a very 
 small country trading with a much larger one. It 
 might represent, to some extent, the circumstances 
 of trade between the Channel Islands and the great 
 markets of England, though, of course, it is never 
 absolutely verified, because the smallest purchasers 
 do affect the market in some degree. The equation 
 still more accurately represents the position of an 
 individual consumer with regard to the aggregate 
 trade of a large community, since he must buy at
 
 Theory of Exchange. 123 
 
 the ciiiTent prices, which he cannot in an appre- 
 ciable degree affect. 
 
 A still simpler formula, however, is needed to 
 represent the conditions of a large part of our 
 purchases. In many cases we want so little of a 
 commodity, that an individual need not give more 
 than a very small fraction of his possessions to 
 obtain it. We may suppose, then, that y in the 
 last problem is a very small part of c, so that 
 ■v/^o(c — ?/) does not differ appreciably from -vj^gc. 
 Taking m as before to be the existing ratio of 
 exchange, we have only one equation, 
 
 or (p20c = m.^2<^' 
 
 This means that C will buy of the commodity until 
 its degree of utility falls below that of the com- 
 modity he gives. A person's expenditure on salt 
 is in this country an inconsiderable item of ex- 
 pense; what he thus spends does not make him 
 appreciably poorer ; yet, if the established price or 
 ratio is one penny for each pound of salt, he buys 
 in any time, say one year, so many pounds of salt 
 that an additional pound would not have so much 
 utility to him as a penny. In the above equation 
 m.\j/2C represents the utility to him of a penny, 
 which being an inconsiderable fraction of his pos- 
 sessions, is approximately invariable in utility.
 
 124 The Theory of Political Economy. 
 
 and he buys salt until (p^^x, which is approxi- 
 mately the utility of the next pound, is equal to, 
 or it may be somewhat less than, that of the 
 penny. But this case must not be confused with 
 that of purchases which appreciably affect the pos- 
 sessions of the purchaser. Thus, if a poor family 
 purchase much butchers'-meat, they Avill probably 
 have to go without something else. The more 
 they buy, the lower the final degree of utility of 
 the meat, and the higher the final degree of utility 
 of something else ; and thus these purchases will be 
 the more narrowly limited. 
 
 Complex Cases of the Theory. 
 
 We have hitherto considered the Theory of Ex- 
 change as applying only to two trading bodies pos- 
 sessing and dealing in two commodities. Exactly 
 the same principles hold true, however numerous 
 and complicated may be the conditions. The main 
 point to be remembered in tracing out the results 
 of the theory is, that the same pair of commodities 
 in the same market can have only one ratio of ex- 
 change, which must therefore prevail between each 
 body and each other, the costs of conveyance being 
 considered as nil. The equations become rapidly 
 more numerous as additional bodies or commo- 
 dities are considered ; but we may exhibit them 
 as they apply to the case of three trading bodies 
 and three commodities.
 
 Tlieory of Exchange. 125 
 
 Thus, suppose that 
 A possesses the stock a of cotton, and gives 
 
 x-^ of it to B, x^ to C. 
 B possesses the stock h of silk, and gives 
 
 ?/i to A, y.2 to C. 
 C possesses the stock c of wool, and gives 
 ^i to A, Z.2 to B. 
 
 We have here altogether six unknown quantities 
 
 — a?i, x.2, 1/1, 1/2, 2i, Z.2,; but we have also sufficient 
 means of determining them. They are exchanged 
 as follows — 
 
 A gives Xi for y^, and x.^ for z^. 
 B „ y^ for Xj, and y.2 for 2^2- 
 C „ z^ for X2, and z.^ for y.^. 
 
 These may be treated as independent exchanges; 
 each body must be satisfied in regard to each of 
 its exchanges, and we must therefore take into 
 account the functions of utility or the final de- 
 grees of utility of each commodity in respect of 
 each body. Let us express these functions as 
 follows — 
 
 <^i' "^1' Xi ^1*^ ^^^^ respective functions of 
 utility for A. 
 
 </>2' ^2' X2 ^• 
 
 <^3> ^3. X.3 C. 
 
 Now A, after the exchange, will hold a — x-^—x.^ of 
 cotton and i/^ of silk ; and B will hold x^ of cotton 
 and h — y^ — ?/., of silk : their ratio of exchange,
 
 126 The Theory of Political Economy. 
 
 i/i for a?!, will therefore be governed by the fol- 
 lowing pair of equations — 
 
 ^^1^1 '«'i ^2(^-^1-^/2) 
 
 The exchange of A with C will be similarly de- 
 termined by the ratio of the degrees of utility of 
 wool and cotton on each side subsequent to the 
 exchange; hence we have 
 
 ^1 (a - d\ - ^2) _^i _ <^3 ^2 ^ 
 
 There will also be interchange between B and C 
 which will be independently regulated on similar 
 principles, so that we have another pair of equa- 
 tions to complete the conditions, namely, 
 
 X2 2;2 2/2 X3(C- ^1-2^2) 
 
 We might proceed in the same way to lay down 
 the conditions of exchange between more numerous 
 bodies, but the principles would be exactly the 
 same. For every quantity of commodity which is 
 given in exchange something must be received; 
 and if portions of the same kind of commodity be 
 received from several distinct parties, then we may 
 conceive the quantity which is given for that com- 
 modity to be broken up into as many distinct por- 
 tions. The exchanges in the most complicated case 
 may thus always be decomposed into simple ex- 
 changes, and every exchange will give rise to two
 
 Theory of Exchange. 127 
 
 equations sufficient to determine the quantities 
 involved. The same can also be done when there 
 are two or more commodities in the possession of 
 each trading body. 
 
 Competition in Exchange. 
 
 One case of the Theory of Exchange is of con- 
 siderable importance, and arises when two parties 
 comj^ete together in supplying a third party with 
 a certain commodity. Thus, suppose that A, with 
 the quantity of one commodity denoted by a, pur- 
 chases another kind of commodity both from B 
 and from C, who respectively possess h and c of it. 
 All the quantities concerned are as follows — 
 
 A gives Xi of a to B and x^ to C, 
 B „ y^ of I to A, 
 C „ y-i of c to A. 
 
 As each commodity may be supposed to be per- 
 fectly homogeneous, the ratio of exchange must be 
 the same in one case as in the other, so that we 
 have one equation thus furnished — 
 
 •-^ = -^. (1) 
 
 Now, provided that A gets the right commodity 
 in the proper quantity, he does not care whence 
 it comes, so that we need not, in his equa- 
 tion, distinguish the source or destination of the
 
 128 The Theory of Political Economy. 
 
 quantities ; he simply gives ,?\ + ci\, and receives in 
 exchange 2/1 + 2/2- Observing, then, that by (1) 
 
 .yi+j/2 ^J/i 
 
 we have the usual equation of exchange — 
 
 <p^{a-a^^-,v^ ^2/i (2) 
 
 ^1(^/1+^2) ^\ 
 But B and C must both be separately satisfied 
 with their shares in the transaction. Thus 
 
 ^2{^-J/l) ^Vl' 
 
 <^3-'^2 ^^2_ (4) 
 
 ^3(^-^/2) ^^'2' 
 
 There are altogether four unknown quantities — 
 "^ij ^\^ y\-> yi 5 ^^d we have four equations by which 
 to determine them. Various suppositions might 
 be made as to the comparative magnitudes of the 
 quantities h and c, or the character of the func- 
 tions concerned; and conclusions could then be 
 drawn as to the effect upon the trade. The general 
 result would be, that the smaller holder must more 
 or less conform to the prices of the larger holder. 
 
 Failure of the Equations of Exchange. 
 
 ■ Cases constantly occur in which equations of 
 the kind set forth in the preceding pages fail to 
 hold true, or lead to impossible results. Such
 
 Theory of Exchange. 120 
 
 failure may indicate that no exchange at all takes 
 place, but it may also have a different meaning*. 
 
 In the first case, it may happen that the com- 
 modity possessed by A has a high degree of utility 
 to A, and a low degree to B, and that vice versd 
 B's commodity has a high degree of utility to B 
 and less to A. This diiference of utility might 
 exist to such an extent, that though B were to 
 receive very little of A's commodity, yet the final 
 degree of utility to him Avould be less than that 
 of his own commodity, of Avhich he enjoys much 
 more. In such a case no benefit can arise from 
 exchange, and no exchange will consequently take 
 place. This failure of exchange will be indicated 
 by a failure of the equations. 
 
 It may also happen that the whole quantities 
 of commodity possessed are exchanged, and yet 
 the equations fail. A may have so low a desire 
 for consuming his own commodity, that the very 
 last increment of it has less degree of utility to 
 him than a small addition to the commodity re- 
 ceived in exchange. The same state of things 
 might happen to exist with B as regards his com- 
 modity : under these circumstances the whole pos- 
 sessions of one might be exchanged for the whole 
 of the other, and the ratio of exchange would of 
 course be defined by the ratio of these quantities. 
 Yet each party might desire the last increment of 
 the commodity received more than he desires the 
 
 K
 
 130 The Theory of Political Economy. 
 
 last increment of that given, so that the equations 
 would fail to be true. This case will hardly occur 
 practically in international trade, since two nations 
 usually trade in many commodities, a fact which 
 would alter the conditions. 
 
 Again, the equations of exchange will fail to be 
 possible when the commodity or useful article pos- 
 sessed on one or both sides is indivisible. We have 
 always assumed hitherto that more or less of a 
 commodity may be had, down to infinitely small 
 quantities. This is approximately true of all ordi- 
 nary trade, especially international trade between 
 great industrial nations. Any one sack of corn 
 or any one bar of iron is practically infinitesimal 
 compared with the quantities exchanged by America 
 and England; and even one cargo or parcel of 
 corn or iron is a small fraction of the whole. But, 
 in exceptional cases, even international trade might 
 involve indivisible articles. We might conceive 
 the British Government giving the Koh-i-noor 
 diamond to the Khedive of Egypt in exchange for 
 Pompey's Pillar, in which case it would certainly 
 not answer the purpose to break up one article or 
 the other". When an island or portion of territory 
 
 n Since the above was written the value of Cleopatra's Needle 
 has actually formed the subject of decision in the Admiralty Court, 
 in connection with the award of salvage. The fact however is that 
 in the absence of any act of exchange concerning such an object, 
 the notion of value is not applicable at all. At the best the value
 
 Theory of Exchange. 131 
 
 is transferred from one possessor to another, it is 
 often necessary to take the whole, or none. America, 
 in purchasing Alaska from Russia, would hardly 
 have consented to purchase less than the whole. 
 In every sale of a house, factory, or other building, 
 it is usually impracticable to make any division 
 without greatly lessening the utility of the whole. 
 In all such cases our equations must fail to exist, 
 because we cannot contemplate the existence of 
 an increment or a decrement to an indivisible 
 article. 
 
 Suppose, for example, that A and B each possess 
 a book : they cannot break up the books, and must 
 therefore exchange them entire, if at all. Under 
 what conditions will they do so ? Plainly on the 
 condition that each makes a gain of utility by so 
 doing. Here we deal not with the final degree of 
 utility depending on an infinitesimal quantity, but 
 on the ivhole utility of the complete article. Now let 
 us assign the symbols as follows : — 
 
 u^ = the utility of A's book to A, 
 1/2 „ „ A's „ to B, 
 
 Vr » » B's „ to A, 
 
 Vz „ „ B's „ to B. 
 
 assigned, namely £25,000, is a mere fiction arbitrarily invented to 
 represent what might conceivably be given for such an object if 
 there were a purchaser. It is, moreover, curious that since the 
 first edition was printed Russia has actually made an exchange 
 of islands with Japan. 
 
 K 2
 
 13iiJ The Theory of Political JEconomy. 
 Then the conditions of exchange are simply 
 
 We might indeed theoretically contemplate the case 
 where the utilities Avere exactly equal on one side ; 
 thus %\ > Ui, 
 
 B would then be wholly indifferent to the ex- 
 change, and I do not see any means of deciding 
 whether he would or would not consent to it. But 
 we need hardly consider the case, as it could 
 seldom practically occur. Were the utilities exactly 
 equal on both sides in respect to both objects, there 
 would obviously be no motive to exchange. Again, 
 the slightest loss of utility on either side would 
 be a complete bar to the transaction, because we 
 are not supposing, at present, that any other com- 
 modities are in possession so as to allow of separate 
 inducements, or that any other motives than such 
 as arise out of simple desire of one's own conveni- 
 ence enter into the question. 
 
 A much more difficult problem arises when we 
 suppose an indivisible article exchanged for a divi- 
 sible commodity. When Russia sold Alaska this 
 was a practically indivisible thing; but it was 
 bought with money of which more or less might be 
 • given to indefinitely small quantities. A bargain 
 of this kind is exceedingly common ; indeed it 
 occurs in the case of every house, mansion, estate.
 
 Theory of Exchange. 133 
 
 factory, ship, or other complete whole, which is 
 sold for money. Our former equations of exchange 
 certainly fail, foj- tliey involve increments of com- 
 modity on both sides. The theory seems to give 
 a very unsatisfactory answer, for the problem 
 l^roves to be, within certain limits, indeterminate. 
 
 Let X be the indivisible article; u^ its utility 
 to its possessor A, and u^ its utility to B. Let 
 y be the quantity of commodity given for it, 
 a commodity wiiich is supposed to be divisible 
 ad infinitum ; let t\ be the total utility of y to A, 
 and V.2 its total utilit}^ to B. Then it is quite 
 evident that, in oi-der to give rise to exchange, v^ 
 must be greater than u^, and u.^ must be greater 
 than v.2 ; that is, there must, as before, be a gain 
 of utility on each side. The quantity y must not 
 be so great then as to deprive B of gain, nor so 
 small as to deprive A of gain. The following is 
 an extract from Mr. Thornton's w^ork which exactly 
 expresses the problem : — 
 
 'There are tw'o opposite extremes — one above 
 w^hich the price of a commodity cannot rise, the 
 other below which it cannot fall. The upper of 
 these limits is marked by the utility, real or sup- 
 posed, of the commodity to the customer ; the lower, 
 of its utility to the dealer. No one will give for 
 a commodity a quantity of money or money's 
 worth, which, in his opinion, would be of more use 
 to him than the connnodity itself No one will
 
 134 The Theor'y of Political Economy. 
 
 take for a commodity a quantity of money or of 
 anything else which he thinks would be of less use 
 to himself than the commodity. The price eventu- 
 ally given and taken may be either at one of the 
 opposite extremes, or may be anywhere interme- 
 diate between them «.' 
 
 Three distinct cases might occur, which can best 
 be illustrated by a concrete example. Suppose we 
 can read the thoughts of the parties in the sale 
 of a house. If A says £1200 is the least price 
 which will satisfy him, and B holds that £800 is 
 the highest price which it will be profitable for him 
 to give, no exchange can possibly take place. If 
 A should find £1000 to be his lowest limit, while 
 B happens to name the same sum for his highest 
 limit, the transaction can be closed, and the price 
 will be exactly defined. But supposing, finally, 
 that A is really willing to sell at £900, and B is 
 prepared to buy at £1100, in what manner can we 
 theoretically determine the price ? I see no mode 
 of solving the question. Any price between £900 
 and £1100 will leave a profit on each side, and 
 both parties will lose if they do not come to terms. 
 I conceive that such a transaction must be settled 
 upon other than strictly economical grounds. The 
 result of the bargain Avill greatly depend upon the 
 comparative amount of knowledge of each other's 
 
 o Thornton ' On Labour ; its Wrongful Claims and Rightful 
 Dues' (1869), p. 58.
 
 Theory of Exchange. 135 
 
 positions and needs Avliicli either bargainer may 
 possess or manage to obtain in the course of the 
 transaction. Thus the power of reading another 
 man's thouglits is of high importance in business, 
 and the art of bargaining mainly consists in the 
 buyer ascertaining the lowest price at wdiicli the 
 seller is willing to part with his object, Avithout 
 disclosing if possible the highest price which he, 
 the seller, is willing to give. The disposition and 
 force of character of the parties, their comparative 
 persistency, their adroitness and experience in busi- 
 ness, or it may be feelings of justice or of kindliness 
 will also influence the decision. These are motives 
 more or less extraneous to a theory of Economics, 
 and yet they appear necessary considerations in 
 this problem. It may be, that indeterminate bar- 
 gains of this kind are best arranged by an arbitrator 
 or third party. 
 
 The equations of exchange may fail again v/hen 
 commodities are divisible, but not to iiihnitely 
 small quantities. There is always, in retail trade, 
 a convenient unit below which we do not descend 
 in purchases. Paper may be bought in quires, or 
 even in packets, which it may not be desirable to 
 break up. Wine cannot be bought from the wine 
 merchant in less than a bottle at a time. In all 
 such eases exchange cannot, theoretically speaking-, 
 be perfectly adjusted, because it will be infinitely 
 improbable that an integral number of units will
 
 136 The Theory of Political Economy. 
 
 precisely verify the equations of exchange. In 
 a large proportion of cases, indeed, the unit may 
 be so small compared with the Avhole quantities 
 exchanged, as practically to be infinitely small. 
 But suppose that a person be buying ink which 
 is only to be had, under the circumstances, in one 
 shilling bottles. If one bottle be not quite enough, 
 how will he decide whether to take a second or 
 not. Clearly by estimating the aggregate utility 
 of the bottle of ink compared with the shilling. 
 If there be an excess, he will certainly purchase 
 it, and proceed to consider whether a third be 
 desirable or not. 
 
 This case might be illustrated by Figure VI. in 
 which the spaces o q^, p^ q-z^ P2 %■> ^c. represent the 
 total utilities of successive bottles of ink ; while 
 the equal spaces )\, i\ r^, &c. represent the total 
 
 p4 b pS 
 
 utilities of successive shillings, which we may 
 assume to be practically invariable. There is no
 
 Theory of Exchange. 137 
 
 doubt that three bottles will be purchased, but the 
 fourth will not be purchased unless the niixtilinear 
 figure ^3 (/a (/4 ^4 exceed in area the rectangle j^g r.^ 
 
 Cases of this kind are similar to those treated 
 in pp. 130-4, where the things exchanged are indivi- 
 sible, except that the question of exchange or no 
 exchange occurs over and over again with respect 
 to each successive unit, and is decided in respect 
 to each by the excess of the total utility of the unit 
 to be received over the total utility of that to be 
 given. There is indeed perfect harmony between 
 the cases where equations can and Avhere they can- 
 not be established ; for we have only to imagine 
 the indivisible units of commodity to be indefi- 
 nitely lessened in size to enable us to pass gradually 
 down to the case where equality of the increments 
 of utility is ultimately established. 
 
 Negative and Zero Value. 
 
 Only a few economists, notably Mr. H. D. Macleod 
 in several of his publications, have noticed the fact 
 that there may be such a thing as negative value. 
 Yet there cannot be the least doubt that people 
 often labour, or pay money to other labourers, in 
 order to get rid of things, and they would not do 
 tliis unless such things were hurtful, that is, had 
 the opposite quality to utility— disutility. Water,
 
 138 The Theory of Political Economy. 
 
 when it gets into a mine, is a costly tiling to get 
 out again, and many people have been ruined by 
 wet mines. Quarries and mines usually produce 
 great quantities of valueless rock or earth, variously 
 called duff, spoil, waste, rubbish, and no inconsi- 
 derable part of the cost of working arises from the 
 need of raising and carrying this profitless mass 
 of matter and then finding land on which to deposit 
 it. Every furnace yields cinders, dross, or slag, 
 which can seldom be sold for any money, and every 
 household is at the expense of getting rid, in one 
 way or another, of sewage, ashes, swill, and other 
 rejectanea. Reflection soon shows, in short, that 
 no inconsiderable part of the values with which we 
 deal in practical economics must be negative values. 
 It will hardly be needful to show at full length 
 that this negative value may be regarded as vary- 
 ing continuously in the same way as positive value. 
 If after a long drought rain begins to fall heavily, 
 it is at first hailed as a great benefit; the rain- 
 water may be so valuable as to produce a crop, 
 when otherwise successful agriculture would have 
 been impossible. Rain may thus avert famine ; 
 but after the rain has fallen for a certain length of 
 time, the farmer begins to think he has had enough 
 of it; more rain will retard his operations, or injure 
 the growing plants. As the rain continues to fall 
 he fears further injury; water begins to flood his 
 land, and there is even danger of the soil and crops
 
 Theory of Exchange. 139 
 
 being all washed away together. But the rain 
 unfortunately pours down more and more heavily, 
 until at length perhaps the crops, soil, house, stock, 
 — nay, the farmer himself, are all swept bodily 
 away. That same water, then, which in moderate 
 quantity would have been of the greatest possible 
 benefit, has only to be supplied in greater and 
 greater quantities, to become injurious until it ends 
 with occasioning the ruin, and even the death of 
 the individual. Those acquainted with the floods 
 and droughts of Australia know that this is no fancy 
 sketch P. 
 
 It many other cases it might be shown similarly 
 that matter, we can hardly call it commodity, ac- 
 quires a higher and higher degree of disutility, the 
 greater the quantity which has to be disposed of. 
 Such is the case with the sewage of great towns, 
 the foul or poisoned water from mines, dye-works, 
 etc. Any obstacle, however, may be regarded as 
 so much discommodity, whether it be a mountain 
 which has to be bored through to make a railway, 
 or a hollow which has to be filled up with an ex- 
 pensive embankment. If a building site requires 
 a certain expenditure in levelling and draining 
 before it can be made use ofj the cost of this work 
 is, of course, subtracted from the value Avhich the 
 
 P See the author's ' History of the Floods and Droughts of New 
 South Wales,' iu the Australian Almanack, Sydney, 1859, p. 61. 
 Aleo Mr. H. C. Russell's ' Climate of New South Wales.'
 
 1 40 The Theory of Political Economy. 
 
 land would otherwise possess. As every advantage 
 in property gives rise to value, so every disad- 
 vantage must be set against that value. 
 
 We now come to the question how negative value 
 is to be represented in our equations. Let us sup- 
 pose a person possessing a of some commodity to 
 find it insufficient : then it has positive degree of 
 utility for him, that is to say (p[a) is positive. 
 Suppose X to be added to a and gradually increased : 
 (p{a + <«') will gradually decrease. Let us assume 
 that for a certain value of w it becomes zero ; then, 
 if the further increase of .v turns utility into dis- 
 utility, <p{a-\-.v) will become a negative quantity. 
 How will this negative sign affect the validity of 
 the equations which we have been employing in 
 preceding pages, and in which each member has 
 appeared to be both formally and intrinsically 
 positive ? It is plain that we cannot equate a posi- 
 tive to a negative quantity; but it will be found 
 that if* at the same time that we introduce 
 negative utility, we also assign to each increment 
 of commodity the positive or negative sign, ac- 
 cording as it is added to or subtracted from the 
 exchanger's possessions, that is to sa}^ received 
 or given in exchange, no such difficulty arises. 
 
 Suppose A and B respectively to hold a and h, 
 and to exchange dx and d^/ of the commodities 
 X and Y. Then it will be apparent from the 
 general character of the argument on pp. 106-108,
 
 TJieorij of Exchange. 141 
 
 that the fundamental equation there adopted will 
 be included in the more general form — 
 
 (p {a ±.i') . dcf + ^ {h ± y) . dy = o. 
 
 In this equation either factor of either term may 
 be intrinsically negative, while the alternative signs 
 before .r and y allov/ for every possible case of 
 giving and receiving in exchange. 
 
 Four possible cases will arise. In the first case, 
 both commodities have utility for each person, 
 that is to say, (p and \|^ are both positive functions ; 
 but A gives some of X in return for some of Y. 
 This means that dcv is negative, and dy positive, 
 while the quantities in possession after exchange 
 are a — j7, and h-{-ij. Thus the equation becomes 
 
 — (p (a— J') . d.r + ^ (h + ?/) . dy = o. 
 
 We should have merely to transpose the negative 
 term to the other side of the equation, and to 
 assume h = o, to obtain the equation on p. 107. 
 
 As the second case, suppose that Y possesses 
 disutility for A, so that the function \/^ becomes for 
 him negative ; in order to get rid of y, he must also 
 pay o' with it, and both these quantities as well 
 as dy and dj? receive the negative sign. Then the 
 equation takes the shape 
 
 (p (a — d") X ( - d.r) — ^{h - ?/) x ( — d?/) = o, 
 or 
 
 - (p {a — .r) . d.f +^ {h —y) . dy = o. 
 
 The third case is the counterpart of the last, and
 
 142 Tlie Theory of Political Economy. 
 
 represents B's position, who receives both cv and y, 
 on the ground that one of these quantities is dis- 
 commodity to him. But putting the matter as the 
 case of A, we may assume (p to be positive, -^ nega- 
 tive, and giving the positive sign to all of a.\ y, dx 
 and dy, we obtain the equation — 
 
 <p{a-\- ai) . dcV — ^ (^ +^) . d.v = o. 
 
 It is possible to conceive yet a fourth case in 
 which people should be exchanging two discom- 
 modities, that is to say, getting rid of one hurt- 
 ful substance by accepting in place of it, what 
 is felt to be less hurtful, though still possessing 
 disutility. In this case we have both (p and \j/- 
 negative, as well as one of the quantities exchanged; 
 taking cv and dd' as positive, and y and dy as nega- 
 tive, the equation assumes the form 
 
 — cj)[a + ai) .d.v — ^ (b —y) . ( — dy) = o, 
 or 
 
 — (p{a + ,'t') . del' + \Jr (1) —y) . dy = o. 
 
 It might be difficult to discover any distinct 
 cases of this last kind of exchange. Generally 
 speaking, when a person receives assistance in 
 getting rid of some inconvenient possession, he 
 pays in money or other commodity for the service 
 of him who helps to remove the burden. It must 
 naturally be a very rare case that the remover has 
 some burden which it would suit the other party 
 to receive in exchange. Yet the contingency may
 
 Theory of Exchange. 143 
 
 and, no doubt, does sometimes occur. Two adjacent 
 landowners, for instance, might reasonably agree 
 that, if A allows B to throw the spoil of his mine 
 on A's land, then A shall be allowed to drain liis 
 mine into B's mine. It might happen that B was 
 comparatively more embarrassed by the great quan- 
 tity of his spoil, than by water, and that A had 
 room for the spoil, but could not get rid of the 
 water in other ways Avithout great difficulty. An 
 exchange of inconveniences would then be plainly 
 beneficial. 
 
 Looking at the equations obtained in the four 
 cases as stated above, it is apparent that the 
 general equation of exchange consists in equating 
 to zero the sum of one positive and one negative 
 term, so that the signs both of the utility functions 
 and of the increments may be disregarded. Thus 
 the fundamental equation may be written in the 
 general form 
 
 <p {a± d') dy 
 
 We may express the result of this theory in general 
 terms by saying that the algebraic sum of the 
 utility or disutility received or parted with, as 
 regards the last increments concerned in an act 
 of traffic, will always be zero. It also follows that, 
 without regard to sign, the increments are in 
 magnitude hiversely as their degrees of utility or 
 disutility. The reader will not fail to notice the
 
 144 The Theory of Political Economy. 
 
 remarkable analogy between this theory and that 
 of the equilibrium of two forces regarded accord- 
 ing to the principle of virtual velocities. A rigid 
 lever will remain in equilibrium under the action 
 of two forces, provided that the algebraic sum of 
 the forces, each multiplied by its infinitely small 
 displacement, be zero. Substitute for force, degree 
 of utility, positive or negative, and for infinitely 
 small displacements, infinitely small quantities 
 of commodity exchanged, and the principles are 
 identical. 
 
 It still remains to consider the imaginary case 
 in which substances possess or are supposed to 
 possess neither utility nor disutility, and are yet 
 exchanged in finite quantities. Substituting the 
 ratio of ?/ and .r for that of dy and da\ the general 
 equation 
 
 (p {a ± <y) 7/ 
 
 will give the value •- = - , both the functions of 
 
 ,«' o 
 
 utility being zero. This means that the quantities 
 exchanged will be indeterminate so far as the 
 theory of utility goes. If one substance possesses 
 utility, and the other does not, the ratio of ex- 
 change becomes either -^ or - , infinity or zero, 
 
 o y 
 
 indicating that there can be no comparison in our 
 theory betAveen things which do and those which
 
 Theory oj Exchange. 145 
 
 do not possess utility. Practically speaking*, such 
 cases do not occur except in an approximate man- 
 ner. Such things as cinders, shavings, night-soil, 
 &c., have either low degrees of utility or disutility. 
 If the dustman takes them away for nothing, they 
 must have utility for him sufficient to pay the cost 
 of removal. When the dust is riddled, one part 
 is usually found to have utility just sufficient to 
 balance the disutility of the remainder, giving us 
 an instance of the second or third form of the 
 equation of exchange according as we regard the 
 matter from the householder's or the dustman's 
 point of view. 
 
 Equivalence of Commodities. 
 
 Much confusion is thrown into the statistical 
 investigation of questions of supply and demand 
 by the circumstance that one commodity can often 
 replace another, and serve the same purposes more 
 or less perfectly. The same, or nearly the same 
 substance, is often obtained from two or three 
 sources. The constituents of wheat, barley, oats, 
 and rye are closely similar, if not identical. Ve- 
 getable structures are composed mainly of the 
 same chemical compound in nearly all cases. 
 Animal meat, again, is of nearly the same com- 
 position from whatever animal derived. There 
 are endless differences of flavour and quality, but 
 
 L
 
 146 The Theory of Political Economy. 
 
 these are often insufficient to prevent one kind 
 from serving in place of another. 
 
 Whenever different commodities are thus ap- 
 plicable to the sam.e purposes, their conditions of 
 demand and exchange are not independent. Their 
 mutual ratio of exchange cannot vary much, for 
 it will be closely defined by the ratio of their 
 utilities. Beef and mutton, for instance, differ so 
 slightly, that people eat them almost indifferently. 
 But the wholesale price of mutton, on an average, 
 exceeds that of beef in the ratio of 9 to 8, and 
 we must therefore conclude that people generally 
 esteem mutton more than beef in this proportion, 
 otherwise they would not buy the dearer meat. 
 It follows, that the final degrees of utility of these 
 meats are in this ratio, or that if <pci' be the degree 
 of utility of mutton, and >//7/ that of beef, we have 
 8 . (pa^ = 9 . ^l^y. 
 
 This equation would doubtless not hold true in 
 extreme circumstances; if mutton became com- 
 paratively scarce, there would probably be some 
 persons willing to pay a higher price, merely be- 
 cause it would then be considered a delicacy. 
 But this is certain, that, so long as the equation 
 of utilities holds true, the ratio of exchange be- 
 tween mutton and beef will not diverge from that 
 •of 8 to 9. If the supply of beef falls off* to a small 
 extent, people will not pay a higher price for it, 
 but will eat more mutton; and if the supply of
 
 Theory of Exchange. 147 
 
 mutton falls oft', they will eat more beef. The 
 conditions of sujiply will have no effect upon the 
 ratio of exchange; we must, in fact, treat beef 
 and mutton as one commodity of two different 
 strengths, just as gold at eighteen and gold at 
 twenty carats are hardly considered as two but 
 rather as one commodity, of which twenty parts 
 of one are equivalent to eighteen of the other. 
 
 It is upon this principle that we must explain, in 
 harmony with Cairnes' views, the extraordinary per - 
 manence of the ratio of exchange of gold and silver, 
 Avhich from the commencement of the eighteenth 
 century np to recent years never diverged much 
 from 15 to 1. That this fixedness of ratio did 
 not depend entirel}^ upon the amount or cost of 
 production is proved by the very slight effect of 
 the Australian and Californian gold discoveries, 
 which never raised the gold price of silver more 
 than about 4| per cent., and failed to have a per- 
 manent effect of more than 1| per cent. This 
 permanence of relative values may have been 
 partially due to the fact, that gold and silver can 
 be employed for exactly the same purposes, but 
 that the superior brilliancy of gold occasions it 
 to be preferred, unless it be about 15 or 15| times 
 as costly as silver. Much more probably, how- 
 ever, the explanation of the fact is to be found 
 in the fixed ratio of 15 J to 1, according to which 
 these metals are exchanged in the currency of 
 
 L 2
 
 148 The Theory of Folitical Economy. 
 
 France and some other continental countries. The 
 French Currency Law of the Year XI established 
 an artificial equation — 
 
 Utility of gold = 15| x Utility of silver; 
 and it is probably not without some reason that 
 Wolowski and other recent French economists 
 attributed to this law of replacement an important 
 effect in preventing disturbance in the relations of 
 gold and silver. 
 
 Since the first edition of this work was pub- 
 lished, the views of Wolowski have received strik- 
 ing verification in the unprecedented fall in the 
 value of silver, which has occurred in the last 
 three or four years. The ratio of equivalent weights 
 of silver and gold, which had never before risen 
 much above 16 to 1, commenced to rise in 1874, 
 and was at one time (July 1876) as high as 22-5 
 to 1 in the London market. Though it has since 
 fallen, the ratio continues to be subject to frequent 
 considerable oscillations. The great production of 
 silver in Nevada may contribute somewhat to this 
 extraordinary result, but the principal cause must 
 be the suspension of the French Law of the Double 
 Standard, and the demonetization of silver in Ger- 
 many, Scandinavia, and elsewhere. As I have treated 
 the subject of the value of silver and the Double 
 Standard elsewhere % I need not pursue it here. 
 
 1 'Serious fall in the value of gold,' 1863, p. 33. 'Money and 
 the Mechanism of Exchange' (International Scientific Series),
 
 Tlieory of Exchange. 149 
 
 Acquired Utility of Commodities. 
 
 The Theory of Exchange, as explained above, 
 rests entirely on the consideration of quantities 
 of utilit}', and no reference to labour or cost of 
 production has been made. The value of a divi- 
 sible commodity, if I may for a moment use the 
 dangerous term, is measured, not, indeed, by its 
 total utility, but by its final degree of utility, 
 that is by the intensity of the need we have for 
 more of it. But the power of exchanging one 
 commodity for another greatly extends the range 
 of utility. We are no longer limited to con- 
 sidering the degree of utility of a commodity as 
 regards the wants of its immediate possessor ; for 
 it may have a higher usefulness to some other 
 person, and can be transferred to that person in 
 exchange for some commodity of a higher degree 
 of utility to the purchaser. The general result of 
 exchange is, that all conmiodities sink, as it were, 
 to the same level of utility in respect of the last 
 portions consumed. 
 
 In the Theory of Exchange we find that the 
 possessor of any divisible commodity will ex- 
 chapter x';i. This chapter has been translated by M. H. Gravez and 
 reprinted in the Bibliothfeque Utile, vol. xliv. (Gernier Bailliere), 
 Pai'is, 1878. See also Papers on the Silver Question road before 
 the American Social Science Association at Saratoga, Sept. 5, 1877, 
 Boston, 1877, and Bankers' Magazine, December, 1877.
 
 150 The Theory of Political Economy. 
 
 change such a portion of it, that the next incre- 
 ment would have exactly equal utility with the 
 increment of other produce which he would re- 
 ceive for it. This will hold good however various 
 may be the kinds of commodity he requires. Sup- 
 pose that a person possesses one single kind of 
 commodity, which we may consider to be money, 
 or income, and that _p, q, r, s, t, &c. are quantities 
 of other commodities which he purchases with 
 portions of his income. Let c*' be the uncertain 
 quantity of money which he will desire not to 
 exchange; what relation will exist between these 
 quantities d% j), q, r, &c. ? This relation will partly 
 depend upon the ratio of exchange, partly on the 
 final degree of utility of these commodities. Let 
 us assume, for a moment, that all the ratios of 
 exchange are equalities, or that a unit of one is 
 always to be purchased with a unit of another. 
 Then, plainly, we must have the degrees of utility 
 equal, otherwise there would be advantage in ac- 
 quiring more of that possessing the higher degree 
 of utility. Let the sign cp denote the function of 
 utility, which will be different in each case ; then 
 we have simply the equations — 
 
 cp^^ = (p.^p = (l)^q = (p^r = (p^s = kc. 
 But, as a matter of fact, the ratio of exchange is 
 seldom or never that of unit for unit; and when 
 the quantities exchanged are unequal, the degrees 
 of utility will not be equal. If for one pound of
 
 Theory of Exchange. 151 
 
 silk I can have three of cotton, then the degree 
 of utility of cotton must he a third that of silk, 
 otherwise I should gain hy exchange. Thus the 
 general result of the facility of exchange pre- 
 vailing in a civilized country is, that a person 
 procures such quantities of commodities that the 
 final degrees of utiliti/ of any pair of commodities 
 are inversely as the ratios of exchange of the com- 
 modities. 
 
 Let a^-i^, cv.2, c«'3, cT^, &c. be the portions of his in- 
 come given for p, (/, r, s, &c. respectively, then 
 we must have 
 
 ^1 ^v 2J ' (p^.i'~ q' (f)^ .1? r ' 
 and so on. The theory thus represents the fact, 
 that a person distributes his income in such a way 
 as to equalise the utility of the final increments of 
 all commodities consumed. As water runs into 
 hollows until it fills them up to the same level, so 
 wealth runs into all the branches of expenditure. 
 This distribution will vary greatly with different 
 individuals, but it is self-evident that the want 
 which an individual feels most acutely at the 
 moment Avill be that upon which he will expend 
 the next increment of his income. It obviously 
 follows that in expending a person s income to the 
 greatest advantage, the algebraic sum of the quanti- 
 ties of commodity received or parted with, each 
 nmltiplied hy its fmd degree of utility , ivill he zero.
 
 152 TJie Theory of Political Economy. 
 
 We can now conceive, in an accurate manner, 
 the utility of money, or of that supply of com- 
 modity which forms a person's income. Its final 
 degree of utility is measured by that of any of 
 the other commodities which he consumes. What, 
 for instance, is the utility of one penny to a poor 
 family earning fifty pounds a year? As a penn}^ 
 is an inconsiderable portion of their income, it 
 may represent one of the infinitely small incre- 
 ments, and its utility is equal to the utility of 
 the quantity of bread, tea, sugar, or other articles 
 which they could purchase with it, this utility 
 depending upon the extent to which they were 
 already provided Avith those articles. To a family 
 possessing one thousand pounds a year, the utility 
 of a penny may be measured in an exactly similar 
 manner; but it will be much less, because their 
 want of any given commodity will be satiated or 
 satisfied to a much greater extent, so that the 
 urgency of need for a pennyworth more of any 
 article is much reduced. 
 
 The general result of exchange is thus to pro- 
 duce a certain equality of utility between different 
 comjnodities, as regards the same individual; but 
 between different individuals no such equality will 
 tend to be produced. In Economics we regard 
 only commercial transactions, and no equalisation 
 of wealth from charitable motives is considered. 
 The degree of utility of wealth to a very rich man
 
 Theory of Exchange. 153 
 
 will be governed by its degree of utility in that 
 branch of expenditure in which he continues to 
 feel the most need of further possessions. His 
 primary wants will long since have been fully 
 satisfied ; he could find food, if requisite, for a 
 thousand persons, and so, of course, he will have 
 supplied himself with as much as he in the least 
 desires. But so far as is consistent with the in- 
 equality of wealth in every community, all com- 
 modities are distributed by exchange so as to 
 produce the maximum of benefit. Every person 
 whose wish for a certain thing exceeds his wish 
 for other things, acquires what he wants, i^rovided 
 he can make a sufficient sacrifice in other respects. 
 No one is ever required to give what he more 
 desires for what he less desires, so that perfect 
 freedom of exchange must be to the advantage 
 of all. ■ 
 
 The Gain hy Exchange. 
 
 It is a most important result of this theory that 
 the ratio of exchange gives no indication of the 
 real benefit derived from the action of exchange. 
 So many trades are occupied in buying and sell- 
 ing, and make their profits by buying low and 
 selling high, that there arises a fallacious ten- 
 dency to believe that the whole benefit of trade 
 depends upon the differences of prices. It is im- 
 plied that to pay a high price is worse than doing
 
 154 The Theory of Political Economy. 
 
 without the article, and the whole financial sys- 
 tem of a great nation may be distorted in the 
 eifort to carry out a false theory. 
 
 This is the result to which some of J. S. Mill's 
 remarks, in his 'Theory of International Trade/ 
 would lead. That theory is always ingenious, and 
 as it seems to me, nearly always true; but he 
 draws from it the following conclusion ^ : — ' The 
 countries which carry on their foreign trade on 
 the most advantageous terms, are those whose 
 commodities are most in demand by foreign coun- 
 tries, and Avhich have themselves the least demand 
 for foreign commodities. From which, among other 
 consequences, it follows, that the richest countries, 
 Gceteris paribus, gain the least by a given amount 
 of foreign commerce : since, having a greater de- 
 mand for commodities generally, they are likely 
 to have a greater demand for foreign commo- 
 dities, and thus modify the terms of interchange 
 to their own disadvantage. Their aggregate gains 
 by foreign trade, doubtless, are generally greater 
 than those of poorer countries, since they carry 
 on a greater amount of such trade, and gain the 
 benefit of cheapness on a larger consumption: 
 but their gain is less on each individual article 
 consumed.' 
 
 J" 'Principles of Political Economy,' book iii. chap. 18, end of the 
 8th section.
 
 Theory of Exchange. 155 
 
 In the absence of any explanation to the con- 
 trary, this passage must be taken to mean, that 
 the advantage of foreign trade depends upon the 
 terms of exchange, and that international trade 
 is less advantageous to a rich than to a poor 
 country. But such a conclusion involves con- , 
 fusion between two distinct things — the price of j-Ar^i 
 a commodity and its total utility, A country is 
 not merely like a great mercantile firm buying 
 and selling goods, and making a profit out of the 
 difference of price ; it buys goods in order to con- 
 sume them. But, in estimating the benefit which 
 a consumer derives from a commodity, it is the 
 total utility which must be taken as the measure, 
 not the final degree of utility on which the terms 
 of exchange depend. 
 
 To illustrate this truth we may employ the 
 curves in Figure VII to represent the functions 
 of utility of two commodities. Let the wool of 
 Australia be represented by the line oh, and its 
 total utility to Australia by the area of the curvi- 
 linear figure ohrp. Let the utility of a second 
 commodity, say cotton goods, to Australia be simi- 
 larly represented in the lower curve, so that the 
 quantity of commodity measured by o'h' gives a 
 total utility represented by the figure d^y^V. 
 Then, if Australia gives half its wool, ah, for the 
 quantity of cotton goods represented by o'c/, it 
 loses the utility o.qrh, but gains that represented
 
 156 The Theory of Political Economy. 
 
 by the larger area op'cjfa'. There is accordingly 
 a considerable net gain of utility, which is the 
 real object of exchange. Even had Australia sold 
 its wool at a lower price, obtaining cotton goods 
 only to the amount of o'c, the utility of this 
 
 y 
 
 amount, oj^sc, would have exceeded that of the 
 Avool given for it. 
 
 So far is Mill's statement from being funda- 
 mentally correct, that I believe the truth lies in 
 the opposite direction. As a general rule, the 
 greatness of the price which a country is willing 
 and able to pay for the productions of other coun- 
 tries, measures, or at least manifests, the greatness
 
 Theory of Exchange. 157 
 
 of the benefit which it derives from such imports. 
 He who pays a high price must either have a very 
 great need of thiit which lie buys, or very little 
 need of that Avliich he pays for it ; on either sup- 
 position there is gain by exchange. In questions i 
 of this sort there is but one rule which can be 
 safely laid down, namely that no one will buy aj 
 thing unless he expects advantage from the pur-' 
 chase ; and perfect freedom of exchange, therefore, 
 tends to the maximising of utility. 
 
 One advantage of the Theory of Economics, 
 carefully studied, will be to make us very careful 
 in our conclusions when the matter is not of the 
 simplest possible nature. The fact that we can 
 most imperfectly estimate the total utility of any 
 one commodity should prevent us, for instance, 
 from attempting to measure the benefit of any 
 trade. Accordingly, when Mill proceeds from his 
 theory of international trade to that of taxation, 
 and arrives at the conclusion that one nation may, 
 by means of taxes on commodities imported, ' ap- 
 propriate to itself, at the expense of foreigners, a 
 larger share than would otherwise belong to it of 
 the increase in the general productiveness of the 
 labour and capital of the worlds' I venture to 
 question the truth of his results. I conceive that 
 his arguments involve a confusion between the 
 ratio of exchange and the total utility of a com- 
 
 3 ' Principles of Political Economy,' book v. cliap. 4, § 6.
 
 158 The Theory of Political Economy. 
 
 modity, and a far more accurate knowledge of 
 economical laws than any one yet possesses would 
 be required to estimate the true effect of a tax. 
 Customs duties may be requisite as a means of 
 raising revenue, but the time is past when any 
 economist should give the slightest countenance 
 to their employment for manipulating trade, or 
 for interfering with the natural tendency of ex- 
 change to increase utility. 
 
 Numerical Determination of the Laws of 
 ■^ Utility. 
 
 I The future progress of Economics as a strict 
 science must greatly depend upon our acquiring 
 more accurate notions of the variable quantities 
 concerned in the theory. We cannot really tell 
 the effect of any change in trade or manufacture 
 until we can with some approach to truth express 
 the laws of the variation of utility numerically. 
 To do this we need accurate statistics of the 
 quantities of commodities purchased by the whole 
 population at various prices. The price of a com- 
 modity is the only test we have of the utility of 
 the commodity to the purchaser ; and if we could 
 tell exactly how much people reduce their con- 
 sumption of each important article when the price 
 rises, we could determine, at least approximately, 
 the variation of the final degree of utility — the 
 all- important element in Economics,
 
 Theory of Exchange. 159 
 
 111 such calculations we may at first make use 
 of the simpler equation given on p. 123. For the 
 first approximation we may assume that the 
 general utility of a person's income is not affected 
 by the changes of price of the commodity; so 
 that if, in the equation 
 
 we have many different corresponding values for x 
 and Wo, Ave may treat \(/c, the utility of money, as 
 a constant, and determine the general character 
 of the function (px, the final degree of utility. 
 This function would doubtless be a purely em- 
 pirical one — a mere aggregate of terms devised 
 so that their sum shall vary in accordance with 
 statistical facts. The subject is too complex to 
 allow of our expecting any simple precise law 
 like that of gravity. Nor, when we have got the 
 laws, shall we be able to give any exact explan- 
 ation of them. They will be of the same cha- 
 racter as the empirical formulae used in many of 
 the physical sciences — mere aggregates of ma- 
 thematical symbols intended to replace a tabular 
 statement*. Nevertheless, their determination will 
 render Economics a science as exact as many of the 
 physical sciences ; as exact, for instance, as Meteor- 
 ology is likely to be for a very long time to come. 
 The method of determining the function of 
 
 *■ See Jevons' ' Principles of iScience,' chapter xxii, New Ed., 
 pp. 487-9, and the references thei'e given.
 
 160 The Theory of Political Economy. 
 
 utility explained above will hardly apply, hoAv- 
 ever, to the main elements of expenditure. The 
 price of bread, for instance, cannot be properly 
 brought under the equation in question, because, 
 when the price of bread rises much, the resources 
 of poor persons are strained, money becomes scarcer 
 with them, and \f/c, the utility of money, rises. 
 The natural result is, the lessening of expendi- 
 ture in other directions; that is to say, all the 
 wants of a poor person are supplied to a less 
 degree of satisfaction when food is dear than when 
 it is cheap. When in the long course of scientific 
 progress, a sufficient supply of suitable statistics 
 has been at length obtained, it will become a mathe- 
 matical problem of no great difficulty how to dis- 
 entangle the functions expressing the degrees of 
 utility of various commodities. One of the first 
 steps, no doubt, will be to ascertain what pro- 
 portion of the expenditure of poor people goes to 
 provide food, at various prices of that food. But 
 great difficulty is thrown in the way of all such 
 inquiries by the vast difierences in the condition 
 of persons, and still greater difficulties are created 
 by the complicated ways in which one commodity 
 replaces, or serves instead of another. 
 
 Opinions as to the Variation of Price. 
 
 There is no difficulty in finding, in works of 
 Economists, remarks upon the relation between
 
 Tlieory of Exchange. 1(^)1 
 
 a change in the supply of a commodity and the 
 consequent rise of price. The general principles 
 of the variation of utility have been familiar to 
 many writers. 
 
 As a general rule the variation of price is much 
 more marked in the case of necessaries of life than 
 in the case of luxuries. This result would follow 
 from the fact observed by Adam Smith, that ' The 
 desire for food is limited in every man by the 
 narrow capacity of the human stomach; but the 
 desire of the conveniences and ornaments of build- 
 ing, dress, equipage, and household furniture, seems 
 to have no limit or certain boundary.' As I assert 
 that value depends upon desire for more, it follows 
 that any excessive supply of food wdll lower itsl 
 price very much more than in the case of articles 
 of luxury. Reciprocally, a deficiency of food will 
 raise its price much more than would happen in 
 the case of less necessary articles. This conclusion 
 is in harmony with facts ; for Chalmers says " : 
 ' The necessaries of life are far more powerfully 
 affected in the price of them by a variation in 
 their quantity, than are the luxuries of life. Let 
 the crop of grain be deficient by one-third in its 
 usual amount, or rather, let the supply of grain 
 in the market, whether from the home produce, 
 or by importation, be curtailed to the same extent, 
 
 " Chalmerb' ' Chribtian and Economic Polity of a Nation,' vol. ii. 
 p. 240. 
 
 H
 
 162 TliG Theory of Political Economy. 
 
 and this will create a much greater addition than 
 of one-third to the price of it. It is not an un- 
 likely prediction, that its cost would be more than 
 doubled by the shortcoming of one-third or one- 
 fourth in the supply.' 
 
 He goes on to explain, at considerable length, 
 that the same would not happen with such an 
 article as rum. A deficiency in the supply of rum 
 from the West Indies would occasion a rise of 
 price, but not to any great extent, because there 
 would be a substitution of other kinds of spirits, 
 or else a reduction in the amount consumed. Men 
 can live without luxuries, but not without neces- 
 saries. 'A failure in the general supply of escu- 
 lents to the extent of one-half, would more than 
 quadruple the price of the first necessaries of life, 
 and would fall with very aggravated pressure on 
 the lower orders. A failure to the same extent 
 in all the vineyards of the world, would most 
 assuredly not raise the price of wine to anything 
 near this proportion. Rather than pay four times 
 the wonted price for Burgundy, there would be 
 a general descent to claret, or from that to port, 
 or from that to the home-made wines of our own 
 country, or from that to its spirituous, or from 
 that to its fermented liquors ^Z He points to sugar 
 especially as an article which would be extensively 
 
 X Chalmers' ' Christian and Economic Polity of a Nation/ vol. ii. 
 p. 242. 
 
 I
 
 Theory of Exchange. 1^3 
 
 thrown out of consumption by any great rise in 
 pricey, because it is a luxury, and at the same 
 time forms a considerable element in expenditure. 
 But he thinks that, if an article occasions a total 
 expenditure of very small amount, variations of 
 price will not much affect its consumption. 
 
 Speaking of nutmeg, he says: — ^ There is not 
 sixpence a year consumed of it for eacli family in 
 Great Britain ; and perhaps not one family that 
 spends more than a guinea on this article alone. 
 Let the price then be doubled or trebled ; this will 
 have no perceptible effect on the demand; and 
 the price will far rather be paid, than that the 
 wonted indulgence should in any degree be fore- 
 gone The same holds true of cloves, and 
 
 cinnamon, and Cayenne pepper, and all the pre- 
 cious spiceries of the East; and it is thus, that 
 while, in the general, the price of necessaries differs 
 so Avidely from that of luxuries, in regard to the 
 extent of oscillation, there is a remarkable ap- 
 proximation in this matter between the very com- 
 monest of these necessaries and the very rarest of 
 these luxuries 2.' 
 
 In these interesting observations Chalmers cor- 
 rectly distinguishes between the effect of desire 
 for the commodity in question and that for other 
 commodities. The cost of nutmeg does not ap- 
 
 y Chalmers' ' Christian and Economic Polity of a Nation,' vol. ii. 
 p. 251. z Jli^l p. 252. 
 
 M 2
 
 164 The Theory of Political Economy. 
 
 preciably affect the general expenditure on other 
 things, and the equation on p. 123 therefore applies. 
 But if sugar become scarce, to consume as before 
 would necessitate a reduction of consumption in 
 other directions; and as the degree of utility of 
 more necessary articles rises much more rapidly 
 than that of sugar, it is the latter article which is 
 thrown out of use by preference. This is a far 
 more complex case, which includes also the case 
 of corn and all large articles of consumption. 
 
 Chalmers' remarks on the price of sugai* are 
 strongly supported by facts concerning the course 
 of the sugar markets in 1855-6. In the year 
 1855, as is stated in Tooke's 'History of Prices V 
 attention was suddenly drawn to a considerable 
 reduction which had taken place in the stocks of 
 sugar. Tlie price rapidly advanced, but before it 
 had reached the highest point the demand became 
 almost wholly susijended. Not only did retail 
 dealers avoid replenishing their stocks, but there 
 was an immediate and sometimes entire cessation 
 of consumption among extensive classes. There 
 Avere instances among the retail grocers of their 
 not selling a single pound of sugar until prices 
 receded to what the public was satisfied was a 
 reasonable rate. 
 
 a Vol. V. p. 324, &c.
 
 Tlieorij of Exchange. 165 
 
 Variation of the Price of Corn. 
 
 As to Chalmers' ingenious remarks upon the 
 consumption of nutmeg, he seems to be at least 
 partially correct. To a certain extent he brings 
 into view the principle explained above, that when 
 only a small quantity of income is required to 
 purchase a certain kind of commodity in sufficient 
 abundance, the degree of utility of income will not 
 be appreciably affected by the price paid, that is 
 to say (p. 123) ^c remains approximately constant. 
 
 It follows that -^ is constant, or in other words 
 
 m 
 
 the final degree of utility of the small commodity 
 purchased must be directly proportional to the 
 price. If then the price rise much, either the 
 consumer must relinquish the use of that com- 
 modity almost entirely, or else he must feel such 
 need of it, that a small decrease of consumption 
 is irksome to him ; that is to say, looking to our 
 curves of utility, either we must recede to a part 
 of the curve very close to the axis of y, or else 
 the curve must be one which rises rapidly as we 
 move towards the origin. Now Chalmers assumes 
 that with nutmeg the latter is the case. People 
 accustomed to use it in his time, were so fond 
 of it that they would pay a much higher price 
 rather than decrease their consumption consi- 
 derably. This means that it possessed a high
 
 166 The Theorij of Political Econohiy. 
 
 degree of utility to them, which could only be 
 overbalanced by some serious increase in the 
 value of \|/c, which would ultimately mean the 
 need of the necessaries of life. 
 
 It is very curious that in this subject, which 
 reaches to the very foundations of Political Eco- 
 nomy, we owe more to early than later writers. 
 Before our science could be said to exist at all, 
 writers on Political Arithmetic had got about as 
 far as we have got at present. In a pamphlet of 
 1737^, it is remarked that 'People who under- 
 stand trade will readily agree with me, that the 
 tenth part of a commodity in a market, more 
 than there is a brisk demand for, is apt to lower 
 the market, perhaps, twenty or thirty per cent., 
 and that a deficiency of a tenth part will cause as 
 exorbitant an advance.' Sir J. Dalrymple^, again, 
 says : — ' Merchants observe, that if the commodity 
 in market is diminished one-third beneath its mean 
 quantity, it will be nearly doubled in value; and 
 that if it is augmented one-third above its mean 
 quantity, it will sink near one-half in its value; 
 or that, by further diminishing or augmenting the 
 quantity, these disproportions between the quantity 
 and prices vastly increase.' These remarks bear 
 little signs of accuracy, indeed, for the writers 
 have spoken, of commodities in general as if they 
 
 ^ Quoted in Lauderdale's ' Inquiry into the Nature and Origin 
 of PuLlic Wealtli/ 2nd Ed., 1819, pp. 51-52. ^' Jbid.
 
 Theory of Exchange. 107 
 
 all varied in jn-ice in a similar degree. It is pro- 
 bable that they were thinking of corn or other 
 kinds of the more necessary food. In the ' Spec- 
 tator' we find a conjectnre^^, that the production 
 of one-tenth part more of grain than is usually 
 consumed would diminish the value of the grain 
 one-half I know nothing more strange and dis- 
 creditable to statists and economists, than that in 
 so important a j^oint as the relations of price and 
 supply of the main article of food, we owe our 
 most accurate estimates to writers who lived from 
 one to two centuries ago. 
 
 There is a celebrated estimate of the variation 
 of the price of corn which I have found quoted in 
 innumerable works on Economics. It is commonly 
 attributed to Gregory King, whose name should be 
 held in honour as one of the fathers of statistical 
 science in England. Born at Lichfield in 1648, 
 King devoted himself much to mathematical studies, 
 and was often occupied in surveying. His prin- 
 cipal public appointments were those of Lancaster 
 Herald and Secretary to the Commissioners of 
 Public Accounts ; but he is known to fame by the 
 remarkable statistical tables concerning the popu- 
 lation and trade of England, which he completed 
 in the year 1696. His treatise was entitled ' Natural? 
 and Political Observations and Conclusions upon' 
 the State and Condition of England, 1696.' It- 
 
 'I No. 200, quoted by Lauderdale, p. 50.
 
 168 
 
 The Theory of Political Economy. 
 
 was never printed in the author's lifetime, but 
 the contents were communicated in a most liberal 
 manner to Dr. Davenant, who, making suitable 
 acknowledgments as to the source of his infor- 
 mation, founded thereupon his 'Essay upon the 
 Probable Methods of making a People gainers in 
 the Balance of Trade ^' Our knowledge of Gregory 
 King's conclusions was derived from this and other 
 essays of Davenant, until George Chalmers printed 
 the whole treatise at the end of the third edition 
 of his well-known 'Estimate of the Comparative 
 Strength of Great Britain.' 
 
 The estimate of which I am about to speak is 
 given by Davenant in the following words f: — 
 'We take it, that a defect in the harvest may 
 raise the price of corn in the following propor- 
 tions : 
 
 Defect. 
 
 
 Above the Common Kate 
 
 1 Tenth ^ 
 
 
 3 Tenths 
 
 2 Tenths 
 
 raises 
 
 8 Tenths 
 
 3 Tenths 
 
 . the < 
 
 1-6 Tenths 
 
 4 Tenths 
 
 price 
 
 2-8 Tenths 
 
 5 Tenths 
 
 
 4-5 Tenths. 
 
 So that when corn rises to treble the common 
 rate, it may be presumed that we want above |^ of 
 
 ■ e ' The Political and Commercial Works of Charles Davenant,' 
 vol. ii. p. 163. 
 f Ibid. p. 224.
 
 Theory of Exchange. 169 
 
 the common produce; and if we should want ~, 
 or half the common produce, the price would rise 
 to near five times the common rate.' 
 
 Though this estimate has always been attri- 
 buted to Gregory King, 1 cannot find it in his 
 published treatise; nor does Davenant, who else- 
 where makes full acknowledgments of what he 
 owes to King, here attribute it to his friend. It 
 is therefore, perhaps, due to Davenant. 
 
 We may re-state this estimate in the folloAv- 
 iug manner, taking the average harvest and the 
 average price of corn as unity — 
 
 Quantity of Corn 
 
 1-0 
 
 •9 
 
 •8 
 
 •7 
 
 •6 
 
 •5 
 
 Price .... 
 
 1-0 
 
 1-3 
 
 1-8 
 
 2-6 
 
 3-8 
 
 5-5 
 
 Many writers have commented on this estimate. 
 Thornton g observes, that it is probably exceed- 
 ingly inaccurate, and that it is not clear whether 
 the total stock, or only the harvest of a single 
 year, is to be taken as deficient. Tooke'\ how- 
 ever, than Avhom. on such a pomt there is no 
 higher authority, believes that King's estimate 'is 
 not very wide of the truth, judging from the 
 repeated occurrence of the fact that the price of 
 corn in this country has risen from one hundred 
 to two hundred per cent, and upwards when the 
 
 s 'An Inquiry into the Nature and Eflfects of the Pajier Credit 
 of Great Britain,' pp. 270, 271. 
 
 1' ' History of Prices,' vol. i. pp. 13-15.
 
 170 The Theory of Political Economy. 
 
 utmost computed deficiency of the crops has not 
 been more than between one-sixth and one-third 
 of an average.' 
 
 I have endeavoured to ascertain the law to 
 which Davenant's figures conform, and the mathe- 
 matical function obtained does not greatly differ 
 from what we might have expected. It is pro- 
 bable that the price of corn should never sink to 
 zero, as, if abundant, it could be used for feeding 
 horses, poultry, and cattle, or for other purposes 
 for which it is too costly at present. It is said 
 that in America corn, no doubt Indian corn, has 
 been occasionally used as fuel. On the other 
 hand, when the quantity is much diminished, the 
 price should rise rapidly, and should become in- 
 finite before the quantity is zero, because famine 
 would then be impending. The substitution of 
 potatoes and other kinds of food renders the 
 famine point very uncertain ; but I think that a 
 total deficiency of corn could not be made up by 
 
 other food. Now a function of the form 
 
 fulfils these conditions ; for it becomes infinite 
 when cV is reduced to h, but for greater values of 
 A' always decreases as .v increases. An inspection 
 of the numerical data shows that n is about equal to 
 2, and, assuming it to be exactly 2, I find that the 
 most probable values of a and h are a = '824 and 
 h = '12. The formula thus becomes
 
 Tlieorii of Exoliamje. Ill 
 
 •824 
 
 price of corn = 
 
 (..-12)^ 
 
 or approximately, = ^ . 
 
 The folloAving- numbers show the degree of ap- 
 proximation between tlie first of these formulae 
 and the data of Davenant — 
 
 Harvest 1-0 "9 -8 •? "6 5 
 
 Price (Davenant) 1-0 1-3 I'S 2-6 3-8 5-5 
 Price calculated . 1-06 1-36 1-78 2-45 3-58 571 
 
 I cannot undertake to saj^ how nearly Dave- 
 nant's estimate agrees with experience ; but, con- 
 sidering the close approximation in the above 
 numbers, we may safely substitute the empirical 
 formula for his numbers ; and there are other rea- 
 sons already stated for supposing- that this for- 
 mula is not far from the truth. Roughly speak- 
 ing, the price of corn may be said to vary inversely 
 as the square of the supply, provided that this 
 supply be not unusually small. I find that this 
 is nearly the same conclusion as Whewell drew 
 from the same numbers. He says i : 'If the above 
 numbers were to be made the basis of a mathe- 
 matical rule, it Avould be found that the price 
 varies inversely as the square of the supply; or 
 rather in a higher ratio.' 
 
 There is further reason for believinii- that the 
 
 'o 
 
 J Six Lectures on Political Economy. Cambridge, 1862.
 
 172 The Theory of Political Economy. 
 
 price of corn varies more rapidly than in the 
 inverse ratio of the quantity. Tooke estimates ^ 
 that in 1795 and 1796 the farmers of England 
 gained seven millions sterling in each year by a 
 deficiency of one-eighth part in the wheat crop, 
 I not including the considerable profit on the rise 
 of price of other agricultural produce. In each 
 of the years 1799 and 1800, again, farmers pro- 
 ibably gained eleven millions sterling by deficiency. 
 If the price of wheat varied in the simple inverse 
 proportion of the quantity, they would neither 
 gain nor lose, and the fact that they gained con- 
 siderably agrees with our formula as given above. 
 
 The variation of utility has not been overlooked 
 by mathematicians, who had observed, as long ago 
 as the early part of last century — before, in fact, 
 there was any science of Political Economy at all — 
 that the theory of probabilities could not be applied 
 to commerce or gaming without taking notice of 
 the very different utility of the same sum of money 
 to different persons. Suppose that an even and 
 fair bet is made between two persons, one of whom 
 has £10,000 a year, the other £100 a year; let it 
 be an equal chance whether they gain or lose £50. 
 The rich person will, in neither case, feel much 
 difference ; but the poor person will receive far 
 more harm by losing £50 than lie can be benefited 
 by gaining it. The utility of money to a poor 
 
 k ' History uf Prices.'
 
 Theory of Exchange. 173 
 
 person varies rapidly with the amount; to a rich 
 person less so. Daniel Bernoulli, according] 3^, dis- 1 jyj^ 
 tinguished in any question of probabilities ])et\veen j "^^ 
 the moral exjjectation and the mathematical expec- 
 tation, the latter being the simple chance of ob- 
 taining some possession, the former the chance as 
 measured by its utility to the person. Having no 
 means of ascertaining numerically the variation 
 of utility, Bernoulli had to make assumptions of 
 an arbitrar}^ kind, and was then able to obtain 
 reasonable answers to many important questions. 
 It is almost self-evident that the utility of money 
 decreases as a person's total wealth increases ; if . 
 
 this be Q-ranted, it follows at once that gaming is, -^^''^^^ 
 ill the long run, a sure way to lose utility ; that y*j!il- 
 every person should, when possible, divide risks, 
 that is, prefer two equal chances of £50 to one 
 similar chance of £100 ; and the advantage of 
 insurance of all kinds is proved from the same 
 theory. Laplace drew a similar distinction be- 
 tween the fortune physique, or the actual amount 
 of a person's income, and the fortune morale, or 
 its benefit to himi.' 
 
 In answer to the objections of an ingenious S^f*tm- 
 correspondent, it may be remarked that when we ' 
 
 say gaming is a sure way to lose utility, we 
 take no account of the utility — that is, the plea- 
 sure attaching to the pursuit of gaming itself; 
 
 1 Todhunter's ' History of tlie Theory of Probability,' chap. xi. &c.
 
 174 The Theory of Political Economy. 
 
 we regard only the commercial loss or gain. If 
 a person with a certain income prefers to rnn the 
 risk of losing a portion of it at play, rather than 
 spending it in any other way, it must no doubt 
 be conceded that the political economist, as such, 
 can make no conclusive objection. If the gamester 
 is so devoid of other tastes that to spend money 
 over the gaming-table is the best use he can dis- 
 cover for it, economically sj^eaking, there is nothing 
 further to be said. The question then becomes 
 a moral, legislative or political one. A source 
 of amusement which, like gaming, betting, dram- 
 drinking, or opium-eating, is not in itself always 
 pernicious, may come to be regarded as immoral, 
 if in a considerable proportion of cases it leads to 
 excessive and disastrous results. But this ques- 
 tion evidently leads us into a class of subjects 
 which could not be appropriately discussed in this 
 work treating of pure economic theory. 
 
 The Origin of Value. 
 
 The preceding pages contain, if I am not mis- 
 taken, an explanation of the nature of value which 
 will, for the most part, harmonise with previous 
 views upon the subject. Ricardo has stated, like 
 niost other economists, that utility is absolutely 
 essential to value ; but that ' possessing utility, 
 commodities derive their exchangeable value from
 
 Theory of Exchange. 175 
 
 two sources : from their scarcity, and from the 
 quantity of labour required to obtain them"^' 
 Senior, again, has admirably defined wealth, or 
 objects possessing value, as 'those things, and^ 
 those things only, which are transferable, are ( 
 limited in supply, and are directly or indirectly/ 
 productive of pleasure or preventive of pain.'^ 
 Speaking only of things which are transferable, 
 or capable of being passed from hand to hand, 
 we find that two of the clearest definitions of 
 value recognise utility a nd sca rcit]^ as the essen- 
 tial qualities. But the moment that we dis- 
 tinguish between the total utility of a mass of 
 commodity and the degree of utility of different 
 portions, Ave may say that it is scarcity which 
 prevents the fall in the final degree of utility. 
 Bread has the almost infinite utility of main- 
 taining life, and when it becomes a question of 
 life or death, a small quantity of food exceeds in 
 value all other things. But when we enjoy our 
 ordinary su2:)plies of food, a loaf of bread has 
 little value, because the utility of an additional 
 loaf is small, our appetites being satiated by our 
 customary meals. 
 
 I have pointed out the excessive ambiguity of 
 the word Value, and the apparent impossibility 
 of using it safely. When intended to express the 
 
 ™ ' Principles of Political Economy and Taxation,' third edition, 
 p. 2.
 
 176 The Theory of Political Economy. 
 
 mere fact of certain articles exchanging in a par- 
 ticular ratio, I have proposed to substitute the 
 unequivocal expression — ratio of exchange. But 
 I am inclined to believe that a ratio is not the 
 meaning which most persons attach to the word 
 Value. There is a certain sense of esteem or 
 desirableness, which we may have with regard to 
 a thing apart from any distinct consciousness of 
 the ratio in which it would exchange for other 
 things. I may suggest that this distinct feeling 
 of value is probably identical with the final degree 
 of utility. While Adam Smith's often-quoted value 
 
 5 in use is the total utility of a commodity to us, 
 the value in exchange is defined by the terminal 
 ^utility,, the remaining desire which we or others 
 (have for possessing more. 
 
 There remains the question of labour as an 
 element of value. Economists have not been want- 
 ing who put forward labour as the cause of value, 
 asserting that all objects derive their value from 
 the fact that labour has been expended on them ; 
 and it is thus implied, if not stated, that value 
 will be proportional to labour. This is a doctrine 
 which cannot stand for a moment, being directly 
 opposed to facts. Ricardo disposes of such an 
 opinion when he says » : ' There are some com- 
 modities, the value of which is determined by 
 
 " * On the Principles of Political Economy and Taxation,' third 
 edition, 1821, p. 2.
 
 Theory of Exchange. Vll 
 
 their scarcity alone. No labour can increase the 
 quantity of such goods, and therefore their value 
 cannot be loAvered by an increased supply. Somef' '^^^*^'*^ 
 rare statues and pictures, scarce books and coins, ''^- 
 wines of a peculiar quality, which can be made 
 only from grapes grown on a particular soil, of 
 which there is a very limited quantity, are all 
 of this description. Their value is wholly inde- 
 pendent of the quantity of labour originally neces- ' - ' 
 sar}'' to produce them, and varies Avith the varying 
 wealth and inclinations of those who are desirous 
 to possess them.' 
 
 The mere fact that there are many things, such 
 as rare ancient books, coins, antiquities, etc., which 
 have high values, and which are absolutely inca- 
 pable of production now, disperses the notion that 
 value depends on labour. Even those things which^ 
 are producible in any quantity by labour seldom ,>^^ 
 exchange exactly at the corresponding values o. 
 The market price of corn, cotton, iron, and most 
 other things is, in the prevalent theories of value, 
 ^..A.> allowed to fluctuate al)Ove or below its natural 
 
 " Ifr. "W. L. Sargant in liis 'Recent Political Economy,' 8vo. 
 London, 1867, p. 99, states that contracts have been made to 
 manufacture the Enfield Rifle, of identically the same pattern, at 
 prices ranging from 70^. each down to 20a\, or even lower. The 
 ■wages of the workmen varied from 40s. or 50s. down to 15s. a 
 week. Such an instance renders it obvious that it is> scarcity which 
 governs value, and that it is th^ value of the produce which deter- 
 mines the wages of the producerf;.
 
 178 The Theory of Political Economy. 
 
 or cost value. There may, again, be any dis- 
 crepancy between the quantity of labour spent 
 upon an object and the value ultimately attach- 
 ing to it. A great undertaking like the Great 
 Western Railway, or the Thames Tunnel, may 
 embody a vast amount of labour, but its value 
 depends entirely upon the number of persons who 
 find it useful. If no use could be found for the 
 Great Eastern steam ship, its value would be nil, 
 except for the utility of some of its materials. 
 On the other hand, a successful undertaking, which 
 happens to possess great utility, may have a value, 
 for a time at least, far exceeding what has been 
 spent upon it, as in the case of the Atlantic cable. 
 The fact is, that laboui' once sj^ent has no influence 
 on the future value of amy article : it is gone and 
 lost for ever. In commerce, by-gones are for ever 
 by-gones ; and we are always starting clear at 
 each moment, judging the values of things with 
 'a view to future utility. Industry is essentially 
 prospective, not retrospective ; and seldom does 
 the result of any undertaking exactly coincide 
 with the first intentions of its promoters. 
 
 But thougli labour is never the cause of value, 
 it is in a large proportion of cases the determining 
 circumstance, and in the following way: — Vahie 
 depends solely on the final degree of utility. How 
 can we vai^y this degree of utility f — By having 
 more or less of the commodity to coJisume. And
 
 -uww^-s-T^-', Y^ /'Lf-ii**' Theox]) of Exfihanae. MJ^r 179 
 
 ^oi'j iViaZ? M'c (/e^ more or less of it f — By spending 
 more or less labour in obtaining a supply. Ac- 
 cording to this view, then, there are two steps 
 between labour and, value. Labour affects supply, 
 and siippiy affects fiie- degree of utility, which 
 governs value, or the ratio of exchanget In order 
 that there may be no possible mistake about this 
 all-important series of relations, I will restate it 
 in a tabular form, as follows, : — , . ^ 
 t-la*^'^^<x< Cost of production determines supply, t v ^A^^/^'^^'^^y^ 
 
 ^ " Sup) ply determines final degree of utility. -M^tx/v**-^ 
 
 Final degree of utility determines value. 'txts-f^^ . 
 
 But it is easy to go too far in considering 
 labour as the regulator of value; it is equally to 
 be remembered that labour is itself of unequal 
 value. Ricardo, by a violent assumption, founded 
 his theory of value on quantities of labour con- 
 sidered as one uniform thing. He was aware that 
 labour differs infinitely in quality and efficiency, 
 so that each kind is more or less scarce, and is 
 consequently paid at a higher or lower rate of 
 wages. He regarded these differences as disturb- 
 ing circumstances which would have to be allowed 
 for; but his theory rests on the assumed equality 
 of labour. This theory rests on a wholly different 
 ground. I_hold labour to be essentially variable, ,■ 
 so that its vfiliii' mustjbe determined hy the value 
 of the p roduce, not the value of tJie produce hy 
 that of tJic l ahour . I hold it to be impossible to 
 
 N 2
 
 180 Tlie Theory of Political Economy. 
 
 compare a priori the productive powers of a 
 navvy, a carpenter, an iron-puddler, a schoolmaster, 
 and a barrister. Accordingly, it will be found that 
 not one of my equations represents a comparison 
 between one man's labour and another's. The 
 equation, if there is one at all, is between the 
 same person in two or more different occupations. 
 The subject is one in which complicated action 
 and re-action takes place, and which we must 
 defer until after we have described, in the next 
 chapter, the Theory of Labour.
 
 CHAPTER V. 
 
 THEORY OF LABOUR. 
 
 Definition of Labour. 
 
 Adam Smith said, ' The real price of everything, 
 what everything really costs to the man who wants 
 to acquire it, is the toil and trouble of acquiring 
 it. . . . Labour was the first price, the original 
 purchase-money, that was paid for all things^.' 
 If subjected to a very searching analysis, this 
 celebrated passage might not prove to be so en- 
 tirely true as it would at first sight seem to most 
 readers to be. Yet it is substantially true, and 
 luminously expresses the fact that labour is the 
 beginning of the processes treated by economists, 
 as consumption is the end and purpose. Labour 
 is the painful exertion which we undergo to 
 ward off" pains of greater amount, or to procure 
 
 •^ ' "Wealth of Natioiis,' book i. cliap. 5
 
 182 The Theory of Folitical Economy. 
 
 pleasures which leave a balance in our favour. 
 Courcelle-Seneuil ^ and Hearn have stated the 
 problem of Economics with the utmost truth and 
 brevity in saying, that it is to satisfy our ivants 
 with the least possible sum of labour. 
 
 In defining labour for the purposes of the eco- 
 nomist we have a choice between two courses. 
 In the first j^lace, we may, if we like, include in 
 it all exertion of body or mind. A game of 
 cricket would, in this case, be labour; but if it 
 be undertaken solel}^ for the sake of the enjoy- 
 ment attaching to it, the question arises whether 
 we need take it under our notice. All exertion 
 not directed to a distant and distinct end must 
 be repaid simultaneously. There is no account 
 of good or evil to be balanced at a future time. 
 We are not prevented in any way from including 
 such cases in our Theory of Economics; in fact, 
 our Theory of Labour will, of necessity, apply to 
 them. But we need not occupy our attention by 
 cases which demand no calculus. When we exert 
 ourselves for the sole amusement of the moment, 
 there is but one rule needed, namely, to stoj) when 
 we feel inclined — when the pleasure no longer 
 equals the pain. 
 
 It will probably be better, therefore, to take 
 •the second course and concentrate our attention 
 
 ^ 'Traits Theorique et Pratique d'Economle Politique,' 2nd 
 edition, vol. i. p. 33.
 
 Theory of Labour. 183 
 
 on such exertion as is not completely repaid by 
 the immediate result. This would give us a de- 
 finition nearly the same as that of Say, who 
 defined labour as ''Action suivee, dirigee vers un 
 but.' Labour, I should say, is any iminful exer- 
 tion of mind or body undergone partly or ivholly 
 until a vieiv to future good ^. It is true that labour 
 may be both agreeable at the time and conducive 
 to future good; but it is only agreeable in a 
 limited amount, and most men are compelled by 
 their wants to exert themselves longer and more 
 severely than they would otherwise do. When 
 a labourer is inclined to stop, he clearly feels 
 something that is irksome, and our theory will 
 only involve the point where the exertion has 
 
 c I have altered this definition as it stood in the first edition by 
 inserting the words 'partly or loliolly, and I only give it noAv as pro- JVrjJPqf 
 visionally the best I can suggest. The subject presents itself to me " 
 
 as one of great difficulty, and it is possible that the true solution 
 •will consist in treating labour as a case of negative utility, or 
 negative mingled with positive utility. We should thus arrive at a 
 higher generalisation which appeal's to be foreshadowed in the 
 remarkable work of Hermann Heinrich Gossen described in the 
 preface to this edition. Every act, whether of production or of 
 consumption, may be regarded as producing what Bentham calls a 
 lot both of pleasures and pains, and the distinction between the two 
 processes will consist in the fact that the algebraic value of the lot 
 in the case of consumption yields a balance of positive utility, while 
 that of production yields a negative or painful balance, at least in 
 that part of the labour involving most effort. In a happy life the 
 negative balance involved in production is more than cleared off 
 by the positive balance of pleasure arising from consumption.
 
 184 The Theory of Political Economy. 
 
 become so painful as to nearly balance all other 
 considerations. Whatever there is that is whole- 
 some or agreeable about labour before it reaches 
 this point may be taken as a net profit of good 
 to the labourer; but it does not enter into the 
 problem. It is only when labour becomes effort 
 that we take account of it, and, as Hearn truly 
 says*^^, 'such effort, as the very term seems to 
 imply, is more or less troublesome.' In fact, we 
 must, as will shortly appear, measure labour by 
 tlie amount of pain which attaches to it. 
 
 Quantitative Notions of Labour. 
 
 Let us endeavour to form a clear notion of what 
 we mean by amount of labour. It is plain that 
 duration Avill be one element of it; for a person 
 labouring uniformly during two months must be 
 allowed to labour twice as much as during one 
 month. But labour may vary also in intensity. 
 In the same time a man may walk a greater or 
 less distance ; may saw a greater or less amount 
 of timber; may pump a greater or less quantity 
 of water; in short, may exert more or less mus- 
 cular and nervous force. Hence amount of labour 
 will be a quantity of two dimensions, the product 
 of intensity and time when the intensity is uni- 
 form, or the sum represented by the area of a 
 curve when the intensity is variable. 
 
 «' ' Plutology,' p. 24.
 
 Theory of Lah')ur. 185 
 
 But intensity of labou r may have more than 
 one meaning ; it may mean the quantity of work 
 done, or the painfuhiess of tlie effort of doing it. 
 Tliese two tilings must be carefully distinguislied, 
 and both are of great importance for the theory. 
 Tlie one is the reward, the other the penalty, of 
 labour. Or rather, as the produce is only of in- 
 terest to ns so far as it possesses utility, we may 
 say that there are three quantities involved in 
 the theory of labour — the amount of painful ex- i. 
 ertiouythe amount of produce^and the amount of "h- 
 utility gained.^ The variation of utility, as depend- 
 ing on the quantity of commodity possessed, has 
 ^ already been considered ; the variation of the 
 <A a moun t of produce will be treated in the next 
 
 chapt er ; we will here give attention to the varia -y 
 y t ion of t he painfulness of labour. 
 
 Experience shows that as labour is prolonged 
 the effort becomes as a general rule more and 
 more painful. A few hours' Avork per day may 
 be considered agreeable rather than otherwise; 
 but so soon as the overflowing energy of the body 
 is drained off, it becomes irksome to remain at 
 work. As exhaustion approaches, continued effort 
 becomes more and more intolerable. Jennings has 
 so clearly stated this law of the variation of labour, 
 that I must quote his words e. ' Between these two 
 points, the point of incipent effort and the point 
 
 e 'Natural Elements of Political Economy,' p. 119.
 
 186 The Theory of Political Economy. 
 
 of painful suffering, it is quite evident that the de- 
 gree of toilsome sensations endured does not vary 
 directly as the quantity of work performed, but 
 increases much more rapidly, like the resistance 
 offered by an opposing medium to the velocity of 
 a moving body. 
 
 'When this observation comes to be applied to 
 the toilsome sensations endured by the working 
 classes, it will be found convenient to fix on a 
 middle point, the average amount of toilsome 
 sensation attending the average amount of labour, 
 and to measure from this point the degrees of 
 variation. If, for the sake of illustration, this 
 average amount be assumed to be of ten hours' 
 duration, it would follow that, if at any period 
 the amount were to be supposed to be reduced 
 to five hours, the sensations of labour would be 
 found, at least by the majority of mankind, to 
 be almost merged in the pleasures of occupation 
 and exercise, whilst the amount of work performed 
 would only be diminished by one half; if, on the 
 contrary, the amount were to be suj^posed to be 
 increased to twenty hours, the quantity of work 
 produced would only be doubled, whilst the amount 
 of toilsome suffering would become insupportable. 
 Thus, if the quantity produced, greater or less than 
 the average quantity, were to be divided into any 
 number of parts of equal magnitude, the amount 
 of toilsome sensation attending each succeeding
 
 Theory of Labour. 
 
 187 
 
 increment would be found greater than that which 
 would attend the increment preceding; and the 
 amount of toilsome sensation attending each suc- 
 ceeding decrement would he found loss than that 
 which would attend the decrement preceding.' 
 
 There can be no question of the general truth 
 of the above statement, although we may not 
 have the data for assigning the exact law of tlie 
 variation. We may imagine the painfulness of 
 
 Ficj. VIII 
 
 labour in proportion to produce to be represented 
 by some such curve as ahcd in Fig. VIII. In this 
 diagram the height of points above the line OcV 
 denotes pleasure, and depth below it pain. At 
 the moment of commencing labour it is usually 
 more irksome than when the mind and body are 
 well bent to the work. Thus, at first, the pain is 
 measured by oa. At h there is neither pain nor
 
 188 TliG TImory of Political Economy. 
 
 pleasure. Between h and c an excess of pleasure 
 is represented as due to the exertion itself. But 
 after c the energy begins to be rapidly exhausted, 
 and the resulting pain is shown by the downward 
 tendency of the line cd. 
 
 We may at the same time represent the degree 
 of utility of the produce by some such curve as jpq, 
 the amount of produce being measured along the 
 line 0A\ Agreeably to the theory of utility, already 
 given, the curve shows that, the larger the wages 
 earned, the less is the pleasure derived from a 
 further increment. There will, of necessity, be. 
 some point m such that qm — chn, that is to say, 
 such that the pleasure gained is exactly equal to 
 the labour endured. Now, if we pass the least 
 beyond this point, a balance of pain will result: 
 there will be an ever-decreasing motive in favour 
 of labour, and an ever-increasing motive against 
 it. The labourer will evidently cease, then, at the 
 point m. It would be inconsistent with human 
 nature for a man to work when the pain of work 
 exceeds the desire of possession, including all the 
 motives for exertion. 
 
 We must consider the duration of labour as 
 measured by the number of hours' work per day. 
 The alternation of day and night on the earth has 
 rendered man essentially periodic in his habits and 
 actions. In a natural and wholesome condition 
 a man should return each twenty-four hours to
 
 Theory of Lcihour. 189 
 
 exactly the same state ; at any rate, the cycle 
 should be closed within the seven days of the week. 
 Thus the labourer must not be supposed to be 
 either increasing or diminishing his normal strength. 
 But the theory might also be made to apply to 
 cases wdiere special exertion is undergone for many 
 days or weeks in succession, in order to complete 
 work, as in collecting the harvest. Adequate 
 motives may lead to and warrant over-work, but, 
 if long continued, excessive labour reduces the 
 strength and becomes insupportable ; and the 
 longer it continues the worse it is, the law being 
 somewhat similar to that of periodic labour. 
 
 Symbolic Statement of the Theory. 
 
 In attempting to represent these conditions of 
 labour with accuracy, we shall find that there are 
 no less than four quantities concerned; let us 
 denote them as follows — 
 
 ^ = time, or duration of labour. 
 / = amount of labour, as meaning the aggregate 
 balance of pain accompanying it, irre- 
 spective of the produce. 
 ./' = amount of commodity produced. 
 '/ = total utility of that commodity. 
 The amount of commodity produced will be very 
 different in different cases. In any one case the 
 rate of production will be determined by dividing
 
 190 Tlie Theory of Political Economy. 
 
 the whole quantity produced by the time of pro- 
 duction, provided that the rate of production has 
 
 been uniform ; it will then be -. But if the rate 
 
 z 
 
 of production be variable, it can only be deter- 
 mined at any moment by comparing a small quan- 
 tity of produce with the small portion of time 
 occupied in its production. More strictly speaking 
 we must ascertain the ratio of an infinitely small 
 quantity of produce to the corresponding infinitely 
 small portion of time. Thus the rate of ^production 
 
 is properly denoted by — - , or at the limit by -=-. 
 
 A t Clt 
 
 Again, the degree of painfulness of labour would 
 
 be - if it remained invariable ; but as it is highly 
 
 variable, we must again compare small increments, 
 
 and — - , or, at the limit, -^ correctly represents the 
 
 degree of painfulness of labour. But we must also 
 take into account the fact, that the utility of com- 
 modity is not constant. If a man works regularly 
 twelve hours a day, he will produce more com- 
 modity than in ten hours; therefore the final 
 degree of utility of his commodity, Avhether he 
 consume it himself or whether he exchange it, will 
 not be quite so high as when he produced less. 
 
 du 
 This degree of utility is denoted, as before, by -^,
 
 Theory of Labour. 191 
 
 the ratio of the increment of ntility to the incre- 
 ment of commodity. 
 
 The amount of reward of labour can now be 
 
 expressed ; for it is — . _ ; that is to say, it is 
 
 the product of the ratio of tlie commodity produced 
 to the time, multiplied by the ratio of the utility 
 to the amount of produce. Thus, the last two 
 h ours of work in the day generally gives less 
 reward, both because less produce is then created 
 in proportion to the time spent, and because tliat 
 produce is less necessary and useful to one who 
 makes enough to support himself in the other ten 
 hours 
 
 We can now ascertain the length of time whicli 
 should be selected as the most advantageous term 
 of labour. A free labourer endures the irksome- 
 ness of work because the pleasure he expects to 
 receive, or the pain he expects to ward off", by 
 means of the produce, exceeds the pain of exertion. 
 When labour itself is a worse evil than that which 
 it saves him from, there can be no motive for fur- 
 ther exertion, and he ceases. Therefore he will 
 cease to labour just at the point when the pain 
 becomes equal to the corresponding pleasure gained ; 
 and we thus have t defined by the equation 
 dl del" du 
 dt dt da? 
 
 In this, as in the other questions of Economics,
 
 192 The. Theory of Political Eco'iwmy. 
 
 all depends upon the final increments, and we have 
 expressed in the above formula the final equivalence 
 oflahour and utility. A man must be regarded as 
 earning all through his hours of labour an excess 
 of utility ; what he produces must be considered 
 not merely the exact equivalent of the labour he 
 gives for it, for it would be, in that case, a matter 
 of indifference whether he laboured or not. As 
 long as he gains, he labom'Sj and when he ceases to 
 gain, he ceases to labour. 
 
 In some cases, as in some kinds of machine 
 labour, the rate of production is uniform or nearly 
 so, and by choice of suitable units may be made 
 equal to unity ; the result may then be put more 
 simply in this way. Labour may be considered as 
 expended in successive small quantities, a/, each 
 lasting, for instance, for a quarter of an hour ; the 
 corresponding benefit derived from the labour will 
 then be denoted by a^^. Now, so long as az^ ex- 
 ceeds in amount of pleasure the negative quantity 
 or pain of a/, the difference of sign being disre- 
 garded, there will be gain inducing to continued 
 labour. Were a u to fall below a I, there would 
 be more harm than good in labouring; therefore, 
 the boundary between lal)our and inactivity will 
 be defined by the equality of a u and a I, and at 
 the limit we have the equation 
 
 du dl 
 d.i' 
 
 l-i^-i"''- i 
 
 ■fc
 
 Theory of Labour. 193 
 
 Dimensions of Labour. 
 
 If I have correctly laid down, in preceding chap- 
 ters, the Theory of Dimensions of Utility and Value, 
 there ought not to he much difficulty in stating the 
 similar theory as regards Labour. We might in 
 fact treat labour as simply one case of disutility 
 or negative utility, that is as pain, or at any rate 
 as a generally painful balance of j^leasure and pain, 
 endured in the action of acquiring commodity. 
 Thus its dimensions might be described as identical 
 with those of utility ; U would then denote in- 
 tensity of labour, or degree of labour, just as it 
 was used to denote degree of utility. If we 
 measure labour with respect to the quantity of 
 commodity produced, that is, if we make commo- 
 dity the variable, then total amount of labour 
 will be the integral of U (i M, and the dimensions 
 of amount of labour will be M U, identical with 
 those of total utility. 
 
 If for any reasons of convenience we prefer to 
 substitute a new symbol, specially appropriated 
 to express the dimensions of labour, and say that 
 intensity of labour is represented by E (Endurance), 
 an d total q uantity of labour incurred in the produc- 
 tion of certain commodity by M E, it must be 
 remembered that the change is one of convenience 
 only ; U and E are essentially quantities of the same 
 nature, and the difference, so far as there is any, 
 

 
 194 Tlie Theory of Political Economy. 
 
 arises from the fact that quantities symbolised 
 by E, will usually be negative as compared with 
 those symbolised by U. Labour, however, is often 
 measured and bought and sold by tiftie, instead 
 of by piecework or commodity produced ; in this 
 case, w^hile E continues to express intensity of 
 labour, E T will express the dimensions of amount 
 of labour. 
 
 Rate of production will obviously possess the 
 same dimensions as rate of consumption (p. 70), 
 namely, M T ~ \ and this quantity forms a link be- 
 tween labour as measured by time and by produce ; 
 for ETxMT-i = ME. It would be possible to 
 invent various other economic quantities, such as 
 acceleration of production, with the dimensions 
 M T~2 J but, until it is apparent how such quantities 
 enter into economic theorems, it seems needless to 
 consider them further. 
 
 Balance between Need and Labour. 
 
 In considering this Theory of Labour, an inter- 
 esting question presents itself Supposing that 
 circumstances alter the relation of produce to 
 labour, what effect will this have upon the amount 
 of labour which will be exerted? There are two 
 effects to be considered. When labour produces 
 more commodity, there is more reward, and there- 
 fore more inducement to labour. If a workman
 
 Theory of Labour. 195 
 
 can earn ninepence an hour instead of sixpence, 
 may he not be induced to extend his hours of 
 labour by this increased result ? This would doubt- 
 less be the case were it not that the very fact 
 of getting half as much more than he did before, 
 lowers the utility to him of any further addition. 
 By the produce of the same number of hours he 
 can satisfy his desires more completely ; and if the 
 irksomeness of labour has reached at all a high 
 point, he may gain more pleasure by relaxing that 
 labour than by consuming more products. The 
 question thus depends upon the direction in which 
 the balance between the utility of further com- 
 modity and the painfulness of prolonged labour 
 turns. 
 
 In our ignorance of the exact form of the func- 
 tions either of utility or of labour, it will be 
 impossible to decide this question in an a priori 
 manner ; but there are a few facts which indicate 
 in which direction the balance does usually turn. 
 Statements are given by Porter, in his ' Progress 
 of the Nation *",' which show that when a sudden 
 rise took place in the prices of provisions in the 
 early part of this century, workmen increased their 
 hours of labour, or, as it is said, worked double 
 time, if they could obtain adequate employment. 
 Now, a rise in the price of food is really the same 
 as a decrease of the produce of labour, since less 
 
 f Edition of 1847, pp. 454, 455. 
 2
 
 196 The Theory of Political Economy. 
 
 of the necessaries of life can be acquired in ex- 
 change for the same money wages. We may 
 conclude, then, that English labourers enjoying 
 little more than the necessaries of life, will work 
 harder the less the produce; or, which comes to 
 the same thing, will work less hard as the produce 
 increases. 
 
 Evidence to the like effect is found in the general 
 tendency to reduce the hours of labour at the pre- 
 sent day, owing to the improved real wages now 
 enjoyed by those employed in mills and factories. 
 'Artisans, mill-hands, and others seem generally 
 I to prefer greater ease to greater wealth, thus 
 I proving that the painfulness of labour varies so 
 rapidly as easily to overbalance the gain of utility. 
 The same rule seems to hold throughout the mer- 
 cantile employments. The richer a man becomes, 
 the less does he devote himself to business. A 
 successful merchant is generally willing to give 
 a considerable share of his profits to a partner, or 
 to a staff of managers and clerks, rather than bear 
 the constant labour of superintendence himself 
 There is also a general tendency to reduce the 
 hours of labour in mercantile offices, due to in- 
 creased comfort and opulence. 
 
 It is obvious, however, that there are many intri- 
 cacies in a matter of this sort. It is not always 
 possible to graduate work to the worker's liking; 
 in some businesses a man who insisted on working
 
 Theory of Labour . . 197 
 
 only a few hours a day would soon have no work 
 to do. In the professions of law, medicine, and the 
 like, it is the reputation of enjoying a large practice 
 which attracts new clients. Thus a successful 
 barrister or j^hysician generally labours more 
 severely as his success increases. This result partly 
 depends upon the fact that the work is not easily 
 capable of being performed by deputy. A suc- 
 cessful barrister, too, soon begins to look forward 
 to the extrinsic rewards of a high judicial or par- 
 liamentary position. But the case of an eminent 
 solicitor, architect, or engineer is one where the 
 work is to a great extent done by employees, and 
 done without reference to social or political rewards, 
 and where yet the most successful man endures 
 the most labour, or rather is most constantly at 
 work. This indicates that the irksomeness of the 
 labour does not increase so as to overbalance the 
 utility of the increment of reward. In some cha- 
 racters and in some occupations, in short, success 
 of labour only excites to new exertions, the work 
 itself being of an interesting and stimulating- 
 nature. But the general rule is to the contrary 
 effect, namely that a certain success disinclines 
 a man to increased labour. It may be added that 
 in the highest kinds of labour, such as those of the 
 philosopher, scientific discoverer, artist, &c., it is 
 questionable how far great success is compatible 
 with ease; the mental powers must be kept in
 
 198 The TJieonj of Political Eco7iomy. 
 
 perfect training by constant exertion, just as a 
 racehorse or an oarsman needs to be constantly 
 exercised. 
 
 It is evident that questions of this kind depend 
 greatly upon the character of the race. Persons 
 of an energetic disposition feel labour less pain- 
 fully than their fellow men, and, if they happen 
 to be endowed with various and acute sensibilities, 
 their desire of further acquisition never ceases. 
 A man of lower race, a negro for instance, enjoys 
 possession less, and loathes labour more; his ex- 
 ertions, therefore, soon stop. A poor savage would 
 be content to gather the almost gratuitous fruits 
 of nature, if they were sufficient to give sustenance ; 
 it is only physical want which drives him to ex- 
 ertion. The rich man in modern society is supplied 
 apparently with all he can desire, and yet he often 
 labours unceasingly for more. Bishop Berkeley, 
 in his 'Querists,' has very well asked, 'Whether 
 the creating of wants be not the likeliest way 
 to produce industry in a people ? And whether, 
 if our (Irish) peasants were accustomed to eat 
 beef and w^ear shoes, they would not be more 
 industrious?' 
 
 Distribution of Labour. 
 
 We now come to consider the conditions which 
 regulate the comparative amounts of different 
 
 g Query No. 20.
 
 Theory of Lahotir. 199 
 
 commodities produced in a country. Tlieoretically 
 speaking, we might regard each person as capable 
 of producing various commodities, and dividing his 
 labour according to certain rules between the dif- 
 ferent employments; it would not be impossible, 
 too, to mention cases where such division does 
 take place. But the result of commerce and the 
 division of labour is usually to make a man find 
 his advantage in performing one trade only; and 
 I give the formulae as they would apply to an 
 individual, only because they are identical in 
 general character with those which apply to a 
 whole nation. 
 
 Suppose that an individual is capable of pro- 
 ducing two kinds of commodity. His sole object, 
 of course, is to produce the greatest amount of 
 utility ; but this will depend partly upon the com- 
 parative degrees of utility of the commodities, and 
 partly on his comparative facilities for producing 
 them. Let c^■ and ?/ be the respective quantities 
 of the commodities already produced, and suppose 
 that he is about to apply more labour ; on which 
 commodity shall he spend the next increment of 
 labour? — Plainly, on that which will yield most 
 utility. Now, if an increment of labour, a/, will 
 yield either of the increments of commodity ^^ 
 and A 1/, the ratios of produce to labour, namely, 
 
 A <r 1 A ?/ 
 
 — ^ and — ~ 
 
 Ai
 
 200 The Theory of Political Economy. 
 
 will form one element in the problem. But to 
 obtain the comparative utilities of these commo- 
 dities, we must multiply respectively by 
 
 For instance, 
 
 ±^ and ^^ 
 
 A Wi A.*" 
 
 A.*" A?i 
 
 expresses the amount of utility which can be 
 obtained by producing a little more of the first 
 commodity; if this be greater than the same ex- 
 pression for the other commodity, it would evi- 
 dently be best to make more of the first com- 
 modity until it ceased to yield any excess of 
 utility. When the labour is finally distributed, 
 we must have the increments of utility from the 
 several emj)loyments equal, and at the limit we 
 have the equation — 
 
 dui del' du.2 dy 
 
 da? dli dy dl2, 
 When this equation holds, there can be no motive 
 for altering or regretting the distribution of labour, 
 and the utility produced is at its maximum. 
 
 There are in this problem two unknown quan- 
 tities, namely the two portions of labour appro- 
 priated to the two commodities. To determine 
 them, we require one other equation in addition 
 to the above. If we put 
 
 " l = l^-\-l,
 
 Theory of Labour. 201 
 
 we have still an unknown quantity to determine, 
 namely, /; but the principles of labour (pp. 187-192) 
 now give us an equation. Labour will be carried 
 on until the increment of utility from any of the 
 employments just balances the increment of pain. 
 This amounts to saying that du, the increment 
 of utility derived from the first employment of 
 labour, is equal in amount of feeling to cll-^, the 
 increment of labour by which it is obtained. This 
 gives us then the further equation — 
 dui dcV 
 
 If we pay regard to sign, indeed, we must re- 
 member that dl is, when measured in the same 
 scale as du, intrinsically negative, but inasmuch 
 as it is given in exchange for du, which is received, 
 it will in this respect be taken negatively, and 
 thus the above equation holds true^. 
 
 Relation of the Theories of Labour and 
 Ecvchange. 
 
 It may tend to give the reader confidence in 
 the preceding theories when he finds that they 
 lead directly to the well-known law, as stated 
 
 t While revising this edition it seems to me probable that this, I 
 as well as some other parts of the theory, might be more simply 
 and generally stated, but what is given is substantially true and/' 
 correct, and it must stand for the present.
 
 202 The Theory of Political Economy. 
 
 in the ordinary language of economists, that value 
 is proportional to the cost of production. As I 
 
 S prefer to state the same law, it is to the effect 
 that the ratio of exchange of commodities will 
 conform in the long run to the ratio of j)roduc- 
 ^tivenes^, which is the reciprocal of the ratio of 
 (the costs of production. The somewhat perplexing 
 relations of these quantities will be fully explained 
 in the next section, but we may now jjroceed to 
 prove the above result symbolically. 
 
 To simplify our expressions, let us substitute 
 
 for the rate of production ^, the symbol ^. 
 
 CI L 
 
 Then w^, ^g, express the relative quantities of two 
 different commodities produced by an increment 
 of labour, and we have the following equation, 
 identical with that on page 200. 
 
 Let us suppose that the person to whom it applies 
 is in a position to exchange with other persons. 
 The conditions of production will now, in all pro- 
 bability, be modified. For ^ the quantity of our 
 commodity may perhaps be increased to cv + d\, 
 and y diminished to y—y^^ by an exchange of the 
 quantities a\ and y^. If this be so, we shall, 
 as shown in the Theory of Exchange, have the 
 •equation 
 
 (^ {w + c^'i) ^ y^
 
 Theory of Labour. 203 
 
 Our equation of production will now be modified, 
 and become 
 
 or < /)(><■ + j-i) ^^2. 
 
 But this equation has its first member identical 
 with the first member of the equation of exchange 
 given above, so that we may at once deduce the 
 all-important equation 
 
 The reader will remember that ^ expresses the 
 ratio of produce to labour; thus we have proved 
 that commodities will exchange in any market 
 in the ratio of the quantities produced by thei 
 same quantity of labour. But as the increment 
 of labour considered is always the final one, our 
 equation also expresses the truth, that articles 
 will exchange in quantities inversely as the costs 
 of production of the mosl costly portions, i.e. the 
 last portions added. This result will prove of great 
 importance in the theory of Rent, 
 
 Let it be observed that, in uniting the theories 
 of exchange and production, a complicated double 
 adjustment takes place in the quantities of com- 
 modity involved. Each party adjusts not only its 
 consumption of articles in accordance with their 
 ratio of exchange, but it also adjusts its pro-
 
 204 The Theory of Political Economy. 
 
 duction of them. The ratio of exchange governs 
 the production as much as the production governs 
 the ratio of exchange. For instance, since the 
 Corn Laws have been abolished in England, the 
 effect has been, not to destroy the culture of 
 wheat, but to lessen it. The land less suitable 
 to the growth of wheat has been turned to grazing 
 or other purposes more profitable comparatively 
 speaking. Similarly the importation of hops or 
 eggs or any other article of food does not even 
 reduce the quantity raised here, but prevents the 
 necessity for resorting to more expensive modes 
 of increasing the supply. It is not easy to express 
 in words how the ratios of exchange are finally 
 determined. They depend upon a general balance 
 of producing power and of demand as measured 
 by the final degree of utility. Every additional 
 supply tends to lower the degree of utility; but 
 whether that suj^ply will be forthcoming from 
 any country depends upon its comparative powers 
 of producing different commodities. 
 
 Any very small tract of country cannot appre- 
 ciably affect the comparative supply of commo- 
 dities : it must therefore adjust its productions in 
 accordance with the general state of the market. 
 The county of Bedford, for instance, avouM not 
 appreciably affect the markets for corn, cheese, 
 or cattle, whether it devoted every acre to corn 
 or to grazing. Therefore the agriculture of Bed-
 
 Theory of Labour. 205 
 
 ford shire, will have to be adapted to circumstances, 
 and each field will be employed for arable or 
 grazing land according as prevailing prices render 
 one employment or the other more profitable. But 
 any large country will affect the markets as well 
 as be affected. If the whole habitable surface of 
 Australia, instead of producing wool, could be 
 turned to the cultivation of wine, the wool market 
 would rise, and the wine market fall. If the 
 Southern States of America abandoned cotton in 
 favour of sugar, there would be a revolution in 
 these markets. It would be inevitable for Aus- 
 tralia to return to wool and the American States 
 to cotton. These are illustrations of the reciprocal 
 relation of exchange and production. 
 
 Relations of Economic Quantities. 
 
 I hope that I may sometime be able, in a future 
 and much larger work, to explain in detail the 
 results which can be derived from the mathe- 
 matical theory expounded in the previous pages. 
 This essay gives them only in an implicit manner. 
 But, before leaving the subject of exchange, it 
 may be well without delay to point out how the 
 results so far set forth connect themselves with 
 the recognised doctrines of political economy. For 
 the sake of accuracy I have avoided the use of the 
 word value ; the expression cost of j^roduction, so
 
 206 The Theory of Political Economy. 
 
 continually recurring in most economical treatises, 
 is also here conspicuous by its absence. The reader 
 then, unless he be very careful, may be thrown 
 into some perplexity, when he proceeds to com- 
 pare my results with those familiar to him else- 
 where. I will therefore proceed to trace out the 
 connections between the several quantitative ex- 
 pressions, which most commonly occur in discus- 
 sions concerning value, exchange, and production. 
 
 In the first place, the ratio of exchange is the 
 actual numerical ratio of the quantities given and 
 received. Let X and Y be the names of the com- 
 modities : a? and y the quantities of them respec- 
 tively exchanged. Then the ratio of exchange is 
 that of y to ^. But the value of a commodity in 
 exchange is greater as the quantity received is 
 less, so that the ratio of the quantities dealt with 
 must be the reciprocal of the ratio of the values 
 of the substances, meaning by value the value per 
 unit of the commodity. Thus we may say 
 
 y _ Value of X per unit 
 
 <?■ ~ Value of Y per unit. 
 
 Value is of course very frequently estimated by 
 price, that is by the quantity of legal money for 
 which the commodity may be exchanged. Price is 
 indeed ambiguous in the same way as value; it 
 means either the 2^rice of the tvhole quantity, or 
 the price per unit of the quantity. Let p-^^ be the 
 price per unit of X, and p.^ the similar price of Y.
 
 Theory of Labour. 207 
 
 Then, it is apparent that 1/ xp.2, will l)e the whole 
 price of y, and d- x jh ^^'iH '^^ the whole price of .^■. 
 These two mnst be equal to each other, so that 
 we get 
 
 ^' Pi 
 
 Thus we find that, when price means price per 
 unit, the quantities exchanged are recijirocally as 
 the prices. When price means price of the whole 
 quantity, the quantities given and received are 
 always of equal price. 
 
 Turning now to the production of commodity, it 
 is sufficiently obvious that the cost of production, 
 so far as this expression can be accurately inter- 
 preted, varies as the reciprocal of the degree of pro- 
 ductiveness. The rate of wages remaining con- 
 stant, the cost per unit of commodity must of 
 course be lower as the quantity produced in 
 return for a certain amount of wages is greater. 
 Thus we may lay down the equation 
 
 Degree of productiveness of,Y 
 Degree of productiveness of X '^'^'"' ■-.*-" 
 
 _ Cost of production of X 
 ~ Cost of production of Y. 
 
 Now, it was shewn in pp. 202-3 that the quantities 
 exchanged are directly proportional to the degrees 
 of productiveness, 
 
 y _ Degree of productiveness of Y 
 a:; ~ Degree of productiveness of X.
 
 208 The Theory of Political Ecbiiomy. 
 
 But the ratio of the values is the reciprocal of ^, 
 
 w 
 
 aud the ratio of the costs of production is the 
 recijDrocal of the other member of the above equa- 
 tion. Thus it follows that 
 
 Value per unit of X Cost of production per unit of X 
 Value per unit of Y ~" Cost of production per unit of Y, 
 
 or, in other words, value is jproportional to cost of 
 production. As, moreover, the final degrees of utility 
 of commodities are inversely as the quantities ex- 
 changed, it follows, that the values per unit are 
 directly proportional to the final degrees of utility. 
 As it is quite indispensable that the student 
 of political economy should keep the relations of 
 these quantities before his mind with perfect clear- 
 ness, I repeat the results in several forms of state- 
 ment. Thus we may group the ratios together — 
 
 Ratio of exchange = - 
 
 _ Quantity of Y given or received 
 ~ Quantity of X received or given 
 Value per unit of X Price per unit of X 
 
 Value per unit of Y ~ Price per unit of Y 
 Final degree of utility of X 
 Final degree of utility of Y 
 
 Cost of production per unit ofX 
 " Cost of production per unit of Y 
 Degree of productiveness of Y 
 
 Degree of productiveness of X. l^^^:r:CLrirj
 
 Theory of Lahour. 209 
 
 We may state the matter more briefly in the fol- 
 lowing words : — The quantities of commodity given\ 
 or received in exchange, are directly j^^^^oportional ' 
 to the degrees of ijroductiveness of labour a]p])lied\ j 
 to their production, and inversely proportional to I 
 the values and prices of those commodities and to > 
 their costs of production per unit, as ivell as to their 
 fined degrees of utility. I will even repeat the 
 same statements once more in the form of a 
 diagram : — 
 
 Quantities of Commodity exchanged vary 
 
 directly as the quantities inversely as their 
 
 produced by the same (1) Values. 
 
 labour. (2) Prices. 
 
 (3) Costs of production. 
 
 (4) Pinal degrees of utility. 
 
 Various Cases of the Theory. 
 
 As we have now reached the principal question 
 in Economics, it will be well to consider the mean- J 
 ing and results of our equations in some detail. 
 
 It will, in the first place, be apparent, that the 
 absolute facility of producing commodities will not 
 determine the character and amount of trade. The 
 
 ratio of exchange '^ is not determined by ^i, nor 
 
 by OTg separately, but by their comparative mag- 
 nitudes. If the producing power of a country were 
 
 p 
 
 'f-f^
 
 210 The Theorxj 0/ Political Economy. 
 
 doubled, no direct effect would be produced upon 
 the terms of its commerce provided that the in- 
 crease were equal in all branches of production. 
 This is a point of great importance, which was 
 correctly conceived by Ricardo, and has been fully 
 explained by J. S. Mill. 
 
 But though there is no such direct effect, it 
 \ may happen that there will be an indire ct effect 
 through the variation in the degree of utility of 
 different articles. When an increased amount of 
 every commodity can be produced, it is not likely 
 that the increase will be equally desired in each 
 branch of consumption. Hence the degree of utility 
 will fall in some cases more than in others. An 
 alteration of the ratios of exchange must result, 
 and the production of the less needed commodities 
 will not be extended so much as in the case of the 
 more needed ones. We might find in such in- 
 stances new proofs that value depends not upon 
 labour but upon the degree of utility. 
 
 It will also be apparent, that nations possessing 
 exactly similar powers of production cannot gain 
 by mutual commerce, and consequently will not 
 have any such commerce, however free from arti- 
 ficial restrictions. We get this result as follows — 
 Taking ^^ ^g, as before, to be the final ratios of 
 •productiveness in one country, and /x^ ^2 in a 
 second, then, if the conditions of production are 
 exactly similar, we have
 
 Theory of Labour. 211 
 
 ^1 Ml 
 
 But when a country does not trade at all, its 
 labour and consumption is distributed according 
 to the condition 
 
 (pa? "=^2 
 
 NoAv, from these equations, it follows necessarily, 
 that 
 
 that is to say, the production and consumptiom'^M'^^/ ^ 
 already conform to the conditions of production/c;;^*^^^^*^ 
 of the second country, and will not undergo any/^^v^v^ 
 alteration when trade with this country becomes^ I^^^ 
 
 ••1 1 •- ,'Lu- ;f?ivc A,^^.) .V^--^-; -■'••■■"■'-'■■■ ■< _■, ■. JL^, . epic 
 
 possiDie. ^^j^^^^;-^ ^-u^-H^o-^^, 5^^.^-^^-. ;;y ^ 'y^j^' 
 
 This is the doctrine usually stated in works on 
 Political Economy, and for Avhich there are good 
 grounds. Bu t I do not t hink the statement will 
 hold true if the co nditions of consumption be very 
 different in two countries. There might be two 
 countries exactly similar in regard to their powers 
 of producing beef and corn, and if their habits of 
 consumption were also exactly similar, there would J]^ T 
 be no trade in these articles. But suppose that 
 the first country consumed proportionally more 
 beef, and the second more corn; then, if there 
 were no trade, the powers of the soil would be 
 
 r 2
 
 212 Tlie Theory of Political Economy. 
 
 differently taxed, and different ratios of exchange 
 
 would prevail. Freedom of trade would cause an 
 
 interchange of corn for beef. Thus I conclude, 
 
 'that it is only where the habits of consumi:>tion, 
 
 ^j^TjK^^ Sas well as the powers of production, are alike, 
 
 — ^ (that trade brings no advantage. 
 
 The general effect of foreign commerce is to 
 disturb, to the advantage of a country, the mode 
 in which it distributes its labour. Excluding from 
 view the cost of carriage, and the other expenses 
 of commerce, we must always have true (?>ja'J"»u 
 
 ^^^ ^1 ^x /^-i 
 
 If, then, OT2 was originally less in proportion to ^^ 
 than is in accordance with these equations, some 
 labour will be transferred from the production 
 of y to that of £c until, by the increased magni- 
 tude of tn-2, and the lessened magnitude of ^i, 
 equality is brought about. 
 — As in the theory of exchange, so in the theory 
 of production, any of the equations may fail, and 
 the meaning is capable of interpretation. Thus, if 
 the equation 
 
 cannot be established, it is impossible that the 
 production of both commodities, y and jp, can go 
 on. One of them will be produced at an expen- 
 diture of labour constantly out of proportion to 
 
 I
 
 Theory of Lahour. 213 
 
 that at M'liich it may be had by exchange. If 
 Ave could not, for instance, import oranges from 
 abroad, part of the labour of the country would 
 probably be diverted from its present employ- 
 ment to raise them ; but the cost of production 
 would be always above that of getting them indi- 
 rectly by exchange, so that free trade necessarily 
 destroys such a wasteful branch of industry. It 
 is on this principle that we import the whole of 
 our wines, teas, sugar, coffee, spices, and many 
 other articles from abroad. 
 
 The ratio of exchange of any two commodities 
 Avill be determined by a kind of struggle between 
 the conditions of consumption and production ; but 
 here again failure of the equations may take place. 
 In the all-important equations 
 
 ^2 expresses the ease with which we may make 
 additions to i/. If we find any means, by ma- 
 chinery or otherwise, of increasing i/ Avithout 
 limit, and Avith the same ease as before, Ave must, 
 
 in all probability, alter the ratio of exchange ^— 
 
 in a corresponding degree. But if Ave could ima- 
 gine the existence of a large population, Avithin 
 reach of the supposed country, Avhose desire to 
 consume the quantity i/^ never decreased, hoAvever 
 large Avas the quantity available, then Ave should
 
 214 The Theory of Political Economy. 
 
 II 'ST 
 
 I never have — equal to — , and the producers of y 
 would make large gains of the nature of rent. 
 
 Joint Production. 
 
 In one of the most interesting chapters of his 
 ' Principles of Political Economy,' Book III, Chap- 
 ter 16, John Stuart Mill has treated of what he 
 calls ' Some peculiar Cases of Value/ Under this 
 title he refers to those commodities which are 
 not produced by separate processes, but are the 
 concurrent or joint results of the same operations. 
 ' It sometimes happens,' he says, ' that two different 
 commodities have what may be termed a joint 
 cost of production. They are both products of 
 the same operation, or set of operations, and the 
 outlay is incurred for the sake of both together, 
 not part for one and part for the other. The 
 same outlay would have to be incurred for either 
 of the two, if the other were not wanted or used 
 at all. There are not a few instances of com- 
 modities thus associated in their production. For 
 example, coke and coal-gas are both produced 
 from the same material, and by the same opera- 
 tion. In a more partial sense, mutton and wool 
 are an example: beef, hides, and tallow: calves 
 and dairy produce: chickens and eggs. Cost of 
 production can have nothing to do with deciding
 
 Tlieory of Labour. 215 
 
 the values of the associated commodities relatively 
 to each other. It only decides their joint value. 
 .... A principle is wanting to apportion the 
 expenses of production between the two.' He 
 goes on to explain that, since the cost of pro- 
 duction principle fails us, we must revert to a 
 law of value anterior to cost of production, and 
 more fundamental, namely the law of supply and 
 demand. 
 
 On some other occasion I may perhaps more 
 fully point out the fallacy involved in Mill's idea 
 that he is reverting to an anterior laiv of value, 
 the law of supply and demand, the fact being 
 that in introducing the cost of production prin- 
 ciple, he had never quitted the laws of supply 
 and demand at all. The cost of production is 
 only one circumstance which governs supply, and 
 thus indirectly influences values. 
 
 Again, I shall point out that these cases of 
 joint production, far from being 'some peculiar 
 cases,' form the general rule, to which it is diffi- 
 cult to point out any clear or important excep- 
 tions. All the great staple commodities at any 
 rate are produced jointly with minor commodities. 
 In the case of corn, for instance, there are the 
 straw, the chaff, the bran, and the different qua- 
 lities of flour or meal, which are products of the 
 same operations. In the case of cotton, there are 
 the seed, the oil, the cotton waste, the refuse, in
 
 216 The Theory of Political Economy. 
 
 addition to the cotton itself. When beer is brewed 
 the grains regularly return a certain price. Trees 
 felled for timber, yield not only the timber, but 
 the loppings, the bark, the outside cuts, the 
 chips, &c. No doubt the secondary products are 
 often nearly valueless, as in the case of cinders, 
 slag from blast furnaces, &c. But even these 
 cases go to show all the more impressively that 
 it is not cost of production which rules values, 
 but the demand and supply of the products. 
 
 The great importance of these cases of joint 
 production renders it necessary for us to con- 
 sider how they can be brought under our theory. 
 Let us suppose that there are two commodities 
 X and Y, yielded by one same operation, which 
 always produces them in the same ratio, say of m of 
 X to ^ of Y. It might seem at first sight as if 
 this ratio would correspond to the ratio of the 
 degrees of productiveness, as shown a few pages 
 above that we might say 
 
 m ^2 _ 2/1 
 n ^1 A\^ 
 
 and thus arrive at the conclusion that things 
 jointly produced would always exchange in the 
 ratio of productiveness. But tliis would be en- 
 tirely false, because that equation can only he 
 established ivhen there is freedom of producing 07ie 
 or the other, at each application of a new incre- 
 ment of labour. It is the freedom of varying the
 
 Theory of Labour. 217 
 
 quantities of each that allows of the produce being- 
 accommodated to the need of it, so that the ratio 
 of the degrees of utility, of the degrees of pro- 
 ductiveness, and of the quantities exchanged are 
 brought to equality. But in cases of joint pro- 
 duction there is no such freedom ; the one sub- 
 stance cannot be made without making a certain 
 fixed proportion of the other, which may have 
 little or no utility. 
 
 It will easily be seen, however, that such cases 
 are brought under our theory by simply aggre- 
 gating together the utilities of the increments of 
 the joint products. If cLv cannot be produced 
 without dy, these being the products of the same 
 increment of labour, dl, then the ratio of produce 
 to labour cannot be written otherwise than as 
 
 dx + dy 
 d!~' 
 
 It is impossible to divide up the labour and say 
 
 that so much is expended on producing X, and 
 
 so much on Y. But we must estimate separately 
 
 the utilities of da/ and dy, by multiplying by their 
 
 clu dtj 
 
 degrees of utility -^ and —- % and we then have 
 d.v dy 
 
 the aggregate ratio of utility to labour as 
 
 du^ dcV ,dii^ dy 
 
 dcV dl dy dl 
 
 It is plain that we have no equation arising out 
 of these conditions of production, so that the ratio
 
 218 The Theory of Political Economy. 
 
 of exchange of X and Y will be governed only by 
 the degrees of utility. But if we compare X and 
 Y with a third commodity Z, as regards its pro- 
 duction, Ave shall arrive at the equation 
 
 dui dcV clu^ dy _ du^ dz 
 
 dx dl dy dl dz dl 
 In other words, the increment of utility obtained 
 by apptying an increment of labour to the pro- 
 duction of Z, must equal the sum of the incre- 
 ments of utility which would be obtained if the 
 same increment of labour were applied to the 
 joint production of X and Y. It is evident that 
 the above equation taken alone gives us no infor- 
 mation as to the ratios existing between the quan- 
 tities dx, dy, and dz. Before we can obtain any 
 ratios of exchange we must have the farther 
 equation between the degrees of utility of X and 
 
 Y, namely 
 
 du^ dy 
 
 dii^ dx 
 
 As a general rule, however, any two processes 
 of production will both yield joint products, so 
 that the equation of productiveness will take the 
 form of a sum of increments of utility on both 
 sides, which we may thus write briefly — 
 
 dui + du2 + .... = dUn + dUn+-^ + , . . . 
 Such an equation becomes then a kind of equa- 
 tion of condition of which the influence may be 
 very slight regarding the ratio of exchange of
 
 Theory of Labour. 219 
 
 any two of the commodities concerned. And if 
 in some cases the terms on one side of such an 
 equation are reduced to one or two, it is probably 
 because the other increments of produce are nearly 
 or quite devoid of utility. As in the cases of 
 cinders, chips, sawdust, spent dyes, potatoe stalks, 
 chaff, &c., &c., almost every process of industry 
 yields refuse results, of which the utility is zero 
 or nearly so. To solve the subject fully, however, 
 we should have to admit negative utilities, as 
 elsewhere explained, so that the increment of 
 utility from any increment dl of labour would 
 really take the form 
 
 du^ ± du.2, ± du^ + . . . . 
 The waste products of a chemical works, for in- 
 stance, will sometimes have a low value ; at other 
 times it will be difficult to get rid of them without 
 fouling the rivers and injuring the neighbouring 
 estates; in this case they are discommodities and 
 take tlie negative sign in the equations. 
 
 Over-production. 
 
 The theory of the distribution of labour enables 
 us to perceive clearly the meaning of over-produc- 
 tion in trade. Early wTiters on Economics Avere 
 always in fear of a supposed glut, arising from 
 the powers of production surpassing the needs of 
 consumers, so that industry would be stopped,
 
 220 Tlie Theonj of Political Economy. 
 
 employment fail, and all but the rich would be 
 starved by the superfluity of commodities. The 
 doctrine is evidently absurd and self-contradictory. 
 As the acquirement of suitable commodities is 
 the whole purpose of industry and trade, the 
 greater the supplies obtained the more perfectly 
 industry fulfils its purpose. To bring about a 
 universal glut would be to accomplish completely 
 the aim of the economist, which is to maximise 
 the products of labour. But the supplies must 
 be suitable — that is, they must be in proportion 
 to the needs of the population. Over-production 
 is not possible in all branches of industry at once, 
 but it is possible in some as compared with others. 
 If, by miscalculation, too much labour is spent 
 in producing one commodity, say silk goods, our 
 equations will not hold true. People will be more 
 satiated with silk goods than cotton, woollen, or 
 other goods. They will refuse, therefore, to pur- 
 chase them at ratios of exchange corresponding 
 to the labour expended. The producers will thus 
 receive in exchange goods of less utility than they 
 might have acquired by a better distribution of 
 their labour. 
 
 In extending industry, therefore, we must be 
 careful to extend it proportionally to all the re- 
 .quirements of the population. The more we can 
 lower the degree of utility of all goods by satiating 
 the desires of the purchasers the better ; but we
 
 TJieory of Labour. 221 
 
 must lower the degrees of utility of different goods 
 in a corresponding manner, otherwise there is an 
 apparent glut and a real loss of labour. 
 
 Limits to the Intensity of Labour. 
 
 I have mentioned (p. 184) that labour may vary 
 either in duration or intensity, but have yet paid 
 little attention to the latter circumstance. We 
 may approximately measure the intensity of labour 
 by the amount of physical force undergone in a 
 certain time, although it is the pain attending 
 that exertion of force which is the all-important 
 element in Economics. Interesting laws have been 
 or may be detected connecting the amount of work 
 done with the intensity of labour. Even where 
 these laws have not been ascertained, long expe- 
 rience has led men, by a sort of unconscious pro- 
 cess of experimentation and inductive reasoning, 
 to select that rate of work which is most advan- 
 tageous. 
 
 Let us take such a simple kind of work as 
 digging. A spade may be made of any size, and 
 if the same number of strokes be made in the 
 hour, the requisite exertion will vary nearly as 
 the cube of the length of the blade. If the spade 
 be small, the fatigue will be slight, but the work 
 done will also be slight. A very large spade, on 
 the other hand, will do a great quantity of work
 
 222 The Theory of Political Economy. 
 
 at each stroke, but the fatigue will be so great 
 that the labourer cannot long continue at his 
 work. Accordingly, a certain medium-sized spade 
 is adojDted, which does not overtax a labourer 
 and prevent him doing a full day's work, but 
 enables him to accomplish as much as possible. 
 The size of a spade should depend partly upon 
 the tenacity and weight of the material, and 
 partly upon the strength of the labourer. It 
 may be observed that, in excavating stiff clay, 
 navvies use a small strong spade ; for ordinary 
 garden purposes a larger sj)ade is employed ; for 
 shovelling loose sand or coals a broad capacious 
 shovel is used; and a still larger instrument is 
 employed for removing corn, malt, or any loose 
 light powder. 
 
 In most cases of muscular exertion the weight 
 of the body or of some limb is of great import- 
 ance. If a man be employed to carry a single 
 letter, he really moves a weight of say a hun- 
 dred and sixty pounds for the purpose of con- 
 veying a letter weighing perhaps half an ounce. 
 There will be no appreciable increase of labour 
 if he carries twenty letters, so that his efficiency 
 will be multiplied twenty times. A hundred let- 
 ters would probably prove a slight burden, but 
 there would still be a vast gain in the work done. 
 It is obvious, however, that we might go on 
 loading a postman with letters until the fatigue
 
 Theory of Labour. 223 
 
 became excessive ; the maximum useful result would 
 be obtained with the largest load which does not 
 severely fatigue the man, and trial soon decides 
 the weight with considerable accuracy. 
 
 The most favourable load for a porter was in- 
 vestigated by Coulomb, and he found that most 
 work could be done by a man walking upstairs 
 without any load, and raising his burden by 
 means of his own weight in descending. A man 
 could thus raise four times as much in a day as 
 by carrying bags on his back with the most 
 favourable load. This great difference doubtless 
 arises from the muscles being perfectly adapted 
 to raising the human body, whereas any addi- 
 tional weight throws irregular or undue stress 
 upon them. Charles Babbage, also, in his admi- 
 rable 'Economy of Manufactures,' has remarked 
 on this subject, and has pointed out that the 
 weight of some limb of the body is an element 
 in all calculations of human labour. 
 
 'The fatigue produced on the muscles of the 
 human frame,' says Babbage, ' does not altogether 
 depend on the actual force employed in each 
 effort, but partly on the frequency with which 
 it is exerted. The exertion necessary to accom- 
 plish every operation consists of two parts: one 
 of these is the expenditure of force which is 
 necessary to drive the tool or instrument; and 
 the other is the effort required for the motion of
 
 224 The Theory of Political Economy. 
 
 some limb of the animal producing the action. 
 In driving a nail into a piece of wood, one of 
 these is lifting the hammer, and p-opelling its 
 head against the nail ; the other is raising the 
 arm itself, and moving it in order to use the 
 hammer. If the weight of the hammer is con- 
 siderable, the former part will cause the greatest 
 portion of the exertion. If the hammer is light, 
 the exertion of raising the arm will produce the 
 greatest part of the fatigue. It does therefore 
 happen, that operations requiring very trifling 
 force, if frequently repeated, will tire more effec- 
 tually than more laborious work. There is also 
 a degree of rapidity beyond which the action of 
 the muscles cannot be pressed V 
 
 It occurred to me, some time since, that this 
 was a subject admitting of interesting inquiry, 
 and I tried to determine, by several series of 
 experiments, the relation between the amount of 
 work done by certain muscles and the rate of 
 fatigue. One series consisted in holding weights 
 varying from one pound to eighteen pounds in 
 the hand while the arm was stretched out at its 
 full length. The trials were two hundred and 
 thirty-eight in number, and were made at inter- 
 vals of at least one hour, so that the fatigue 
 of one trial should not derange the next. The 
 
 i BaLbage, ' On the Economy of Macliinery and Manufactures,' 
 § 32, p. 30.
 
 Theory of Labour. 225 
 
 average number of seconds during which each 
 weight could be sustained was found to be as 
 follows — 
 
 Weight in pounds . . 18 14 10 7 4 2 1 
 Time in seconds . . 15 32 60 87 148 219 321. 
 
 If the arm had been thus employed in any kind 
 of useful work, we should have estimated the use- 
 ful effect by the product of the weight sustained 
 and the time. The results would be as follows, 
 in pound-seconds — 
 
 Weight 18 14 10 7 4 2 1 
 
 Useful effect . . .266 455 603 612 592 438 321. 
 
 The maximum of useful effect would here appear 
 to be about seven pounds, which is about the 
 weight usually chosen for dumb-bells and other 
 gymnastic instruments. Details of the other series 
 of experiments are described in an article in Nature 
 (30th June, 1870, vol. ii. p. 158). 
 
 I undertook these experiments as a mere illus- 
 tration of the mode in which some of the laws 
 forming the physical basis of Economics might 
 be ascertained. I was unaware that Professor S. 
 Haughton had already, by experiment, arrived at! 
 a theory of muscular action, communicated to the] 
 Royal Society in 1862. I was gratified to find| 
 that my entirely independent results proved to 
 be in striking agreement with his principles, as
 
 226 TJie Theory of Political Economy. 
 
 was pointed out by Professor Haughton in two 
 articles in Nature'^. 
 
 I am not aware that any exact experiments 
 upon walking or marching have been made, but, 
 as Professor Haughton has remarked to me, they 
 might easily be carried out in the movements of 
 an army. It would only be necessary, on each 
 march Avhich is carried up to the limits of en- 
 durance, to register the time and distance passed 
 over. Had we a determination of the exact rela- 
 tions of time, space, and fatigue, it would be 
 possible to solve many interesting problems. For 
 instance, if one person has to overtake another, 
 what should be their comparative rates of walk- 
 ing? Assuming the fatigue to increase as the 
 square of the velocity multiplied by the time, we 
 easily obtain an exact solution, showing that the 
 total fatigue will be least when one person 
 walks twice as quickly as he whom he wishes 
 to overtake. 
 
 In different cases of muscular exertion we shall 
 find different problems to solve. The most advan- 
 tageous rate of marching will greatly depend upon 
 
 k Vol. ii. p. 324 ; vol. iii. p. 289. See also Haughton's ' Prin- 
 ciples of Animal Mechanics,' 1873, pp. 444-450. The subject has 
 since been followed up with much care and ability by Professor 
 Francis E. Nipher, of the "Washington University, St. Louis, Mis- 
 souri, U.S. Details of his experiments will be found in the American 
 Journal of Science, vol. ix, pp. 130-7, vol. x. etc, ; Nature, vol. xi. 
 pp. 25G, 276, etc.
 
 Theory of Lahour. 227 
 
 whether the loss of time or the fatigue is the most 
 imjDortant. To march at the rate of four miles 
 an hour would soon occasion enormous fatigue, 
 and could only be resorted to under circumstances 
 of great urgency. The distance passed over would 
 hear a much higher ratio to the fatigue at the 
 rate of three, or even two and a half miles an 
 hour. But, if the speed were still further re- 
 duced, a loss of strength would again arise, owing 
 to that expended in merely sustaining the body, 
 as distinguished from that of moving it forward. 
 
 The Economics of Labour will constantly in- 
 volve questions of this kind. When a work has 
 to be completed in a brief space of time, work- 
 men may be incited by unusual reward to do far 
 more than their usual amount of work ; but so 
 high a rate would not be profitable in other cir- 
 cumstances. The fatigue alwaj^s rapidly increases 
 when the speed of work passes a certain point, so 
 that the extra result is far more costly in reality. 
 In a regular and constant employment the greatest 
 result will always be gained by such a rate as 
 allows a workman each day, or each week at the 
 most, to recover all fatigue and recommence with 
 an undiminished store of energy. 
 
 Q 2
 
 CHAPTER VI. 
 
 THEORY OF RENT. 
 
 Accepted Opinions concerning Rent. 
 
 The general correctness of the views put forth 
 in preceding chapters derives great probabiUty 
 from their close resemblance to the Theory of 
 Rent, as it has been accepted by English writers 
 for nearly a century. It has not been usual to 
 state this theory in mathematical symbols, and 
 clumsy arithmetical illustrations have been em- 
 ployed instead; but it is easy to show that the 
 fluxional calculus is the branch of mathematics 
 which most correctly applies to the subject. 
 
 The Theory of Rent was first discovered and 
 clearly stated by James Anderson in a tract pub- 
 lished in 1777, and called 'An Inquiry into the 
 Nature of the Corn Laws, with a view to the Corn 
 Bill proposed for Scotland.' An extract from this 
 work may be found in MacCulloch's edition of 
 the 'Wealth of Nations,' p. 453, giving a most
 
 Theonj of Rent . 229 
 
 clear explanation of the effect of the various fer- 
 tility of land, and showing that it is not the rent 
 of land which determines the price of its produce, 
 but the price of the produce which determines tlie 
 rent of the land. The following- passage must be 
 given in Anderson's own words ^ : — 
 
 * ... In evei'y country there is a variety of 
 soils, differing considerably from one another in 
 point of fertility. These we shall at present sup- 
 pose arranged into different classes, which we 
 shall denote by the letters A, B, C, D, E, F, &c., 
 the class A comprehending the soils of the greatest 
 fertility, and the other letters expressing different 
 classes of soils, gradually decreasing in fertility 
 as you recede from the first. Now, as the expense 
 of cultivating the least fertile soil is as great, or 
 greater than that of the most fertile field, it neces- 
 sarily follows, that if an equal quantity of corn, 
 the produce of each field, can be sold at the same 
 price, the profit on cultivating the most fertile soil 
 must be much greater than that of cultivating the 
 others; and as this continues to decrease as the 
 sterility increases, it must at length happen, that I 
 the expense of cultivating some of the inferior soils I 
 will equal the value of the whole produce.' 
 
 The theory really rests upon the principle, which 
 I have called the Law of Indifference, that for 
 the same commodity in the same market there can 
 
 a * Inquiry,' &c. p. 45 ; note.
 
 230 The Theory of Political Economy. 
 
 only be one price or ratio of exchange. Hence, 
 if different qualities of land yield different amounts 
 of produce to the same labour, there must be an 
 excess of profit in some over others. There will 
 be some land which will not yield the ordinary 
 wages of labour, and which will, therefore, not 
 be taken into cultivation, or if, by mistake, it is 
 cultivated, will be abandoned. Some land will 
 just pay the ordinary wages ; better land will 
 yield an excess, so that the possession of such 
 land wi ll become a matter of competition, and 
 the owner will be able to exact as rent from the 
 cultivators the whole excess above what is suffi- 
 cient to pay the ordinary wages of labour. 
 
 There is a secondary origin for rent in the fact, 
 that if more or less labour and capital be applied 
 to the same portion of land, the produce will not 
 increase proportionally to the amount of labour. 
 It is quite impossible that we could go on con- 
 stantly increasing the yield of one farm without 
 limit, otherwise Ave might feed the Avhole country 
 upon a single farm. Yet there is no definite limit ; 
 for, by better and better culture we may always 
 seem able to raise a little more. But the last 
 increment of produce will come to bear a smaller 
 and smaller ratio to the labour required to pro- 
 duce it, so that it soon becomes, in the case of all 
 land, undesirable to apply more labour. 
 
 MacCulloch has given, in his edition of the
 
 Theory of Rent. 23l 
 
 'Wealth of Nations'^,' a supplementary note, in 
 which he explains, with the utmost clearness and 
 scientific accuracy, the nature of the theory. This 
 note contains by far the best statement of the 
 theory, as it seems to me, and I will therefore 
 quote his recapitulation of the principles which he 
 establishes. 
 
 ' 1. That if the produce of land could always be 
 increased in proportion to the outlay on 
 it, there would be no such thing as rent. 
 ' 2. That the produce of land cannot, at an 
 average, be increased in proportion to 
 the outlay, but may be indefinitely in- 
 creased in a less proportion. 
 ' 3. That the least productive portion of the 
 outlay, which, speaking generally, is the 
 last, m ust yield the ordinary profits of 
 stock. And 
 ' 4. That all which the other portions yield more 
 than this, being above ordinary profits, is 
 rent.' 
 A most satisfactory account of the theory is 
 also given in James Mill's 'Elements of Political 
 Economy,' a work which I never read without 
 admiring its brief, clear, and powerful style. James 
 Mill constantly uses the exj^ression dose of capital 
 'The time comes,' he says, 'at which it is neces- 
 sary either to have recourse to land of the second 
 
 b New edition, 1839, p. 444.
 
 232 The Theory of Political Economy. 
 
 quality, or to apply a second dose of capital less 
 productively upon land of the first quality/ He 
 evidently means by a dose of ccqntal a little more 
 capital, and though the name is peculiar, the 
 meaning is simply that of an increment of capital. 
 The number of doses or increments mentioned is 
 only three, but this is clearly to avoid prolixity 
 of explanation. There is no reason why we should 
 not consider the whole capital divided into many 
 more doses. The same general law which makes 
 the second dose less productive than the first, 
 will make a hundredth dose, speaking generally, 
 less productive than the preceding ninety-ninth 
 dose. Theoretically speaking, there is no need or 
 possibility of stopping at any limit. A mathe- 
 matical law is in theory always continuous, so 
 that the doses considered are indefinitely small 
 and indefinitely numerous. I consider, then, that 
 James Mill's mode of expression is exactly equi- 
 valent to that which I have adopted in earlier 
 parts of this book. As mathematicians have in- 
 vented a precise and fully recognised mode of 
 expressing doses or increments, I know not why 
 we should exclude language from Economics Avhich 
 is found convenient in all other sciences. It is 
 mere pedantry to insist upon calling that a dose 
 in Economics, which in all the other sciences is 
 called by the perfectly established and expressive 
 term increment.
 
 Theory of Rent. 233 
 
 The following are James Mill's general conclu- 
 sions as to the nature of Rent ^. 'In applying 
 capital, either to lands of various degrees of fer- 
 tility, or in successive doses to the same land, 
 some portions of the capital so employed are 
 attended with a greater produce, some with a less. 
 That which yields the least, yields all that is"J 
 necessary for re-imbursing and rewarding the capi-^ 
 talist. The capitalist will receive no more than 
 this remuneration for any portion of the capital 
 Avhich he employs, because the competition of others 
 will prevent him. All that is yielded above this 
 remuneration the landlord will be able to appro- 
 priate. Rent, therefore, is the difference between 
 the return yielded to that portion of the capital 
 which is employed upon the land with the least 
 effect, and that which is yielded to all the other 
 portions employed upon it with a greater effect.' 
 
 Symholic Statement of the Theory. 
 
 The accepted Theory of Rent, as given above, 
 needs little or no alteration to adapt it to ex- 
 pression in mathematical symbols. For doses or 
 increments of capital I shall substitute increments 
 of labour, partly because the functions of capital 
 remain to be considered in the next chapter, 
 and partly because James Mill, J. S. Mill, and 
 
 c 'Elements,' p. 17.
 
 234 The Theory of Political Economy. 
 
 MacCulloch hold the application of capital to be 
 synonymous with the application of labour. This 
 assumption is implied in James Mill's statement 
 (p. 13); it is expressly stated in J. S. Mill's 'First 
 Fundamental Proposition concerning the Nature 
 of Capital d;' and MacCulloch adds a foot-note ^ 
 to make it clear, that as all capital was originally 
 produced by labour, the application of additional 
 capital is the application of additional labour. 
 ' Either the one phrase or the other may be used 
 indiscriminately/ This doctrine is in itself alto- 
 gether erroneous, but H will not be erroneous to 
 assume as a mode of simplifjdng the problem that 
 the increments of labour applied are equally as- 
 sisted by capital. It is a separate and subsequent 
 problem to determine how rent or interest arises 
 when the same labour is assisted by diiferent 
 quantities of capital. 
 
 I shall suppose that a certain labourer, or, 
 what comes to exactly the same thing, a body 
 of labourers, expend labour on several different 
 pieces of ground. On what principle will they 
 distribute their labour between the several pieces ? 
 Let us imagine that a certain amount has been 
 spent upon each, and that another small portion, 
 aZ, is going to be applied. Let there be two 
 pieces of land, and let Aaj^, A.r2» t>e the incre- 
 ments of produce to be expected from the pieces 
 
 fl Book i. chapter 5, § 1. e ' AVealth of Nation!?/ p. 445.
 
 Theory of Rent. 235 
 
 respectively. They will naturally apply the labour 
 to the land which yields the greatest result. So 
 long as there is any advantage in one use of 
 labour over another, the most advantageous will 
 certainly be adopted. Therefore, when they are 
 perfectly satisfied with the distribution made, the 
 increment of produce to the same labour will be 
 equal in each case; or we have 
 
 To attain scientific accuracy, we must decrease 
 the increments infinitely, and then we obtain the 
 equation — 
 
 dl ~ dl 
 Now represents the ratio of produce, or the 
 
 productiveness of labour, as regards the last in- 
 crement of labour applied. We may say, then,i 
 that whenever a labourer or body of labourers 
 distribute their labour over pieces of land with 
 perfect economy, the final ratios of produce to 
 labour ivill he equcd. 
 
 We may now take into account the general 
 law, that when more and more labour is ap- 
 plied to the same piece of land, the produce 
 ultimately does not increase proportionately to 
 
 dor 
 the labour. This means that the function -y~ 
 
 dl 
 
 diminishes without limit towards zero after .v has
 
 236 The Theory of Political Economy. 
 
 passed a certain quantity. The whole produce of a 
 
 piece of land is <?', the whole labour spent upon it 
 
 is I; and a? varies in some way as I varies, never 
 
 decreasing when I increases. We may say, then, 
 
 that ,/' is a function of / ; let us call it PI. When 
 
 a little more labour is exj)ended, the increment 
 
 dPl 
 of produce dx is dPl, and — — - is the final rate 
 
 dl 
 
 of production, the same as was previously de- 
 noted by -— . 
 dl 
 
 In the Theory of Labour it was shown that no 
 increment of labour would be expended unless 
 there was sufficient recompense in the produce, but 
 that labour would be expended up to the point 
 at Avhich the increment of utility exactly equals 
 the increment of pain incurred in acquiring it. 
 Here we find an exact definition of the amount of 
 labour which will be profitably applied. 
 
 It was also shown that the last increment of 
 
 labour is the most painful, so that if a person is 
 
 recompensed for the last increment of labour which 
 
 doc 
 he applies to land by the rate of production -^r, 
 
 it follows that all the labour he applies might be 
 
 recompensed sufficiently at the same rate. The 
 
 whole labour is I, so that if the recompense Avere 
 
 doc 
 equal over the whole, the result would be / . -7^-
 
 Theory of Rent. 237 
 
 Consequently, he obtains more than the necessary 
 return to labour by the amount 
 
 or, as Ave may write it, 
 
 Pl-l.Fl, 
 in which Fl is the differential coefficient of PI, or 
 the final rate of production. This expression repre- 
 sents the advantage he derives from the possession 
 of land in affording him more profit than other j 
 methods of employing his labour. It is therefore J 
 the rent which he would ask before yielding it up 
 to another person, or equally the rent which he 
 Avould be able and willing to pay if hiring it from 
 another. 
 
 The same considerations apply to every piece 
 of land cultivated. When the same person or body A 
 of labourers cultivates several pieces, Fl will be of,^ 
 the same magnitude in each case, but the quantities ) 
 of labour, and possibly the functions of labour, will 
 be different. Thus with two pieces of land the 
 rent may be represented as 
 
 or, speaking generally of any number of pieces, 
 it is the sum of the quantities of the form PI, minus 
 the sum of the quantities of the form I . FL
 
 238 The Theory of Political Economy. 
 
 Illustratio7is of the Theory. 
 
 It is very easy to illustrate the Theory of Rent by 
 diagrams. For, let distances along the line ox denote 
 quantities of labour, and let the curve ajpc repre- 
 sent the variation of the rate of production, so that 
 the area of the curve will be the measure of the 
 produce. Thus when labour has been applied to 
 the amount om, the produce will correspond to the 
 area apmo. Let a small new increment of labour, 
 
 FL7.1X 
 
 mm\ be applied, and suppose the rate of production 
 equal over the whole of the increment. Then the 
 small parallelogram, pj/rn'm, will be the produce. 
 This will be proportional in quantity to ^m, so that 
 the height of any point of the curve perpendicularly 
 above a point of the line ox represents the rate 
 of production at that point in the application of 
 labour. 
 
 If we further suppose that the labourer considei's
 
 Theory of Rent. 239 
 
 his labour, mm', repaid b}'' the produce iwi\ there is 
 no reason why any other part of his labour sliould 
 not be repaid at the same rate. Drawing, then, 
 a horizontal line, rpq, through the point p, his 
 whole labour, om, will be repaid by the produce 
 represented by the area oriym. Consequently, the 
 overlying area, rap, is the excess of produce which 
 can be exacted from him as rent, if he be not him- 
 self the owner of the land. 
 
 Imagining the same person to cultivate another 
 piece of land, we might take the curve, hqc, to 
 represent its productiveness. The same rate of 
 production will repay the labourer in this case as 
 in the last, so that the intersection of the same 
 horizontal line, rpq with the curve, will determine 
 the final point of labour, n. The area, rn, will be 
 the measure of the sufiicient recompense to the 
 whole labour, on, spent upon the land ; and the 
 excess of produce or rent will be the area, rlq. 
 In a similar manner, any number of pieces of land 
 might be considered. The figure might have been 
 drawn so that the curves would rise on leaving the 
 initial line oy, indicating that a very little labour 
 w^ill have a poor rate of production; and that 
 a certain amount of labour is requisite to develop 
 the fertility of the soil. This may often or 
 always be the case, as a considerable quantity of 
 labour is generally requisite in first bringing land 
 into cultivation, or merely keeping it in a fit
 
 240 The Theory of Political Economy. 
 
 state for use. The laws of rent depend on the 
 undoubted principle, that the curves always ulti- 
 mately decline towards the base line ox, that is, 
 the final rate of production always ultimately sinks 
 towards zero.
 
 CHAPTER VII. 
 
 THEOEY OF CAPITAL 
 
 The Function of Capital. 
 
 In considering the nature and principles of 
 Capital, we enter a distinct branch of our subject. 
 There is no close or necessary connection between 
 the employment of capital and the processes of 
 exchange. Both by the use of capital and by ex- 
 change we are enabled vastly to increase the sum 
 of utility which we enjoy; but it is conceivable 
 that we might have the advantages of capital 
 without those of exchange. An isolated man like 
 Alexander Selkirk might feel the benefit of a stock 
 of provisions, tools, and other means of facilitating 
 industry, although cut off from traffic with other 
 men. Economics, then, is not solely the science 
 of Exchange or Value: it is also the science of| 
 Capitalisation. 
 
 The views which I shall endeavour to establish 
 on this subject are in fundamental agreement with
 
 242 The Theory of Political Economy. 
 
 those adopted by Ricardo ; but I shall try to put 
 the Theory of Capital in a more simple and con- 
 sistent manner than has been the case with some 
 later economists. We are told, with perfect truth, 
 that capital consists of wealth employed to facili- 
 tate production; but when economists proceed to 
 enumerate the articles of wealth constituting 
 capital, they obscure the subject. 'The capital 
 of a country,' says MacCulloch ^ * consists of those 
 portions of the produce of industry existing in it, 
 which may be directly employed either to support 
 human beings, or to facilitate production.' Pro- 
 fessor Fawcett again says ^ : ' Capital is not confined 
 to the food which feeds the labourers, but includes 
 machinery, buildings, and in fact, every product 
 due to man's labour which can be applied to assist 
 his industry ; but capital which is in the form of 
 food does not perform its functions in the same 
 way as capital that is in the form of machinery : 
 the one is termed circulating capital, the other fixed 
 capital.' 
 
 The notion of capital assumes a new degree of 
 simplicity as soon as we recognise that what has 
 been called a part is really the whole. Capital, as 
 I regard it, consists merely in the aggregate of those 
 commodities which are requii^ed for sustaining la- 
 bourers of any hind or class engaged in tvork. A 
 
 a ' Principles of Political Economy/ p. 100. 
 
 ^ 'Manual of Political Economy,' second edition, p. 47.
 
 Theory of Capital. 243 
 
 stock of food is the main element of capital ; but 
 supplies of clothes, furniture, and all the other 
 articles in common daily use are also necessary 
 parts of capital. The current means of sustenance h 
 constitute capital in its free or uninvested form. The*! 
 single and all-important function of capital is to 
 enable the labourer to await the result of any 
 long-lasting work, — to put an interval between the 
 beginning and the end of an enterprise. 
 
 Not only can we, by the aid of capital, erect 
 large works which would otherwise have been im- 
 possible, -but the production of articles which would 
 have been very costly in labour may be rendered 
 far more easy. Capital enables us to make a greats 
 outlay in providing tools, machines, or other pre- 
 liminary works, which have for their sole object 
 the production of some important commodity, and 
 which will greatly facilitate production when we 
 enter upon it. 
 
 Capital is concerned ivith Time. 
 
 Several economists have clearly perceived that 
 the time elapsing between the beginning and end 
 of a work is the difficulty which capital assists us 
 to surmount. Thus James Mill has said — ' If the 
 man who subsists on animals cannot make sure of 
 his prey in less than a day, he cannot have less 
 than a whole day's subsistence in advance. If 
 
 R 2
 
 244 Tlie Theory of Political Economy. 
 
 hunting excursions are undertaken which occupy a 
 week or a month, subsistence for several days may 
 be required. It is evident, when men come to live 
 upon those productions which their labour raises 
 from the soil, and which can be brought to maturity 
 only once in the year, that subsistence for a whole 
 year must be laid up in advance c.' 
 
 Much more recently. Professor Hearn has said, 
 Ijin his admirable work entitled ' Plutology ^ ' — ' The 
 first and most obvious mode in which capital directly 
 operates as an auxiliary of industry is to render 
 possible the performance of work which requires 
 for its completion some considerable time. In the 
 simplest agricultural operations there is the seed 
 time and the harvest. A vineyard is unproductive 
 for at least three years before it is thoroughly fit 
 for use. In gold mining there is often a long delay, 
 sometimes even of five or six years, before the gold 
 is reached. Such mines could not be worked by 
 poor men unless the storekeepers gave the miners 
 credit, or, in other words, supplied capital for the 
 . adventure. But, in addition to this great result, 
 I capital also implies other consequences which are 
 I hardly less momentous. One of these is the stead- 
 iness and continuity that labour thus acquires. 
 I A man, when aided by capital, can afford to remain 
 
 c 'Elements of Political Economy,' third edition, 1826, p. 9. 
 <1 ' Plutology ; or the Theory of the Efforts to Satisfy Human 
 Wants,' 1864 (Macmillan), p. 139.
 
 Theory of Ca;pital. 245 
 
 at his work until it is finished, and is not compelled 
 to leave it incomplete while he searches for the 
 necessary means of subsistence. If there were no 
 accumulated fund upon which the labourer could 
 rely, no man could remain for a single day exclu- 
 sively engaged in any other occupation than those 
 which relate to the supply of his primary wants. 
 Besides these wants, he should also from time to 
 time search for the materials on which he was to 
 work.' 
 
 These passages imply, as it seems to me, a 
 clear insight into the nature and purposes of 
 capital, except that the writers have not with 
 sufficient boldness followed out the consequences 
 of their notion. If we take a comprehensive vicAv 
 of the subject, it will be seen that not only the 
 chief, but the sole purpose of capital is as above 
 described. Capital simply allows us to expend\ 
 labour in advance. Thus, to raise corn we need 
 to turn over the surface of the soil. If we pro- 
 ceed straight to the work, and use the implements 
 with which nature has furnished us — our fingers 
 — we should spend an enormous amount of pain- 
 ful labour with very little result. It is far better, 
 therefore, to spend the first part of our labour in 
 making a spade or other implement to assist the 
 rest of our labour. This spade represents so much 
 labour which has been invested, and so far spent ; 
 but if it lasts three years, its cost may be con-
 
 246 Tlie Theo7'y of Political Economy. 
 
 J sidered as repaid gradually during those three 
 years. This labour, like that of digging, has for 
 its object the raising of corn, and the only essen- 
 
 j tial difference is, that it has to precede the pro- 
 
 I duction of corn by a longer interval. The average 
 interval of time for which labour will remain 
 invested in the spade is half of the three years. 
 Similarly, if we possess a larger capital, and expend 
 it in making a plough, which will last for twenty 
 years, we invest at the beginning a great deal 
 of labour which is only gradually repaid during 
 those twenty years, and which is therefore, on 
 the average, invested for about ten years. 
 
 ' It is true that in modern industry we should 
 seldom or never find the same man making the 
 spade or plough, and afterwards using the im- 
 plement. The division of labour enables me, with 
 much advantage, to expend a portion of my capital 
 in purchasing the implement from some one who 
 devotes his attention to the manufacture, and 
 probably expends capital previously in facilitating 
 the work. But this does not alter the principles 
 of the matter. What capital I give for the spade 
 merely replaces what the manufacturer had already 
 invested in the expectation that the spade would 
 be needed. Exactly the same considerations may 
 be applied to much more complicated applications 
 of capital. The ultimate object of all industry 
 engaged with cotton is the production of cotton
 
 Theory of Capital 247 
 
 goods. But the complete process of producing 
 those goods is divided into many parts; and it is 
 necessary to begin the spending of labour a long 
 time before any goods can be finished. 
 
 In the first place, labour will be required to till 
 the land which is to bear the cotton plants, and 
 probably two years at least will elapse between 
 the time when the ground is first broken and the 
 time when the cotton reaches the mills. A cotton 
 mill, again, must be a very strong and durable 
 structure, and must contain machinery of a very 
 costly character, which can only repay its owner 
 by a long course of use. We might spin and 
 weave cotton goods as in former times, or as it 
 is done in Cashmere, with a very small use of 
 capital ; but then the labour required would be 
 enormously greater in proportion to the produce. 
 It is far more economical in the end, to spend a 
 vast amount of labour and capital in building 
 a substantial mill and filling it with the best 
 machinery, which will then go on working with 
 unimpaired efficiency for thirty years or more. 
 This means that, in addition to the labour spent 
 in superintending the machines at the moment 
 when goods are produced, a great quantity of 
 labour has been spent from one to thirty years 
 in advance, or, on the average, fifteen years in 
 advance. This expenditure is repaid by an an- 
 nuity of profit extending over those thirty years.
 
 248 The Theory of Political Economy, 
 
 The interval elapsing between the first exer- 
 tion of labour and the enjoyment of the result 
 is further increased by any time during which 
 the raw material may lie in warehouses before 
 reaching the machines ; and by the time employed 
 in distributing the goods to retail dealers, and 
 through them to the consumers. It may even 
 happen that the consumer finds it desirable to 
 keep a certain stock on hand, so that the time 
 when the real object of the goods is fulfilled be- 
 ' comes still further deferred. During this time, 
 also, capital seems to me to be invested, and only 
 as actual utilisation takes place is expenditure 
 repaid by corresponding utility enjoyed. 
 
 I would say, then, in the most general manner, 
 that whatever improvements in the supply of com- 
 modities lengthen the average interval between the 
 moment ivhen labour is exerted and its ultimate 
 result or purpose accomplished, such improvements 
 / depend upon the use of capital. And I would add, 
 Vthat this is the sole use of capital. Whenever we 
 overlook the irrelevant complications introduced 
 by the division of labour and the frequency of 
 exchange, all employments of capital resolve them- 
 selves into the fact of time elapsing between the 
 beginning and the end of industry.
 
 Theory of Capital. 249 
 
 Quantitative Notions concerning Capital. 
 
 One main point which has to be clearly brought 
 before the mind in this subject is the difference 
 between the amount of capital invested and the 
 amount of investment of capital. The first is a 
 quantity of one dimension only — the quantity of 
 capital; the second is a quantity of two dimen- 
 sions, namely, the quantity of capital, and the 
 length of time during which it remains invested. 
 If one day's labour remains invested for two years, 
 the capital is only that equivalent to one day; 
 but it is locked up twice as long as if it were 
 invested for only one year. Now all questions 
 in which we consider the most advantageous em- 
 ployment of capital turn upon the length of in- 
 vestment quite as much as upon the amount. 
 The same capital will serve for twice as much^ 
 industry if it be absorbed or invested for only half 
 the time. 
 
 The amount of investment of capital will evi- 
 dently be determined by multiplying each por- 
 tion of capital invested at any moment by the 
 length of time for which it remains invested. 
 One pound invested for five years gives the same 
 result as five pounds invested for one year, the 
 product being five pound-years^ Most commonly, 
 however, investment proceeds continuously or at
 
 250 The Theory of Political Economy. 
 
 intervals, and we must form clear notions on the 
 subject. Thus, if a workman be employed during 
 one year on any work, the result of which is com- 
 I plete, and enjoyed at the end of that time, the 
 j absorption of capital will be found by multiplying 
 I each day's wages by the days remaining till the 
 end of the year, and adding all the results toge- 
 ther. If the daily wages be four shillings, then 
 we have 
 
 4x364 + 4x363 + 4x362 +4x1; 
 
 . 365x364 
 
 or. 
 
 or 265,720 shilling-days. 
 
 We may also represent the investment by a 
 diagram such as Fig. X. The length along the 
 line ox indicates the duration of investment, and 
 
 Ft0.X 
 
 the height attained at any point, a, is the amount 
 of capital invested. But it is the whole area of 
 the rectangles up to any point, a, which measures 
 the amount of investment during the time oa. 
 
 The whole result of continued labour is not 
 often consumed and enjoyed in a moment; the 
 result generally lasts for a certain length of time. 
 We must then conceive the capital as being pro-
 
 Theory of Cajjital. 251 
 
 gressively uninvested. Let us, for sake of simple 
 illustration, imagine the labour of producing the 
 harvest to be continuously and equally expended 
 between the first of September in one year and 
 the same day in the next. Let the harvest be 
 then completely gathered and its consumption 
 begin immediately and continue equally during 
 the succeeding twelve months. Then the amount 
 of investment of capital will be represented by the 
 area of an isosceles triangle, as in Fig. XI, the 
 
 base of which corresponds to two years of dura- 
 tion. Now the area of a triangle is equal to the 
 height multiplied by half the base; and as the 
 height represents the greatest amount invested, 
 that upon the first of September, when the har- 
 vest is gathered ; half the base, or one year, is the 
 average time of investment of the ivhole amount. 
 
 In the 37th proposition of the first book of 
 Euclid it is proved that all triangles upon the 
 same base and between the same parallels are 
 equal in area. Hence we may draw the conclu- 
 sion that, provided capital be invested and unin- 
 vested continuously and in simple proportion to
 
 252 The Theory of Political Economy. 
 
 the time, we need only regard the greatest amount 
 
 invested and the greatest time of investment. 
 
 Whether it be all invested suddenly, and then 
 
 gradually withdrawn; or gradually invested and 
 
 i suddenly withdrawn ; or gradually invested and 
 
 I gradually withdrawn; the amount of investment 
 
 will be in every case the greatest amount of 
 
 ; capital multiplied by half the time elapsing from 
 
 \ the beginning to the end of the investment. 
 
 Expression for Amount of Investment. 
 
 To render our notions of the subject still more 
 exact and general, let us resort once more to ma- 
 thematical symbols. 
 
 Let Aj) = amount of capital supposed to be 
 invested in the time a^; let t = time elapsing 
 before its result is enjoyed, the enjoyment taking 
 place in an interval of time a^, which may be 
 disregarded in comparison with t. Then t . Ap is 
 the amount of investment ; and if the investment 
 is repeated, the sum of the quantities of the 
 nature of t . ^p, or, in the customary mode of 
 expression, Xt.^p is the total amount of invest- 
 ment. But it will seldom be possible to assign 
 each portion of result to an exactly corresponding 
 portion of labour. Cotton goods are due to the 
 aggregate industry of those who tilled the ground, 
 grew the cotton, plucked, transported, cleaned.
 
 Theory of Capital. 253 
 
 spun, wove, and dyed it; we cannot distinguish 
 the moment when each labourer's work is sepa- 
 rately repaid. To avoid this difficulty, we must 
 fix on some moment of time when the whole 
 transaction is closed, all labour upon the ground 
 repaid, the mill and machinery worn out and sold, 
 and the cotton goods consumed. Let t now denote 
 the time elapsing from any moment up to this 
 final moment of closing the accounts. Let a^ 
 be as before an increment of capital invested, and 
 let A g be an increment of capital uninvested by 
 the sale of the products and their enjoyment by 
 the* consumer. Thus it will be pretty obvious 
 that the sum of the quantities ^ . ajp, less by the 
 sum of the quantities t . ^q will be the total 
 investment of capital, or expressed in symbols: 
 2 1 . A jo — 'Zt.Aq. 
 
 Dimensions of Capital, Credit and Debit. 
 
 As the subject presents itself to me at present,! 
 I apprehend that capital is to be regarded simply 
 as commodity. If so, the dimension of capital 
 will be represented by M, and the amoimt of 171- 
 vestment of capital, possessing the additional dimen- 
 sion of time, will have the symbol MT. How then 
 are we to determine the quantitative nature of 
 what Senior called Abstinence, that temporary 
 sacrifice of enjoyment which is essential to the
 
 254 The Theory of Political Economy. 
 
 existence of capital. Senior thus explicitly de- 
 fined what he meant by the word^: — 'By the 
 word Abstinence, we wish to express that agent, 
 distinct from labour and the agency of nature, 
 the concurrence of which is necessary to the exist- 
 ence of capital, and which stands in the same 
 relation to profit as labour does to wages/ He 
 goes on to explain that abstinence, though usually 
 accompanying labour, is distinct from it. A care- 
 ful consideration of Senior's remarks shows that 
 in reality abstinence is the endurance of want, 
 the abstaining from the enjoyment of utility which 
 might be enjoyed. Now the degree or intensity 
 of want is measured by the degree of utility of 
 commodity if it were consumed. Great degree 
 of utility simply means great want, so that one 
 dimension of abstinence must be U, and time 
 being also obviously an element of abstinence, 
 the required symbolic statement of its dimensions 
 will be UT. This result satisfactorily corresponds 
 with Senior's definition, for he says that abstinence 
 is to profit as labour is to wages. Now profit or 
 interest is clearly symbolised by M, and wages 
 also by M, both consisting simply of quantities 
 of commodity. Thus UT bears just the same 
 relation to M that ET does to M, for E signifies 
 
 ^ 'Political Economy,' by Nassau W. Senior. 5th ed., 1863, 
 p. 59.
 
 Theory of Capital. 255 
 
 the degree of painfulness of labour, and can barely 
 be distinguished from U, except in sign. 
 
 The relation of abstinence, UT, to total utility, 
 MU, also confirms our result. For if we convert 
 abstineiice into satisfaction, by giving a supply of 
 commodity for consumption, this action is symbo- 
 lically represented by multiplying UT into MT~^ 
 which yields MU, or utility. 
 
 It will need no argument to show that the i, 
 dimension of debit and credit, having regard only 
 to what is borrowed and owed, will be the dimen- 
 sion of commodity simply, or M. According to 
 the practice of commerce, a contract of debt is a 
 contract to return a certain physically defined 
 quantity of a specified substance, such as an 
 ounce of gold, a ton of pig iron, a hogshead of 
 palm oil. No attempt is made to define quan- 
 tities of utility, so that the debt when repaid 
 shall yield utility equal to what it possessed 
 when lent. The borrower and lender either take 
 their chance about this, or provide for it in the 
 rate of interest to be paid. It is equally obvious 
 that in another sense the amoimt of credit or debit 
 will be proportional to the duration of the opera- 
 tion, and will have the dimensions MT. 
 
 Effect of the Duration of Work. 
 
 Perhaps the most interesting point in the Theory I 
 of Capital is the advantage arising from the rapid I
 
 256 The Theory of Political Economy. 
 
 performance of work, if it is capable of being 
 done with convenience and with the same ultimate 
 result. To investigate this point, suppose that 
 w = the whole amount of wages which it is re- 
 quisite to pay in building a house, and that this 
 does not alter when we vary, within certain limits, 
 the time employed in the work, denoted by t. If 
 the work goes on continuously, we shall, during 
 each unit of time, have an amount invested equal 
 to the t^^ part of w. The whole amount of invest- 
 ment of capital will therefore be represented by 
 the area of a triangle whose base is t and height 
 w; that is, the investment is \tiv. Thus when 
 the whole expenditure is ultimately the same, the 
 amount of investment is simply proportional to 
 the time. The result would be more serious if the 
 accumulation of compound interest during the time 
 were taken into account; but the consideration 
 of compound interest would render the formulae 
 very complex, and is not requisite for the purpose 
 in view. 
 
 We must clearly distinguish the case treated 
 above, in which the amount of labour is the same, 
 but spread over a longer time, from other cases 
 where the labour increases in proportion to the 
 time. The investment of capital, then, grows in 
 ah exceedingly rapid manner. Neglecting the first 
 cost of tools, materials, and other preparations, let 
 the first day's labour cost a; during the second
 
 Theory of Capital. 
 
 257 
 
 day this remains invested, and the amount of 
 capital a is added ; on each following day a like 
 addition is made. The amount of capital invested 
 is evidently 
 
 At beginning of second day a, 
 „ „ third „ «+«, 
 „ „ fourth „ a + a + a ; 
 and so on. If the work lasts during n + 1 days, 
 the total amount of investment of capital will be 
 
 a + 2 « + 3 a + 4 a + na. 
 
 The sum of the series is 
 
 which increases by a term involving the square 
 of the time. The employment of capital thus I 
 grows in proportion to the triangular numbers! 
 
 1, 3, 6, 10, 15, 21, &c. 
 
 If we regard the investment as taking place 
 
 continuously, the whole absorption of capital is 
 
 
 bl b2 b3 ii- bS 
 
 represented by the area of a right-angled tri- 
 angle (Fig. XII), in which o\, h^ h.;., h., h^, &c. are the 
 
 s
 
 258 Tlie Theory of Political Economy. 
 
 successive units of time. The heights of the lines 
 a-^\, a^h^ represent the amounts invested at the 
 ends of the times. The daily investment being 
 
 a, the total amount of investment will be a—, 
 
 increasing as the square of the time. 
 
 Cases of this kind continually occur, as in sink- 
 ing a deep mine, of which the requisite depth 
 cannot be previously known with accuracy. Any 
 
 j large work, such as a breakwater, an embank- 
 ment, the foundations of a great bridge, a dock, 
 a long tunnel, the dredging of a channel, involves 
 a problem of a similar nature; for it is seldom 
 
 I known what amount of labour and capital will 
 be required; and if the work lasts much longer 
 than was expected, the result is usually a financial 
 disaster. 
 
 Illustrations of the Investment of Capital. 
 
 The time during which capital remains invested, 
 and the circumstances of its investment and repro- 
 duction, are exceedingly various in different em- 
 ployments. If a person plants cabbages, they will 
 be ready in the course of a few months, and the 
 labour of planting and tending them, together with 
 a part of the labour of preparing and manuring the 
 ■ soil, yields its results with very little delay. In 
 planting a forest tree, however, a certain amount 
 of labour is expended, and no result obtained until
 
 Theory of Ccqntal. 259 
 
 after the lapse of 30, 40, or 50 years. The first 
 cost of enclosing, preparing, and planting a planta- 
 tion is considerable ; and though, after a time, the 
 loppings and thinnings of the trees repay the cost 
 of superintendence and repairs, yet the absorption 
 of capital is great, and we may thus account for 
 the small amount of planting which goes on. The 
 ageing of wine is a somewhat similar case. A certain 
 amount of labour is expended without result for 
 10 or 15 years, and the cost of storage is incurred 
 during the whole time. To estimate the real cost 
 of the articles at the end of the time, we must, 
 in all such cases, add compound interest, and this 
 grows in a rapid manner. Every pound invested 
 at the commencement of a business becomes 1*63 
 poimds at the end often years, 11-47 pounds at the 
 end of fifty years, and no less than 131-50 pounds at 
 the end of a century, the rate of interest being taken 
 at five per cent. Thus it cannot be profitable to store 
 wine for fifty 3^ears, unless it become about twelve 
 times as valuable as it was when new. It cannot pay 
 to plant an oak and let it live a century, unless the 
 timber then repays the cost of planting 132 times. 
 If an annual charge however small, has to be 
 incurred (for instance, the cost of storage and 
 superintendence), the expense mounts up in a still 
 more alarming manner. Thus, if the cost of any 
 investment is one pound per annum, the amount 
 invested, with compound interest at five per cent., 
 
 S 2
 
 260 The Theory of Political Economy. 
 
 becomes 12-58 pounds at the end of ten years, 
 209-35 i30iinds at the end of fifty years, and the 
 enormous amount of 261003 at the end of a 
 century. We shall almost always have to take into 
 account both the original and continuous cost 
 of an investment. Thus if a stock of wine worth 
 £100 be laid by for fifty years, and the cost of 
 storage be £l per annum, the total cost at the end 
 of the time will be £1147-0 on account of original 
 cost, and £209-35 for storage, or in all £1356-35. 
 
 It is to be feared that the rapid accumulation 
 of compound interest is often overlooked in esti- 
 mating the cost of public works and other under- 
 ^takings of considerable duration. A great fort, 
 breakwater, or canal (the Caledonian Canal for 
 instance) is often not completed for twenty years 
 after its commencement, and in the meantime 
 it may be of little or no use. Suppose that its cost 
 has been £10,000 each year; then the aggregate 
 cost would seem to be £200,000, but allowing for 
 interest at five per cent, it is really £330,000. The 
 French engineer and economist, Minard f fully 
 understood this point of finance, and showed that 
 in the case of some public works, such as the great 
 digue of Cherbourg harbour, and canals, the execu- 
 tion of which is allowed sometimes to drag on for 
 half a century, before any adequate result is 
 
 ^ Minard, 'Annalcs des Fonts ct Chaussees,' 1850, l^r Semestre, 
 IX 57.
 
 Theory of Capital. 261 
 
 returned, the real cost is incomparably greater than 
 it is represented to be by merely stating the sums 
 of money expended. In some cases, such as the 
 first canal of Saint Quentin, a work after being- 
 long prosecuted, is abandoned, and the loss by first 
 cost and interest becomes enormous. The Guernsey 
 Harbour is a case in point, and the English dock- 
 yards would supply abundance of similar facts. 
 
 An interesting example of the investment of 
 capital occurs in the case of gold and silver, 
 a large stock of which is maintained either in the 
 form of money, or plate and jewellery. Labour 
 is spent in the digging or mining of the metals, 
 which is gradually repaid by the use or satisfaction 
 arising from the possession of the metals during 
 the whole time for which they continue in use. 
 Hence the investment of capital extends over the 
 average duration of the metals. Now, if the stock 
 of gold requires one per cent, of its amount to 
 maintain it undiminished, it will be apparent that 
 each particle of gold remains in use 100 years on 
 the average ; if | per cent, is sufficient, the average 
 duration will be 200 years. We may state the 
 result thus : 
 
 Loss of 
 
 gold or silver 
 annually. 
 
 1 per cent. 
 
 i 
 
 2 » 
 
 1 
 
 T » 
 
 tt? » 
 
 Average 
 of each 
 in 
 
 duration 
 particle 
 
 use. 
 
 100 
 
 years 
 
 200 
 
 )) 
 
 400 
 
 j> 
 
 1000 
 
 >i
 
 262 The Theory of Political Economy. 
 
 The wear and loss of the precious metals in 
 a civilised country is probably not more than -—^ 
 part annually, including plate, jewellery, and 
 money in the estimate, so that the average invest- 
 ment will be for 200 years. It is curious that, if 
 we regard a quantity of gold as wearing away 
 annually by a fixed percentage of what remains, 
 the duration of some part is infinite, and yet the 
 average duration is finite. Some of the gold pos- 
 sessed by the Romans is doubtless mixed with 
 what we now possess ; and some small part of it will 
 be handed down as long as the human race exists. 
 
 Fixed and Circulating Capital. 
 
 Economists have long been accustomed to distin- 
 guish capital into the two kinds, fixed and circu- 
 lating. Adam Smith called that circulating which 
 passes from hand to hand, and yields a revenue by 
 being parted with. The fact of being frequently 
 exchanged is, however, an accidental circumstance 
 which leads to no results of importance. Ricardo 
 altered the use of the terms, applying the name 
 circidating to that which is frequently destroyed, 
 and has to be reproduced. He says unequivocally g 
 — *In proportion as fixed capital is less durable, 
 it approaches to the nature of circulating capital. 
 
 g ' On the Principles of Political Economy and Taxation,' cliap. 1, 
 § 5, third edition, p. 36.
 
 Theory of Capital. 263 
 
 It will be consumed, and its value reproduced in 
 a shorter time, in order to preserve the capital of 
 the manufacturer.' Accepting this doctrine, and 
 carrying it out to the full extent, we must say that 
 no precise line can be drawn between the two 
 kinds. The difference is one of amount and degree.' 
 The duration of capital may vary from a day to 
 several hundred years ; the most circulating is the 
 least durable ; the most fixed the most durable. 
 
 Free and Invested Capital. 
 
 I believe that the clear explanation of the doc- 
 trine of capital requires the use of a term /"ree 
 capital, which has not been hitherto recognised by 
 economists. By free capital I mean the wages of 
 labour, either in its transitory form of money, or its 
 real form of food and other necessaries of life. The 
 ordinary sustenance requisite to support labourers 
 of all ranks when engaged upon their work is really 
 the true form of capital. It is quite in agreement 
 with the ordinary language of commercial men 
 to say, not that a factory, or dock, or railway, or 
 ship, is cajfital, but that it represents so much capital', 
 sunk in the enterprise. To invest capital is to spend ' 
 money, or the food and maintenance which money 
 purchases, upon the completion of some work. The 
 capital remains invested or sunk until the work
 
 ^. 
 
 laiw^ / 
 
 264 The Theory of Political Economy. 
 
 has returned profit, equivalent to the first cost, 
 Avith interest. 
 
 Much clearness would result from making the 
 language of Economics more nearly coincident with 
 that of commerce. Accordingly, I would not say 
 that a railway isjixed capital, but that capital is 
 'ifixecl in the raihvay. The capital is not the rail- 
 Iway, but the food of those who made the railway. 
 I Abundance of free capital in a country means that 
 j there are copious stocks of food, clothing, and every 
 [article which people insist upon having — that, in 
 short, everything is so arranged that abundant 
 subsistence and conveniences of every kind are 
 forthcoming without the labour of the country 
 being much taxed to provide them. In such cir- 
 cumstances it is possible that a part of the labourers 
 of the country can be employed on works of which 
 the utility is distant, and yet no one will feel 
 scarcity in the present. 
 
 Unifoy^mity of the Rate of Interest. 
 
 A most important principle of this subject is, 
 thatyree capital can he indifferently employed in any 
 branch or kind of industry. Free capital, as we 
 have just seen, consists of a suitable assortment 
 of all kinds of food, clothing, utensils, furniture, 
 and other articles which a community requires for 
 its ordinary sustenance. Men and families consume
 
 Theory of Capital. 265 
 
 much the same kind of commodities, whatever may 
 be the branch of manufacture or trade by which 
 they earn a living. Hence there is nothing in the 
 nature of free capital to determine its employment 
 to one kind of industry rather than another. The / 
 very same wages, whether we regard the money! 
 wages, or the real wages purchased with the money, 
 will support a man whether he be a mechanic, 
 a weaver, a coal miner, a carpenter, a mason, or 
 any other kind of labourer. 
 
 The necessary result is, that the rate of interest 
 for free capital will tend to and closely attain 
 uniformity in all employments. Tlie market for 
 capital is like all other markets: there can he hut 
 one 2'>'t"ice for one article at one time. It is a case 
 of the Law of Indifference (p. 98). Now the article 
 in question is the same, so that its price must 
 be the same. Accordingly, as is well known, the 
 rate of interest, when freed from considerations of 
 risk, trouble, and other interfering causes, is the 
 same in all trades; and every trade will employ || 
 capital up to the point at which it just yields the \\ 
 current interest. If any manufacturer or trader 
 employs so much capital in supporting a certain 
 amount of labour that the return is less than in 
 other trades, he will lose ; for he might have 
 obtained the current rate by lending it to other 
 traders.
 
 266 The Theory of Political Economy. 
 
 General Expression for the Rate of Interest. 
 
 We may obtain a general expression for the rate 
 of interest yielded by capital in any employment 
 provided that we may suppose the produce for the 
 same amount of labour to vary as some continuous 
 function of the time elapsing between the expen- 
 diture of the labour and the enjoyment of the 
 result. Let the time in question be t, and the 
 produce for the same amount of labour the func- 
 tion of t denoted by Ft, which may be supposed 
 always to increase with t. If we now extend the 
 time to t + /J., the produce will be F{t+ a^), and 
 the increment of produce F [t-\- a ^) — Ft. The 
 ratio which tliis increment bears to the increment 
 of investment of capital will determine the rate 
 of interest. Now, at the end of the time t, we 
 might receive the product Ft, and this is the 
 amount of capital which remains invested Avhen 
 we extend the time by a^. Hence the amount of 
 increased investment of capital is At . Ft; and, 
 dividing the increment of produce by this last 
 expression, we have 
 
 F {t+ At) -Ft 1^ 
 At "" Ft' 
 
 When we reduce the magnitude of At infinitely, 
 the limit of the first factor of tlie above expression 
 is the differential coefficient of Ft, so that we find 
 the rate of interest to be represented by
 
 Theory of Capital. 267 
 
 dFt 1^ , F^ 
 
 dt ' Ft ^^' Ti ' 
 
 The interest of capital is, in other words, the rate 
 of increase of the 'produce divided hy the ivhole 
 produce ; but this is a quantity which must rapidly 
 approach to zero, unless means can he found of 
 continually maintaining the rate of increase. Unless 
 a body moves with a rapidly increasing speed, the 
 space it moves over in any unit of time must ulti- 
 mately become inconsiderable compared with the 
 whole space jiassed over from the commencement. 
 There is no reason to suppose that industry, gene- 
 rally speaking, is capable of returning any such 
 vastly increasing produce from the greater appli- 
 cation of capital. Every new machine or other 
 great invention will usually require a fixation of 
 capital for a certain average time, and may be 
 capable of paying interest upon it ; but when this 
 average time is reached, it fails to afford a return 
 to more prolonged investments. 
 
 To take an instance, let us suppose that the pro- 
 duce of labour in some case is proportional to the 
 interval of abstinence t ; then we have say Ft = a .t, 
 in Avhich a is an unknown constant. The differen- 
 tial coefficient i^'^ is now a ; and the rate of interest 
 
 1^^ or —or-; or the rate of interest . varies in'-'^^t'^^ 
 
 Ft at t ' 
 
 versely as the time of investment. ' ? ' '^li/
 
 268 The Theory of Political Economy. 
 
 Dimension of Interest. 
 
 The formula which we obtained in the preceding 
 section, has been subjected to close criticism by 
 an eminent mathematician, who proposed several 
 alternative formulae, but finally accepted my solu- 
 tion of the question as correct. As Professor 
 Adamson, however, has also raised some objections 
 to the formula, it seems desirable to explain its 
 meaning and mode of derivation more fully than 
 was done in the first edition. 
 
 In the first place, as regards the theory of dimen- 
 sions the formula is clearly correct. The rate of 
 interest expresses the ratio which the annual sum 
 paid per annum for the l9an of capital bears to 
 the capital. The interest, and the capital are 
 \ quantities of the same nature, their ratio being an 
 (^ abstract number. Dividing by length of time rate 
 of interest will have the dimension T~^. 
 
 Or we may put it in this way — Interest is paid 
 per annum, or per month, or per other unit of time, 
 and the less the magnitude of this unit, the less 
 must be the numerical expression of the rate of 
 interest. Simple interest at five per cent, per 
 annum is 0-416 .... per cent, per month, and so 
 on. Hence time enters negatively, and the dimen- 
 sion of the rate of interest will be T~^. Or, again, 
 we may state it thus symbolically — The capital 
 advanced may be taken as liaving the dimension
 
 Theory oj Capital. 269 
 
 If; the annual return has the dhnensions MT. y*^^^ 
 Dividing the former by the latter we obtain 
 M 
 
 MT 
 
 = T- 
 
 F't 
 Now the formula -^^ clearly agrees with this 
 
 result ; for the denominator is a certain unknown 
 function of the time of advance of the capital t. 
 We may assume that it can be expressed in a finite 
 series of the powers of t, and the numerator, being 
 the differential coefficient of the same function, will 
 be of one degree of power less than Ft. Hence 
 the dimensions of the formula will be 
 
 rpn ) ^'- rp ) 
 
 or T- 
 
 It must be carefully remembered that it is the rate 
 of interest which has the dimension T~^, not interest 
 itself, which being simply commodity of some kind, 
 has the dimension of commodity, namely If, of the 
 same nature, and having the same dimensions. 
 
 The function of capital is simply this, that labour 
 which would produce certain commodity m^, if that 
 commodity were needed immediately for the satis- 
 faction of wants, is applied so as to j^roduce m^ 
 after the lapse of the time t. Tlie reason for this 
 deferment is that m 2 usually exceeds mi, and the 
 difference or interest m. 2- m^, is commodity having 
 the same dimensions as mj. Hence the rate of 
 interest, apart from the question of time, would be
 
 270 The Theory of Political Economy. 
 
 0712 — mi, divided by Wi, and the quantities being 
 of the same nature, the ratio will be an abstract 
 number devoid of dimensions. But the time for 
 which the results of labour are foregone is as 
 important a matter as the quantity of commodity. 
 The amount of deferment is on-^^t, so that the rate 
 of interest is m^—m,-^ divided by m-^t, which will 
 have the dimension J'~\ 
 
 Exactly the same result would be obtained, 
 however, if we regarded the use of capital from 
 a different point of view. Capital and deferment 
 of consumption are not needed only in order to 
 increase production, that is to say, the manufacture 
 of goods ; they are needed also to equalise con- 
 summation, and to allow commodity to be consumed 
 when its utility is at the highest point. Now, when 
 certain commodity is consumed within an interval 
 of time, the utility produced will, as we have seen, 
 possess the dimensions MUT~^T, or MU. Sup- 
 pose that instead of being consumed within that 
 interval, the commodity is held in hand for a time, 
 before being consumed at all. Then the amount 
 of deferment of utility will be proportional both 
 to the interval of time over which it is deferred, 
 and to the utility which is deferred. Thus the 
 amount of deferment will have the dimensions 
 MUT. The increase of utility due to deferment 
 will clearly have the same dimensions as were pre- 
 viously determined, namely MU. Hence the ratio
 
 Tlieory of Capital. 271 
 
 of this increase to the amount of deferment, will 
 
 have the dimensions TfYrr ^^ ^~^' ^^^ *^^^^ result 
 
 corresponds with the dimension of the rate of 
 interest as otherwise reached. 
 
 Peacock on the Dimensions of Interest. 
 
 The need of some care in forming our conceptions 
 of these quantities is strikingly illustrated hy the 
 fact that not quite fifty years ago so profound and 
 philosophic a mathematician as the late Dean 
 Peacock completely misapprehended the matter. 
 In the first edition of his celebrated and invaluable 
 'Treatise on Algebra,' published in 1830, he gives 
 (j» 111, p. 91) the interest of money as an example 
 of a quantity of three dimensions, and one which 
 may be represented by a solid. He says — ' If p 
 represent the principal or sum of money lent or 
 forborne, r the rate of interest (of £l for one year), 
 and t the number of years, then the interest ac- 
 cumulated or due will be represented by prt\ for 
 if r be the interest of £l for one year, p r will be 
 the interest of a sum of money denoted by p for 
 one year, and therefore p r t will be the amount of 
 this interest in t years, no interest being reckoned 
 upon interest due : such would be the result accord- 
 ing to the principles of Arithmetical Algebra. 
 
 ' If we now suppose j^ ^' i represented respectively
 
 272 The llieory of Political Economy. 
 
 by lines, which form the adjacent edges of a paral- 
 lelopipedon, the solid thus formed will represent 
 the interest accumulated or due: in other words, 
 it will represent whatever is represented by the 
 general formula 'prt when specific values and sig- 
 nifications are given to its symbols : for in what- 
 ever manner we may suppose any one of the 
 symbols of jj r t to vary, the solid will vary in the 
 same proportion. 
 
 'The lines which we assume to represent units 
 of j9, r, and t, are perfectly arbitrary, whether they 
 are made equal to each other or not : this is clearly 
 the case with ^ and t which are quantities of a dif- 
 ferent nature: and the third quantity is likewise 
 different from the other two, being an abstract 
 numerical quantity : for it expresses the relation 
 between the interest of £1 and £1, or between the 
 interest of £100 and £100, which is the quotient 
 of the division of one quantity by another of the 
 same nature : thus, if the interest be 5 per cent., 
 then r = yIo ^^ Fo • if ^ P^^' cent., then r = ^ or ^ : 
 and similarly in other cases: the line, therefore, 
 which is assumed to represent the abstract unit to 
 which r is referred, is independent of the lines 
 which represent units of ]) and of t, and may 
 therefore be assumed at pleasure, equally with 
 those lines. 
 
 ' The lines which represent p and t form a rect- 
 angular area, which is the geometrical repre-
 
 Theorij of Ca/pital 273 
 
 sentatioii of their product: the third quantity r, 
 being merely numerical, may either be represented 
 by a line, as in the case just considered, when 
 a solid parallelopipedon is made the representative 
 of prt\ or we may consider the area ])t as repre- 
 senting the product i^rt when r=l, and that this 
 product in any other case is represented by a rect- 
 angle which bears to the rectangle ])t the ratio 
 of r to 1 : this may be effected by increasing or 
 diminishing one of the sides of the rectangle in the 
 required ratio: the product prt may therefore be 
 correctly represented either by a solid or an area, 
 Avhen one of the factors is an abstract number.' 
 
 The conclusion at which he arrives is a lame 
 one, for he thinks that the same kind of quantity 
 may be represented indiffereritly by a solid or an 
 area. The fact is that Peacock confused a product \ \ 
 of three factors with a quantity of three dimensions. ! \ 
 He took these dimensions as if they were, say 
 il/= money, /? = rate of interest, and T=tmiQ. If 
 we simply multiply these together, as Peacock 
 first does, we get a quantity apparently of three 
 dimensions, MR T. If according to Peacock's sub- 
 sequent idea we take R to be an abstract nu- 
 merical quantity, then we have tAVO dimensions left, 
 namely, MT, He overlooks the fact that the rate 
 of interest involves time negatively, although he 
 describes r as ' the rate of interest (of £l for one 
 year).' Correctly stated, the dimensions of j)rt,
 
 274 The Theory of Political Economy. 
 
 the quantity of interest are M xT'^ >iT ov M, that 
 is simply the dimension of the money advanced. 
 
 If you say, for instance, that the simple interest 
 of £300 at 5 per cent, per annum for five years 
 is £75, there remains no reference in this result 
 to time : £75 is simply £75, and is of exactly the 
 same nature as the £300 which bore the interest. 
 
 That Peacock subsequently discovered error, or 
 at least difficulty, in this section, is rendered pro- 
 bable by the fact that he omitted the illustration 
 altogether in his second edition ; but he does not, 
 so far as I have observed, give any explanation. 
 
 Tendency of Profits to a Minimum. 
 
 It is one of the favourite doctrines of Economists 
 since the time of Adam Smith, that as society 
 progresses and capital accumulates, the rate of 
 profit, or more strictly speaking, the rate of interest, 
 tends to fall. The rate will always ultimately sink 
 so low, they think, that the inducements to further 
 accumulation will cease. This doctrine is in strik- 
 ing agreement with the result of the somewhat 
 abstract analytical investigation given above. Our 
 formula for the rate of interest shows that unless 
 there be constant progress in the arts, the rate 
 must tend to sink towards zero, supposing accumu- 
 lation of capital to go on. There are sufficient 
 statistical facts, too, to confirm this conclusion
 
 Theory of Capital. 275 
 
 historically. The only question that can arise 
 is as to the actual cause of this tendency. 
 
 Adam Smith vaguely attributed it to the com- 
 petition of capitalists, saying, ' The increase of 
 stock which raises wages, tends to lower profit. 
 When the stocks of many rich merchants are 
 turned into the same trade, their mutual com- 
 petition naturally tends to lower its profit; and 
 when there is a like increase of stock in all the 
 different trades carried on in the same society, the 
 same competition must produce the same effect in 
 them allii.' 
 
 Later economists have entertained different views. 
 They attributed the fall of interest to the rise in 
 the cost of labour. The produce of labour, they 
 said, is divided between capitalists and labourers, 
 and if it is necessary to give more to labour, there 
 must be less left to capital, and the rate of profit 
 will fall. I shall discuss the validity of this theory 
 in the final chapter, and will only remark here, 
 that it is not in agreement with the view which 
 I have ventured to take concerning the origin of 
 interest. I consider that interest is determined 
 ])y the increment of produce which it enables a 
 labourer to obtain, and is altogether independent 
 of the total return which he receives for this 
 labour. Our formula (p. 267) shows that the rate 
 of interest will be greater as the whole produce 
 
 'i ' Wealth of Nations,' book i. chapter 9, second paragraph. 
 
 T 2
 
 276 The Theory of Political Economy. 
 
 Ft is less, if the adyantage of more capital, mea- 
 sured by F't, remains unchanged. In many ill- 
 governed countries, where the land is wretchedly 
 tilled, the average produce is small, and yet the 
 rate of interest is high, simply because the want 
 of security prevents the due supply of capital : 
 hence more capital is urgently needed, and its 
 price is high. In America and the British Colonies 
 the produce is often high, and yet interest is high, 
 because there is not sufficient capital accumulated 
 to meet all the demands. In England and other 
 old countries the rate of interest is generally lower 
 because there is an abundance of capital, and the 
 urgent need of more is not actually felt. 
 
 I conceive that the returns to capital and labour 
 are independent of each other. If the soil yields 
 little, and capital will not make it yield more, 
 then both wages and interest will be low, provided 
 that the capital be not attracted away to more 
 profitable employment. If the soil yields much, 
 and capital will make it yield more, then both 
 wages and interest will be high ; if the soil yields 
 much, and capital will not make it yield more, 
 then wages will be high and interest low, unless 
 the capital finds other investments. But the sub- 
 ject is much complicated by the interference of 
 rent. When we speak of the soil jdelding much, 
 we must distinguish between the whole yield and 
 the final rate of yield. In the Western States of
 
 Theory of CajjltaL 277 
 
 America the land yields a large total, and all at 
 a high final rate, so that the labourer enjoys the 
 result. In England there is a large total yield, 
 but a small final yield, so that the landowner re- 
 ceives a large rent and the labourer small wages. 
 The more fertile land having here been long in 
 cultivation, the wages of the labourer are mea- 
 sured by what he can earn by cultivating sterile 
 land which it only just pays to take into cul- 
 tivation. 
 
 Advantage of Cajntal to Industry. 
 
 We must take great care not to confuse the 
 rate of interest on capital with the whole ad- 
 vantage which it confers on industry. The rate 
 of interest depends on the advantage of the last 
 increment of capital, and the advantages of pre- 
 vious increments may be greater in almost any 
 ratio. In considering the laws of utility, we found 
 that an article possessing an immensely great 
 total utility, for instance corn or Avater, might 
 have a very low final degree of utility, because 
 our need of it was almost entirely satisfied ; 
 3^et the ratio of exchange always depends u23on; 
 the final, not the previous degree of utility. The I 
 case is the same with capital. Some capital may 
 be indispensable to a manufacture ; hence the 
 benefit conferred by the capital is indefinitely 
 great, and were there no more capital to be had,
 
 278 The Theory of Political Economy. 
 
 the rate of interest which could be demanded, 
 assuming the article manufactured to be neces- 
 sary, would be almost unlimited. But as soon 
 as ever a larger supply of capital becomes avail- 
 able, the prior benefit of capital is overlooked. 
 As free capital is always the same in quality, the 
 second portion may be made to replace the first 
 if needful : hence capitalists can never exact from 
 labourers the whole advantages which their capital 
 confers — they can exact only a rate determined by 
 the advantage of the last increment. A lender of 
 capital cannot say to a borrower who wants £3,000 
 — 'I know that £1,000 is indispensable to your 
 business, and therefore will charge you 100 per 
 cent, interest upon it; for the second £1,000, which 
 is less necessary, I will charge 20 per cent. ; and 
 as upon the third £1,000 you can only earn the 
 common profit, I will only ask 5 per cent.' The 
 answer w^ould be, that there are many people 
 only earning 5 per cent, on their capital who 
 would be glad to lend enough at a small advance 
 of interest ; and it is a matter of indifference who 
 is the lender. 
 
 The general result of the tendency to uniformity 
 of interest is, that employers of capital always 
 get it at the lowest prevailing rate; they always 
 borrow the capital wdiicli is least necessary to 
 others, and either the labourers themselves, or 
 the public generally as consumers, gather all the
 
 Theory of Cajjital. 
 
 279 
 
 excess of advantage. To illustrate this result, let 
 distances along the line ox, in Fig. XIII, mark 
 quantities of capital employing in any branch of 
 industry a fixed number of labourers. Let the 
 area of the curve denote the whole produce of 
 labour and capital. Thus to the capital, on, re- 
 sults a produce measured by the area of the curvi- 
 linear figure between the upright lines oij and qn. 
 But the amount of increased produce which would 
 
 FiqXJir 
 
 be due to an increment of capital would be mea- 
 sured by the line qn, so that this will represent 
 F't (p. 267). The interest of the capital will be 
 its amount, on, multiplied by the rate qn, or the 
 area of the rectangle oq. The remainder of the 
 produce, jj^t?/, will belong to the labourer. But 
 had less capital been available, say not more than 
 om, its rate of interest would have been measured 
 by j)m, the amount of interest by the rectangle op,
 
 
 280 The Theoivj of Political Economy. 
 
 while the labourer must have remained contented 
 with the smaller share, imy. I will not say that 
 the above diagram represents with strict accuracy 
 the relations of capital, produce, wages, rate of 
 interest, and amount of interest ; but it may serve 
 roughly to illustrate their relations. I see no way 
 of representing exactly the theory of capital in 
 the form of a diagram. 
 
 Are Articles in the Consumers hands Capital f 
 
 The views of the nature of capital expressed 
 in this chapter generally agree with those enter- 
 tained by Ricardo and various other economists; 
 but there is one point in which the theory leads 
 'me to a result at variance with the opinions of 
 almost all writers. I feel quite unable to adopt 
 the opinion that the moment goods pass into the 
 possession of the consumer they cease altogether 
 to have the attributes of capital. This doctrine 
 descends to us from the time of Adam Smith, 
 and has generally received the undoubting assent 
 of his followers. The latter, indeed, have gene- 
 rally omitted all notice of such goods, treating 
 them as if no longer under the view of the eco- 
 nomist. Adam Smith, although he denied the 
 possessions of a consumer the name of capital, 
 took care to enumerate them as part of the stock 
 of the community. He divides into three portions
 
 Theory of Cajjital. 281 
 
 the general stoclv of a country, and wliile the 
 second and third portions are fixed and circulating 
 capital, the first is described as follows i — 
 
 'The first is that portion which is reserved for 
 immediate consumption, and of which the cha- 
 racteristic is, that it affords no revenue or profit. 
 It consists in the stock of food, clothes, household 
 furniture, &c., wdiich have been purchased by their 
 proper consumers, but which are not yet entirely 
 consumed. The whole stock of mere dwelling- 
 houses too subsisting at any one time in the 
 country, make a part of this first portion. The 
 stock that is laid out in a house, if it is to be the 
 dwelling-house of the proprietor, ceases from that 
 moment to serve in the function of a capital, or to 
 afford any revenue to its owmer. A dwelling-house, 
 as such, contributes nothing to the revenue of its 
 inhabitant ; and though it is, no doubt, extremely 
 useful to him, it is as his clothes and household 
 furniture are useful to him, which, however, make 
 a part of his expense, and not of his revenue.' 
 
 MacCulloch, indeed, in his edition of the ' Wealth 
 of Nations' (p. 121), has remarked upon this pas- 
 sage, that ' The capital laid out in building houses 
 for such persons is employed as much for the 
 public advantage as if it were vested in the tools 
 or instruments they make use of in their respec- 
 tive businesses.' He appears, in fact, to reject the 
 
 > 'Wealth of Nations,' book ii. chap. 1, twelfth paragraph.
 
 282 The Theory of Political Economy. 
 
 doctrine, and it is surprising that economists have 
 generally acquiesced in Adam Smith's view, though 
 it leads to manifest contradictions. It leads to the 
 absurd conclusion, that the very same thing ful- 
 filling the very same purposes will be capital or 
 not according to its accidental ownership. To 
 procure good port wine, it is necessary to keep it 
 for a number of years, and Adam Smith would 
 not deny that a stock of wine kept in the wine 
 merchant's possession for this purpose is capital, 
 because it yields him revenue. If a consumer 
 buys it when new, and keeps it to improve, it 
 will not be capital, although it is evident that 
 he gains the same profit as the merchant by buy- 
 ing it at a lower price. If a coal merchant lays 
 in a stock of coal when cheap, to sell when dear, 
 it is capital ; but if a consumer lays in a stock, it 
 is not. 
 
 Adam Smith's views seem to be founded upon 
 a notion, that caj)ital ought to give an annual 
 revenue or increase of wealth li]^ a field yields 
 a crop of corn or grass. Speaking of a dwelling- 
 house, he says : ' If it is to be let to a tenant for 
 rent, as the house itself can produce nothing, the 
 tenant must always pay the rent out of some 
 other revenue, which he derives either from labour, 
 or stock, or land. Though a house, tlierefore, may 
 yield a revenue to its proprietor, and thereby serve 
 in the function of a capital to him, it cannot yield
 
 Theory of Cajjikd. 283 
 
 any to the public, nor serve in the function of a 
 capital to it, and the revenue of the whole bodv 
 of the people can never be in tlie smallest degree 
 increased by it. Clothes and household furniture, 
 in the same manner, sometimes yield a revenue, 
 and thereby serve in the function of a capital 
 to particular persons. In countries where mas- 
 querades are common, it is a trade to let out 
 masquerade dresses for a night. Upholsterers fre- 
 quently let furniture by the month, or by the year. 
 Undertakers let the furniture of funerals by the 
 day and by the week. Many people let furnished 
 houses, and get a rent, not only for the use of the 
 house, but for that of the furniture. The revenue, 
 however, which is derived from such things, must 
 always be ultimately drawn from some other 
 source of revenue k.' 
 
 This notion that people live upon a kind of net 
 revenue flowing in to them appears to be derived 
 from the old French economists, and plays no part 
 in modern Economics. Nothing is more requisite 
 than a dwelling-house, and if a person cannot hire 
 a house at the required spot, he must find capital 
 to build it. I think that no economist would 
 refuse to count among the fixed capital of the 
 country that which is sunk in dwelling-houses. 
 Capital is sunk in farming that we may have 
 
 ^ 'Wealth of Nations,' book ii. chap. 1, twelfth paragraph 
 continued.
 
 284 The Theory of Political Economy. 
 
 bread, in cotton-mills that we may he clothed, 
 and why not in houses that we may be lodged? 
 If land yields an annual revenue of corn and 
 wool, milk, beef, and other necessaries, houses 
 yield a revenue of shelter and comfort. The sole 
 end of all industry is to satisfy our wants; and 
 if capital is requisite to supply shelter, and fur- 
 niture and useful utensils, as it undoubtedly is, 
 why refuse it the name which it bears in all other 
 employments ? 
 
 Can we deny that the property of a hotel- 
 keeper is capital and yields a revenue to its 
 owner? Yet it is invested in pots and pans, and 
 beds, and all kinds of common furniture. In 
 America it is not uncommon for people to live 
 all their lives in hotels or boarding-houses ; and 
 we might readily conceive the system to advance 
 until no one would undertake housekeeping except 
 as a profession. Now if we allow to what is in- 
 vested in hotels, hired furnished houses, lodgings, 
 and the like, the nature of capital, I do not see 
 how we can refuse it to common houses. We should 
 thus be led into all kinds of absurdities. 
 
 For instance, if two people live in their own 
 houses, these are not, according to present opinion, 
 capital; if they find it convenient to exchange 
 •houses and pay rent each to the other, the houses 
 are capital. At great watering-places lilce Brighton 
 it is a regular business to lease houses, fill them
 
 Theory of Cajjihd. 285 
 
 with furniture, and then let them for short periods 
 as furnished houses : surely it is capital which is 
 embarked in the trade. If a private individual 
 happens to own a furnished house wiiich he does 
 not at the time want, and lets it, can we refuse 
 to regard liis house and furniture as capital? 
 Whenever one person provides the articles and 
 another uses them and pays rent, there is capital. 
 Surel}^, then, if the same person uses and owns 
 them, the nature of the things is not funda- 
 mentally different. There is no need for a money 
 payment to pass ; but every person who keeps 
 accurate accounts should debit those accounts with 
 an annual charge for interest and depreciation on 
 Avhat he has invested in house and furniture. 
 Housekeeping is an occupation involving wages, 
 capital and interest, like any other business, ex- 
 cept that the owner consumes the whole result. 
 
 By accepting this view of the subject, we shall 
 avoid endless difficulties. What, for instance, 
 shall we say to a theatre? Is it not the product 
 of capital? Can it be erected Avithout capital? 
 Does it not return interest, if successful, like any 
 cotton mill, or steam vessel? If the economist 
 agrees to this, he must allow, on similar grounds, 
 that a very large part of the aggregat-e capital 
 of the country is invested in theatres, hotels, 
 schools, lecture rooms, and institutions of various 
 kinds which do not belong to the industry of the
 
 286 The Theory of Political Economy. 
 
 country, taken in a narrow sense, but which none 
 the less contribute to the wants of its inha- 
 bitants, which is the sole object of all industry. 
 
 I may add, that even the food, clothes, and 
 many other possessions of extensive classes are 
 often indubitable capital ; they are bought upon 
 credit, and interest is undoubtedly paid for the 
 capital sunk in them by the dealers. There is 
 hardly, I suppose, a man of fashion in London who 
 walks in his own clothes, and the tailors find in 
 the practice a very profitable investment for capital. 
 Except among the poorer classes, and often among 
 them, food is seldom paid for until after it is con- 
 sumed. Interest must be paid one way or another 
 upon the capital thus absorbed. Whether or not 
 ! these articles in the consumers' hands are capital, 
 I at any rate they have capital invested in them — 
 j that is, labour has been spent upon them of which 
 ! the whole benefit is not enjoyed at once. 
 
 I might also point out at almost any length, 
 that the stock of food, clothing, and other requi- 
 site articles of subsistence in the country are a 
 main part of capital according to the statements 
 of J. S. Mill, Professor Fawcett, and most other 
 economists. Now what does it really matter if 
 these articles happen to lie in the warehouses of 
 traders, or in private houses, so long as there is 
 a stock ? At present it is the practice for farmers 
 and corn merchants to hold the produce of the
 
 Theory of Capital. 287 
 
 harvest until the public buys and consumes it. 
 Surely the stock of corn is capital. But if it 
 were the practice of every housekeeper to buy 
 up corn in the autumn and keep it in a private 
 granary, would it not serve in exactly the same 
 way to subsist the population ? Would not every- 
 thing go on exactly the same, except that every 
 one would be his own capitalist in regard to corn 
 in place of paying farmers and corn merchants for 
 doing the business ?
 
 CHAPTER VIII. 
 
 ONCLUDING REMARKS. 
 
 The Doctrine of Population. 
 
 It is no part of my purpose in this work to 
 attempt to trace out, with any approach to com- 
 pleteness, the results of the theory given in the 
 preceding chapters. When the views of the nature 
 of Value, and the general method of treating the 
 subject by the application of the fluxional cal- 
 culus, have received some recognition and accept- 
 ance, it will be time to think of results. I shall 
 therefore only occupy a few more pages in point- 
 ing out the branches of economic doctrine which 
 have been passed over, and in indicating their 
 connection with the theory. 
 
 The doctrine of population has been conspicu- 
 ously absent, not because I doubt in the least its 
 truth and vast importance, but because it forms 
 no part of the direct problem of Economics. I 
 do not remember to have seen it remarked that
 
 Concluding Remarks. 289 
 
 it is an inversion of the problem to treat labour 
 as a varying- quantity, when we originally start 
 with labour as the first element of production, 
 and aim at the most economical employment of 
 that labour. The problem of Economics may, as \ 
 it seems to me, be stated thus: — Given, a cer- 
 tain ^oimlation, with various needs and powers of 
 production, in possession of certain lands and other 
 sources of material: required, the mode of employ- 
 ing their lahour lohich will maximise the utility of\ 
 the produce. It is what mathematicians would 
 call a change of the variable, afterwards to treat 
 that labour as variable which was originally a 
 fixed quantity. It really amounts to altering the 
 conditions of the problem so as to create at each 
 change a new problem. The same results, how- 
 ever, would generally be obtained by supposing 
 the other conditions to vary. Given, a certain 
 population, we may imagine the land and capital 
 at their disposal to be greater or less, and may 
 then trace out the results which Avill, in many 
 respects, be applicable respectively to a less or 
 greater population with the original land and 
 capital. 
 
 Relation of Wages and Profit. 
 
 There is another inversion of the problem of 
 Economics which is generally made in works 
 upon the subject. Although labour is the start- 
 
 u
 
 290 The Theory of Political Economy. 
 
 ing-point in production, and the interests of the 
 labourer the very subject of the science, yet eco- 
 nomists do not progress far before they suddenly 
 turn round and treat labour as a commodity 
 which is bought up by capitalists. Labour be- 
 comes itself the object of the laws of supply and 
 demand, instead of those laws acting in the dis- 
 tribution of the products of labour. Economists 
 have invented, too, a very simple theory to deter- 
 mine the rate at which capital can buy up labour. 
 The average rate of wages, they say, is found by 
 dividing the whole amount of capital appropriated 
 to the payment of wages by the number of the 
 labourers paid ; and they wish us to believe that 
 this settles the question. But a little consider- 
 ation shows that this proposition is simply a truism. 
 The average 7'ate of tvages must he equal to what is 
 appropynated to the purpose divided by the num- 
 ber ivho share it. The whole question will con- 
 sist in determining how much is appropriated for 
 the purpose; for it certainly need not be the 
 whole existing amount of circulating capital. Mill 
 distinctly says, that because industry is limited 
 by capital, we are not to infer that it always 
 reaches that limit ^ ; and, as a matter of fact, we 
 often observe that there is abundance of capital 
 to be had at low rates of interest, while there are 
 also large numbers of artisans starving for want 
 
 '^ ' Principles of Political Economy,' book i. chap. 5, § 2.
 
 Concluding Remarks. 291 
 
 of employment. The wage-fund theory is there- 
 fore illusory as a real solution of the problem, 
 though I do not deny that it may have a certain 
 limited and truthful application, to be shortly 
 considered. 
 
 Another part of the current doctrines of Eco- 
 nomics determines the rate of profit of capitalists 
 in a very simple manner. The whole produce 
 of industry must be divided into the portions 
 paid as rent, taxes, profits, and wages. We may 
 exclude taxes as exceptional, and not very im- 
 portant. Rent also may be eliminated, for it is 
 essentially variable, and is reduced to zero in the 
 case of the poorest land cultivated. We thus 
 arrive at the simple equation — 
 
 Produce = profit + Avages. 
 
 A plain result also is drawn from the formula; 
 for we are told that if wages rise, profits must 
 fall, and vice versd. But such a doctrine is radi- 
 cally fallacious; it iyivolves the attempt to deter- 
 mine tivo unknoivn quantities from one equation. 
 I grant that if the produce be a fixed amount, 
 then if wages rise profits must fall, and vice versd. 
 Something might perhaps be made of this doc- 
 trine if Ricardo's theory of a natural rate of 
 wages, that which is just sufficient to support 
 the labourer, held true. But I altogether ques- 
 tion the existence of any such rate. 
 
 The wages of working men in this kingdom 
 
 u 2
 
 292 The Theory of Political Economy. 
 
 vary from perhaps ten shillings a week up to 
 forty shillings or more; the minimum in one part 
 of the country is not the minimum in another. 
 It is utterly impossible, too, to define exactly what 
 are the necessaries of life. I am inclined, there- 
 fore, to reject altogether the current doctrines as 
 to the rate of wages; and even if the theory held 
 true of any one class of labourers separately, there 
 is the additional difficulty that we have to account 
 for the very different rates which prevail in dif- 
 ferent trades. It is impossible that we should 
 accept for ever Ricardo's sweeping simplification 
 of the subject, involved in his assumption, that 
 there is a natural ordinary rate of wages for com- 
 mon labour, and that all higher rates are merely 
 exceptional instances, to be explained away on 
 other grounds. 
 
 The view which I accept concerning the rate of 
 wages is not more difficult to comprehend than the 
 current one. It is that the ivages of a vjorking man 
 are ultimately coincidevit vjith what he produces, 
 after the deduction of rent, taxes, and the interest 
 of capital. I think that in the equation 
 
 Produce = profit + wages, 
 the quantity of produce is essentially variable, and 
 j that profit is the part to be first determined. If 
 we resolve profit into wages of superintendence, 
 insurance against risk, and interest, the first part 
 is really wages itself; the second equalises the
 
 Concluding Remarks. 293 
 
 result in different employments ; and the interest 
 is, I believe, determined as stated in the last chapter. 
 The reader will observe the important qualification, 
 that wages are only ultimately thus determined — 
 that is, in tlie long run, and q\\ the average of any 
 one branch of employment. 
 
 The fact that workmen are not their own capi- 
 talists introduces complexity into the problem. 
 The cajiitalists, or entrepy^eneurs, enter as a distinct 
 interest. It is they who project and manage 
 a branch of production, and form estimates as to 
 the expected produce. It is the amount of this 
 produce which incites them to invest capital and 
 buy up labour. They pay the lowest current rates 
 for the kind of labour required ; and if the pro- 
 duce exceeds the average, those who are first in 
 the field make large profits. This soon induces 
 competition on the part of other capitalists, who, 
 in trying to obtain good workmen, will raise the 
 rate of wages. Competition will proceed until the 
 point is reached at which only the market rate 
 of interest is obtained for the capital invested. At 
 the same time wages will have been so raised, that 
 the workmen reap the whole excess of produce, 
 unless indeed the price of the produce has fallen, 
 and the public, as consumers, have the benefit. 
 Whether this latter result will follow or not, 
 depends upon the number of labourers who are 
 fitted for the work. Where much skill and educa-
 
 294 The Theory of Political Economy. 
 
 tion is required, extensive competition will be 
 impossible, and a permanently high rate of wages 
 will exist. But if only common labour is requisite, 
 the price of the goods cannot be maintained, wages 
 will fall to their former point, and the public will 
 gain the advantage of cheaper supplies. 
 
 It will be observed, that this account of the 
 matter involves the temporary application of the 
 wage-fund theory. It is the proper function of 
 capitalists to sustain labour before the result is 
 accomplished, and as many branches of industry 
 require a large outlay long previous to any definite 
 result being arrived at, it follows that capitalists 
 must undertake the risk of any branch of industry 
 where the ultimate profits are not accurately 
 known. But we now have some clue as to the 
 amount of capital which will be appropriated 
 to the payment of wages in any trade. The 
 amount of capital will depend upon the amount 
 of anticipated profits, and the competition to obtain 
 proper workmen will strongly tend to secure to the 
 latter all their legitimate share in the ultimate 
 produce. 
 
 For instance, let a number of schemes be set on 
 foot for laying telegraphic cables. The ultimate 
 profits are very uncertain, depending upon the 
 utility of the cables as compared with their cost. 
 If capitalists make a large estimate of those pro- 
 fits, they will apply much capital to the imme-
 
 Concluding Remarks. 295 
 
 diate manufacture of the cables. All workmen 
 competent at the moment to be employed will be 
 hired, and high wages j^aid if necessary. Every 
 man who has peculiar skill, knowledge, or experi- 
 ence, rendering his assistance valuable, will be 
 hired at any requisite cost. At this point it is the 
 Avage-fund theory that is in operation. But, after 
 a certain number of years, the condition of affairs 
 Avill be totally different. Capitalists will learn, by 
 experience, exactly wdiat the profits of cables may 
 be ; that amount of capital will be thrown into 
 the work which finds the average amount of profits, 
 and neither more nor less. The cost of transmit- 
 ting messages will be reduced by competition, so 
 that no excessive profits will be made by any 
 of the parties concerned ; the rate of wages, there- 
 fore, of every species of labour Avill be reduced to 
 the average proper to labour of that degree of skill. 
 But if there be required in any branch of the work 
 a very special kind of skilled and experienced 
 labour, it will not be affected by competition in the 
 same way, and the wages or salary Avill remain 
 high. 
 
 I think that it is in this way quite possible to 
 reconcile theories which are at first sight so dif- 
 ferent. The wage-fund theory acts in a wholly 
 temporary manner. Every labourer ultimately 
 receives the due value of his produce after paying 
 a proper fraction to the capitalist for the remunera-
 
 296 Tlie Theory of Political Economy. 
 
 tion of abstinence and risk. At the same time 
 workers of different degrees of skill, receive very 
 different shares according as they contribute a com- 
 mon or a scarce kind of labour to the result. 
 
 Professor HearrCs Views. 
 
 I have the more pleasure and confidence in 
 putting forward these somewhat heretical views 
 concerning the general problem of Economics, in- 
 asmuch as they are nearly identical with those 
 arrived at by Professor Hearn, of Melbourne Univer- 
 sity. It would be a somewhat long task to trace 
 out exactly the coincidence of opinions between us, 
 but he certainly adopts the notion that the capitalist 
 merely buys u|) temporarily the prospects of the 
 concern he manages and the labourers he employs. 
 Thus he says — ' In place of having a share in the 
 undertaking, the co-operator sells for a stipulated 
 price his labour or the use of his capital. The case 
 therefore comes within the ordinary conditions of 
 exchange ; and the price of labour and the price 
 of capital are determined in the same manner as 
 all other questions of price are determined. Yet 
 the general character of the partnership is not 
 destroyed. Although each particular transaction 
 amounts to a sale, yet for the continuance of the 
 business a nearer connection arises. Although the 
 whole loss of the undertaking, if the undertaking
 
 Concluding Remarks. 297 
 
 be unfortunate, falls upon the last proprietor, and 
 the interests of the other parties have been previ- 
 ously secured, yet each such loss prevents a repeti- 
 tion of the transaction from which it arose. The 
 capital which ought to have been replaced, and 
 which if replaced would have afforded the means 
 of employing labour and of defraying the interest 
 upon other capital, has disappeared ; and thus the 
 market for labour and for capital is by so much 
 diminished. Both the labourer and the interme- 
 diate capitalist are therefore directly concerned 
 in the success of every enterprise towards which 
 they have contributed. If it be successful, they 
 feel the advantage; if it be not successful, they 
 feel in like manner the loss. But this community 
 of interest is no longer direct, but is indirect 
 merely; and it arises not from the gains or the 
 losses of partners, but from the increased ability, 
 or the diminished demands, of customers ^.' 
 
 This passage really contains a statement of the 
 views which I am inclined wholly to accept; but 
 no passages which I can select will convey an 
 adequate notion of the enlightened view which 
 Professor Hearn takes of the industrial structure 
 of society in his admirable work on Plutology. 
 
 b ' Plutology : or the Theory of the Efforts to satisfy human 
 wants.' By William Edwai'd Hearn, LL.D., Professor of History 
 and Political Economy in the University of Melbourne. London 
 (Macmillan and Co.), 1864, p. 329.
 
 298 The Theory of Political Eco7iomy. 
 
 The Noxious Injiuence of Authority. ■ 
 
 I have but a few lines more to add. I have ven- 
 tured in tlie preceding pages to call in question not 
 a few of the favourite doctrines of economists. To 
 me it is far more pleasant to agree than to differ ; 
 but it is impossible that one who has any regard 
 for truth can long avoid protesting against doctrines 
 which seem to him to be erroneous. There is ever 
 a tendency of the most hurtful kind to allow 
 opinions to crystallise into creeds. Especially does 
 this tendency manifest itself when some eminent 
 author, enjoying power of clear and comprehensive 
 exposition, becomes recognised as an authority. 
 His works may perhaps be the best which are 
 extant upon the subject in question ; they may 
 combine more truth with less error than we can 
 elsewhere meet. But 'to err is human,' and the 
 best works should ever be open to criticism. If, 
 instead of welcoming inquiry and criticism, the 
 admirers of a great author accept his writings as 
 authoritative, both in their excellences and in 
 their defects, the most serious injury is done to 
 truth. In matters of philosophy and science author- 
 ity has ever been the great opponent of truth. 
 A despotic calm is usually the triumph of error. 
 "In the republic of the sciences sedition and even 
 anarchy arc beneficial in the long run to the 
 greatest happiness of the greatest number.
 
 Concluding Remarks. 299 
 
 In the physical sciences authority has greatly 
 lost its noxious influence. Chemistry, in its brief 
 existence of a century, has undergone three or four 
 complete revolutions of theory. In the science of 
 light, Newton's own authority was decisively set 
 aside, though not until after it had retarded for 
 nearly a century the progress of inquiry. Astro- 
 nomers have not hesitated, within the last few 
 years, to alter their estimates of all the dimensions 
 of the planetary system, and of the universe, be- 
 cause good reasons have been shown for calling 
 in question the real coincidence of jn-evious mea- 
 surements. In science and philosophy nothing 
 must be held sacred. Truth indeed is sacred ; but, 
 as Pilate said, 'What is truth?' Show us the un- 
 doubted infallible criterion of absolute truth, and 
 we will hold it as a sacred inviolable thing. But 
 in the absence of that infallible criterion, we 
 have all an equal right to grope about in our 
 search of it, and no body and no school nor 
 clique must be allowed to set up a standard of 
 orthodoxy which shall bar the freedom of scientific 
 inquiry. 
 
 I have added these words because I think there 
 is some fear of the too great influence of author- 
 itative writers in Political Economy. I protest 
 against deference for any man, whether John Stuart 
 IMill, or Adam Smith, or Aristotle, being allowed 
 to check inquiry. Our science has become far too
 
 300 The Theory of Political Economy. 
 
 much a stagnant one, in which opinions ratlier 
 than experience and reason are appealed to. 
 
 There are valuable suggestions towards the im- 
 provement of the science contained in the works 
 of such writers as Senior, Cairnes, Macleod, Cliffe- 
 Leslie, Hearn, Shadwell, not to mention a long 
 series of French economists from Baudeau and 
 Le Trosne down to Bastiat and Courcelle-Seneuil ; 
 but they are neglected in England, because the 
 excellence of their works w^as not comprehended 
 by David Ricardo, the two Mills, Professor Fawcett, 
 and others who have made the orthodox Ricardian 
 school what it is. Under these circumstances it is 
 a positive service to break the monotonous repeti- 
 tion of current questionable doctrines, even at the 
 risk of new error. I trust that the theory now 
 given may prove accurate ; but, however this may 
 be, it will not be useless if it cause inquiry to be 
 directed into the true basis and form of a science 
 which touches so directly the material welfare of 
 the human race. 
 
 FINIS.
 
 APPENDIX I. 
 
 List of Mathematico-Economic Books, Memoirs, and other 
 published writings. 
 
 Remarks upon the purpose and some of the contents of this list 
 will be found in the preface to the second edition of this book. 
 
 1720. HuTCHESON (Francis). An Inquiry into the Original of 
 
 our Ideas of Beauty and Virtue. London. 8vo. (3rd Edition, 
 
 1729, xxii, 304 pp.) 
 1728. HuTCHESON (Francis). An Essay on the Nature and 
 
 Conduct of the Passions and Affections, with Illustrations on 
 
 the Moral Sense. London. 8vo. xxiv, 333 pp. 
 1765. Beccaria (Cesare). Tentativo analitico sui contrab- 
 
 bandi. Estratto dal foglio periodico intitolato : II Gaffe (vol. i. 
 
 Brescia). Cu&todi's Scrittori classici Italiani di Economia politica. 
 
 Parte Moderna, vol. xii, pp. 235-241. Milano, 1804. 
 1771. Anonymous. An Essay on the Theory of Money. London. 
 
 8vo. IGl pp. (attributed to Major-General Henry Lloyd). 
 1776. CoNDiLLAC (Etienne Bonnot de). Le Commerce et le 
 
 Gouverneraent. Paris. 
 1781. Anonymous (A. N. Isnard). Traite des Eichesses. Londres 
 
 et Lausanne. 2 vols. 8vo. xxiv, 344, 327 pp. 
 
 1792. SiLio (Guglielmo). Saggio sull' Influenza dell' Analisi 
 nelle scienze politiche ed economiche. (In vol. v. of the collec- 
 tion Nuova Raccolta d' opuscoli di Autori Siciliani. Palermo). 
 
 1793. Lang. Historische Entwickelung der Deutschen Steuerver- 
 fassung. Riga. 
 
 1801. Canard (Nicolas Frangois). Principes d'Economie Poli- 
 tique; Ouvrage couronne par I'lnstitut. Paris. 8vo, 384 pp. 
 1801. Canard (Nicolas Fran9ois). M^moire sur la question
 
 302 Appendix I. 
 
 s'il est vrai que, clans un pays agricole, toute espfece d'impot 
 
 retombe sur les proprietaires fouciers. Paris. 
 1802. Brisson (B.) Essai sur la Navigation. Paris. 
 1802. Keoncke (C). Versuch einer Theorie des Fuhrwerks mit 
 
 Anvendung auf dem Strassenbau. Giessen. 8vo. 
 1804. Keoncke (C). Das Steuerwesen nacli seiner Natur und 
 
 seinen Wirkungen untersucht. Giessen. 8vo. 
 1807. Lang. Ueber den obersten Grundsatz der Politischen 
 
 Oeconomie. Eiga. 8vo. 
 1815. BuQUOT (G. Graf von). Theorie der Nationalwirthschaft 
 
 nach einem neuen Plane, und nach mehreren eigenen Ansichten 
 
 dai'gestellt. Leipzig; hierzu 3 Nachtrage, 1816-18. 4to. 
 
 524 pp. 
 
 1824. Thompson (T. Perronet). Westminster Review, No. I, vol. i, 
 pp. 171-205. Article on the Instrument of Exchange. (Re- 
 printed in 1830, 27 pp.) 
 
 1825. Fuoco (Francesco). Saggi Economici. Prima Serie. 2 torn, 
 8vo. Pisa, 1825-27. 
 
 1829. Whewell (William). Mathematical Exposition of some 
 i Doctrines of Political Economy. Cambridge Philosophical 
 ' Transactions, vol. iii, pp. 191-230. Cambridge. 4to. 
 
 1831. Waleas (Auguste). De la Nature de la Richesse et de 
 I'origine de la Valeur. Paris. 8vo. xxiv, 334 pp. 
 
 1831. Whewell (William). Mathematical Exposition of the 
 
 (Leading Doctrines in Mr. Ricardo's ' Principles of Political 
 Economy and Taxation.' Cambridge Philosophical Transactions, 
 vol. iv, pp. 155-198. Cambridge. 4to. 
 
 1832. Lube (D. G.) Argument against the Gold Standard. 
 London. 8vo. iv 192 pp. 
 
 1838. CouENOT (Augustin). Recherches sur les Principes Math6- 
 matiques de la Theorie des Richesses. Paris. 8vo. xi, 
 198 pp. 
 
 1838. Tozee (John). Mathematical Investigation of the Effect of 
 Machinery on the Wealth of a Community in which it is 
 employed, and on the Fund for the Payment of Wages. Cam- 
 bridge Philosophical Transactions, vol. vi, pp. 507-522, 
 Cambridge. 4to.
 
 Mathematico-Economic Books. 303 
 
 1839. Hagen (Karl Heiuricli). Von der Staat^lelue unci von der 
 Vorbereitung zum Dienste in der Staatsverwaltung. Aufsatze 
 gerichtet an angehende Cameralisten, zuuachst an seine Herren 
 Zuhorer, von K. H. H. Koenigsherg. 8vo. 477 pp. 
 
 1840. Anonymous. On Cui-rency. London (Charles Knight and 
 Co.). 8vo. viii, 43, xxi pp. 
 
 1840. TozER (John). On the Effect of the Non-Residence of 
 
 Landlords, &c., on the "Wealth of a Community. Cambridge 
 
 Philosophical Ti'ansactions, vol. vii, pp. 189-196. Cambridge. 
 
 4to. 
 1842. Thompson (T. Perronet). Exercises, Political and others. 
 
 Vol. iii, pp. 295-343. On the Instrument of Exchange. See 
 
 1824, Thompson. 
 1844. DuPUiT (Etienne Juvenal). De la Mesure de TUtilit^ 
 
 des Travaux Publics. Annales des Ponts et Chauss^es. 2^ Eerie. 
 
 Tome viii, pp. 332-375. Paris. 8vo. 
 1844. Hagen (K. H.). Die Nothwendigkeit der Handelsfreiheit 
 
 fiir das Nationaleinkommen, mathematisch nachgewiesen. Koe- 
 
 nigsberg. 8vo. 32 pp. 
 1844. Hagen (K. H.). System of Political Economy. Translated ' 
 
 from the German by John Prince Smith. London. 8vo. 
 
 viii, 88 pp. 
 1844. De Quincy (Thomas). Logic of Political Economy. 
 
 Edinburgh, London. 8vo, 260 pp. 
 
 1847. BoKDAS. De la Mesure de I'TItiUt^ des Travaux Publics. 
 Annales des Ponts et Chauss^es, 1847, l^r semestre, 2^^ s6rie, 
 tome xiii, p. 249. Paris. 8vo. 
 
 1848. Mill (John Stuart). Principles of Political Economy, with 
 some of their applications to Social Philosophy. London. 2 
 vols. 8vo. (Book iii, chapters xvii, xviii. See 3rd Edition, 
 1852, vol ii. pp. 143-4. 
 
 1849. EsMENARD Bu Mazet (Camille). Nouveaux Principes 
 d'Economie Politique. Paris. 8vo. ix, 456 pp. 
 
 1849. DuPUiT (E. J.). De I'lnfluence des Peages sur I'Utilit^ des 
 Voies de Communication. Annales des Ponts et Chaussees. 
 No. 207. 2e serie, 1849, ler semestre. Paris. 8vo. (Pp. 
 170-248).
 
 304 Ap'pendix I. 
 
 1850. MiNAED, De I'llsage Gratuit des Constructions stabiles 
 aux Frais de I'Etat. Annales des Fonts et Chauss^es, 2^ serie, 
 1 er semestre. Paris. 8vo. (p. 27.) 
 
 1850. Laednek (Dionysius), Railway Economy. London. 8vo. 
 (Chapter xiii.) 
 
 1850. Whewell (William). Mathematical Exposition of Certain 
 Doctrines of Political Economy. Second and Third memoirs, 
 Cambridge Philosophical Transactions. Vol. ix. pp. 128-149, 
 and Part II, pp. [1-7]. Cambridge. 4to. 
 
 1851. EsMENAED DU Mazet. De la Valeur : Lettre a M. J. 
 Gamier. Paris. 8vo. 
 
 1851. De Thunen. Recherches sur I'Influence que le Prix des 
 Grains, la Eichesse du Sol, et les Impots exercent sur les 
 Systfemes de Culture. Traduit par Laverrifere. Paris. 8vo. 
 
 1854. WoLKOFF (Mathieu). Opuscules sur la Rente Fonciere. 
 Paris. 8vo. 231 pp. 
 
 1854. GossEN (Hermann Heinrich). Eutwickelung der Gesetze 
 des menschliohen Verkehrs, und der daraus fliessenden Eegeln 
 fiir menschliches Handeln. Braunschweig. 8vo. 278 pp. 
 
 1855. Jennings (Richard, M.A.). Natural Elements of Political 
 Economy. London. 8vo. 275 pp. 
 
 1856. Bennee. Th^orie Math^matique de I'Economie Politique. 
 •1856. "WoLKOFF (M.). Journal des Economistes, Aout, 1856. 
 
 Paris. 8vo. 
 
 1857. De Thunen. Le Salaire N"aturel, et son rapport au taux de 
 rinter^t. Traduit de I'Allemand par Mathieu WolkofF. Paris. 
 
 1857. Macleod (Henry Dunning). The Elements of Political 
 
 Economy. London. 8vo. 
 1857. Boccaedo (Gerolamo). Dizionario della Economia Politica 
 
 e Commercio, &c. Torino. 4to. (Vol. ii. pp. 653-9, etc.) 
 
 1860. Du Mesnil-Maeigny. Les Libre Echangistes et les Pro- 
 tectionnistes Concili^s. 8vo. Paris. 
 
 1861. WoLKOFF (M.). Lectures d'Economie Politique Rationelle. 
 • Paris. 12 mo. 
 
 !1862. Jevons (William Stanley). Notice of a General Mathe- 
 matical Theory of Political Economy. Report of the 32nd 
 mcetinsf of the British Association for the Advancement of
 
 Mathematico-Economic Books. 305 
 
 Science, held at Cambridge in October, 1862. Reports of Sec- 
 tions, p. 158. London, 1863. 8vo. 
 
 1862. Macleod (H. D.). On the Definition and Nature of the 
 Science of Political Economy. Report of the 32 nd meeting 
 of the British Association, &c. Reports of Sections, pp. 
 159-161. 
 
 1863. CouRNOT (Augustin). Principes de la Theorie des Richesses. \i\ 
 Paris. 8vo. iv, 527 pp. 
 
 1863. Macleod (H. D.). A Dictionary of Political Economy: 
 Biographical, Bibliographical Historical, and Practical. Vol. i. 
 London. 8vo. (Article Credit, p. 567.) 
 
 1863. Du Mesnil-Maeigny. Catechisme de I'Economie politicpie 
 basee sur des principes rationnels. Paris. 18mo. 355 pp. 
 
 1863. Mangoldt (H. von). Grundriss der Volkswirthschafts- 
 lehre. Stuttgart, xvi, 224. 
 
 1864. Fauveau (G.). Considerations Mathematiques sur la 
 Theorie de I'lmpot. Paris. 8vo. 64 pp. 
 
 1865. Knapp (George Friedrich). Zur Priifung der Untersuchungen 
 Thiineu's iiber Lohn und Zinsfuss im isolirten Staate. Braun- 
 schweig. Svo. 35 pp. 
 
 1866. Jevons (W. S.). Brief Account of a General Mathematical ' 
 Theory of Political Economy. Journal of the Statistical Society ,j 
 of London, June, 1866. Vol. xxix, pp. 282-287. London.^' 
 8vo. 
 
 1867. Courcelle-Seneuil (J. G.). Traito Th6orique et Pratique 
 d'Economie Politique. 2'"^ Ed. Paris. 8vo. Tome I, livre i, 
 chap. 2. 
 
 1867. Fauveau (G.). Considerations math^matiqucs sur la theorie 
 de la valeur. Journal des Ecouomistes. 3^ s6rie, 2° annee, 
 t. V, pp. 31-40. 
 
 1867. Brentako (L. J.). Ueber J. H. von Thiineu's Naturge- 
 miissen Lohn und Zinsfuss. Gottingen. 61 pp. 
 
 1868. Rau (Kai-1 Heinrich). Grmidsiitze der Volkswirthshafts- 
 lehre. Achte Ausgabe. Erste Abtheilung, p. 368. Leii^zig 
 tend Heidelberg. 8vo. 
 
 1868. Jexkin (Fleeming). Trades Unions. How far Legitimate, 
 North British Review, March 1858. 8vo. (Foot note.) 
 
 X
 
 306 Appendio' I. 
 
 1868. WoLKOFF (Mathieu). Precis cl'economie politique~ration- 
 nelle. Paris. In-18, 329 pp. 
 
 1869. Fauveau (G.). Etude sur la theoiie de Timpot. Journal 
 des Economistes, 3** s^rie, 4^ aun6e, t. xiii, pp. 391-403. 
 
 1869. Fauveau (G.). L'impot sur le revenu du capital et sur le 
 revenu du travail. Journal des Economistes, 3^ serie, 4^ annee, 
 t. xvi, pp. 466-468. 
 
 1869. Schumacher (H.). Ueber J. H. von Thiinen's Gesetz voni 
 naturgemassen Arbeitslohue. Rostock. 84 pp. 
 
 1870. Jenkin (Fleeming). The Graphic Representation of the 
 Laws of Supply and Demand, and their application to Labour. 
 Recess Studies, edited by Sir Alexander Grant. Edinburgh. 
 8vo. (pp. 151-185). 
 
 1871. Jevons (AV. S.). The Theory of Political Economy. 8vo. 
 London, xvi, 267 pp. 
 
 1871. Jenkin (Fleeming). On the Principles which regulate the 
 incidence of Taxes, Proceedings of the Royal Society of Edin- 
 burgh. Session 1871-72. (pp. 618-631). 
 
 1871. Fauveau (G.). Rendement maximum de l'impot indirect. 
 Journal des Economistes. 3'^ serie, 6^ annee, t. xxiv, pp. 445-8. 
 
 1872. Marchand (J.). Recherche sur la methode a adopter pour 
 la discussion des elements de la statistique. Journal des Ac- 
 tuaires frangais. T. i, pp. 267-273 and 393-409. 
 
 1873. BiNG oa Petersen. Bestemmelse af den rationelle Arbeids- 
 lon samt nogle Bemserkninger om Oekonomiens Methode. Na- 
 tionaloekonomisk Tidsskrift. Forste Bind, p. 296. Goi^enhagen. 
 
 1873. Marchand (J.). Recherche sur la methode {\ adopter pour 
 la discussion des elements de la statistique. Journal des 
 Actuaires frangais. T. ii, pp. 58-78 et 251-263. 
 
 1873. Petersen, Frederiksen, etc. Nationaloekonomisk Foren- 
 ing. Diskussion om Oekonomiens Methode. Nationaloekononiisk 
 Tidsskrift, Maanedsskrift for Oekonomi, etc. Andet Bind, p. 248. 
 Cojienhagen. 
 
 1873. Pochet (L6on). Geometric des jeux de Bourse. Journal 
 des Actuaires francais. T. ii, pp. 153-160. 
 
 1873. Lefevre (H.). Physiologic et m<^canique sociales. Journal 
 des Actuaires franrais. T. ii, pp. 211-250 et 351-388.
 
 Mathematico-Economic Boohs. 307 
 
 1874. Walras (Leon). Principe d'une theoric niath^matique de 
 
 r^change. Menioire lu a 1' Academic des sciences morales et poli- 
 
 tiques (Seaucesdes 16 et 23aout 1873). Orleans. 8vo, 24 pp. 
 1874. Jevons et Walkas. Correspondance. Extrait du Journal 
 
 desEconomistes (nuni^ro du 15 jnin 1874). Paris. 8vo. 8 pp. 
 1874. BoccAEDO (Gerolamo). Dizionario Universale della Econ- 
 
 omia Politica e del Commercio. Milano. 8vo. 
 1874. Lefevre (H.). Principe de la Science de la Bourse. 
 
 Methode approuvce par la Chambi-e syndicale des Agents de 
 
 Change de Paris. Paris. 8vo. 113 pp. 
 1874. Walras (Leon). Elements d'economie politique pure, ou 
 
 theorie de la richesse sociale. Premier fascicule. Lausanne, 
 
 Paris et Bdle. 8vo. viii, 208 pp. 
 1874. Zanon (Giovanni Antonio). Sulla teoria matematica dello 
 
 scambio del professore M. L. AValras, lettera al professore 
 
 Alberto Errera. Estratto dalla Eassegna di Agricoltura^ Indus- 
 
 tria e Commercio. Padova. 8vo. 7 pp. 
 1874. Letort (Charles). De I'application des mathematiques a 
 
 I'etude de I'economie politique. L'Economiste francais, 31 
 
 octobre 1874, p. 540. 
 1874. D'AuLNis DE BouEOUiLL (Johan). Het Inkomen der Maats- 
 
 chappij. Eene Proeve van theoretische Staathuishoudkunde. 
 
 Leiden. Svo. xiii, 215 pp. 
 1874. Lefevre (H.). Physiologic et m^canique sociales. Journal 
 
 des Actuaires frangais. T. iii, pp. 93-118. 
 1874. DoRMOY (Emile). Les matiferes premieres. Etablissement 
 
 des coefficients d'elaboration. Journal des Actuaires frangais. 
 
 T. iii, pp. 142-162. 
 1874. AviGDOR (Septime N".), Question d'economie sociale. 
 
 Journal des Actuaires fran9ais. T. iii, pp. 300-306. 
 
 1874. Marchand (J.). Recherche sur la methode a adopter pour 
 la discussion des elements de la statistique. Journal des 
 Actuaires frangais. T. iii, pp. 307-325. 
 
 1875. Jevoxs (AV. Stanley). The progress of the mathematical 
 theory of Political Economy, with an explanation of the prin- 
 ciples of the theory. Transactions of the Manchester Statistical 
 Sociely. pp. 1-19. Svo. (Read Nov. 11, 1874.) 
 
 X 2
 
 308 Appendix I. 
 
 1875. Darwin (George H.). The Theory of Exchange Value. 
 
 Fortnightlj^ Review. New series, Voh xvii, pp. 243-253. 
 
 London. 8vo. 
 1875. BoccAEDO (Gerolamo). Del metodo in econoinia j)olitica. 
 
 Estratto dal Giornale degli Economisti. Paclova. 8vo. 23 pp. 
 1875. BoccARDO (Gerolamo). L'economia politica odiema come 
 
 scienza le come ordinamento sociale. Introduzione generale alia 
 
 Biblioteca dell' Economista. 3^ serie, pp. 1-43. 
 1875. Ereeea (Alberto). Ajjpunto bibllografico. Elements 
 
 d'^conomie politique pure par L^on "Walras. Estratto dal 
 
 giornale La Perseveranza. Milano. 18mo. 16 pp. 
 1875. BoccAEDO (Gerolamo). Dell' applicazione dei metodi 
 
 quantitativi alle scienze economiche, statistiche e sociali. Saggio 
 
 di logica economica. Prefazione al 2° volume della Biblioteca 
 
 deir Economista. Pp. i.-lxxii. 
 1875. Whewell (W.). Esposizione matematica di alcune dot- 
 trine di economia politica. Due Memorie. Biblioteca dell' 
 
 Economista. 3* serie. Vol. ii, pp. 1-65. 
 1875. CouRNOT (Agostino). Eicerche intoruo ai principii mate- 
 
 matici della teorica delle ricchezze. Biblioteca dell' Economista. 
 
 3a serie. Vol. ii, pp. 67-170. 
 1875. Jevons ("W. Stanley). La teorica dell' economia politica. 
 
 Biblioteca dell' Economista. 3''^ serie. Vol. ii, pp. 173-311. 
 1875. Newcomb (Simon). North American Eeview, No.CCXLIX. 
 
 Review of Caimes' Logical Method of Political Economy. 
 1875. PiEESOK (N. G.). Grondbeginselen der Staathuishoud- 
 
 kunde. Haarlem. 1875-6. 2 vols. 
 1875. AcHARD (M. A.). Influence des taxes qui frappent les 
 
 obligations sur leur prix d'nprfes nn taux d6termin6. Journal 
 
 des Actuaires fran^ais. T. iv, pp. 70-74. 
 1875. FoNTANEAU (E.). Principes de chrematistique. Journal 
 
 des Actuaires fran^ais. T. iv, pp. 75-83 et 151-172. 
 1875. Laurekt (H.). Demonstration simple du principe de 
 
 M. Menier. Journal des Actuaires francais. T. iv, pp. 
 
 84-87 (also jirinted in Menier's Theorie et A2:)plication de I'lm- 
 
 pot sur le Capital. 2™°. Ed. Paris. 1875. 12mo. Appendice, 
 
 pp. 607-12).
 
 Mathematlco-Economic Boohs. 309 
 
 1875. FoNTANEAU (E.) De la valeur. Journal dcs Actuaircs 
 fran^ais. T. iv, pp. 175-199 et 267-277. 
 
 1875. Falck (Gr. von). Die Thiinensche Lehre vom Bildungsgesetz 
 des Zinsfusses und vom naturgemassen Arbcitslolni. Leipzig. 
 55 pp. 
 
 1876. "Walras (Leone). Un nuovo ramo della matcmatica. 
 Dell' applicazione delle matematiche aU'ecouomia politica. 
 Estratto dal Griornale degli Economisti. Padova. Bvo. Vol. iii. 
 Fascicolo N. I. Aprile, 1876. 40 pp. 
 
 1876. Walras (L^on). Equations de I'ecliange. Equations de 
 
 la production. Memoires lus a la Societe vaudoise des sciences 
 
 naturelles. (Stances des l^r et 15 d^cenibre 1875, 19 Janvier et 
 
 16 fevrier 1876.) Lausanne. 8vo. 66 pp. 
 1876. Zambelli (Andrea). La teoria matematica dello scambio 
 
 del signor Leone "VValras. Lettera diretta al prof. Errera dott. 
 
 Albei'to. Padova. Gr. in-8. 28 pp. 
 1876. Jevons ("W. Stanley). The Future of Political Economy. 
 
 Fortnightly Review, November 1, 1876. vol. xx. pp. 617-631. 
 1876. Walras (L^on). Equations de la capitalisation. Me- 
 
 moire lu a la Soci6te vaudoise des sciences naturelles (Seance du 
 
 5 juillet 1876). Bvo. 40 pp. 
 1876. FoNTANEAU (E.). Chrematistique. Journal des Actuaires 
 
 frangais. T. v, pp. 70-96 et 341-365. 
 
 1876. Madsen (C. L.). Den Sandsynlige Lov for den Inter- 
 nationale Telegraftrafik. Copenhagen. 8vo. 
 
 1877. Madsen (C. L.). Recherches sur la loi du Mouvemcnt 
 tel6graphique international. Copenhague, Paris. 8vo. ix, 68 
 pp., avec 10 tableaux. 
 
 1877. Jevons (W. Stanley). Le passe et I'avenir de I'economie 
 politique. Les m^thodes. Les economistes contemporains. Le 
 political economy club. Journal des Economistes. Mars 1877. 
 3e. serie. T. xlv, pp. 325-342. 
 
 1877. Walras (Leon). Elements d'economie politique pure, ou 
 theorie de la richesse sociale. Deuxieme fascicule. Lausanne, 
 Paris et Bdle. pp. 209-407. 8vo. 
 
 1877. Moll (L. A.). Der "Wcrth. Eine neue Theorie desselbcn. 
 Leipzig. 48 pp.
 
 310 A][)pendi^ I. 
 
 1878. AVesteegaard (Harald). Den Saiidsynlige Lov for den 
 Internationale Telegraftrafik Anmeldt af H. W. Natioual- 
 oekonomisk Tidsskrift. Bind xi. Co2)enhagen. Svo. 
 
 1878, Du Mesnil-MaeiCtNY. L'^conomie politique devenue 
 science exacte ou les libre-echangistes et les protectionnistes 
 concilies. 3^ edition. Paris. Gr. in-8. 413 pp. 
 
 1878. "Waleas (Leone). Teoria matematica della richezza sociale. 
 Quattro memorie lette all' Accademia delle science morali e 
 politiche, a Parigi, ed alia Societa Valdese delle scienze natui'ali, 
 a Losanna. Biblioteca dell' Economista. 3^ serie. Yol. ii, 
 pp. 1289-1388. 
 
 1878. "Weisz (Dr. Bela, of Budapestli, Hungary). Die Mathe- 
 niatische Methode in der Nationalcikononiie. Hildebrandt's 
 Jahrbiicher fiir Nationalokonomie und Statifctik. Article VI, vol. 
 xxxi, pp. 295-316. Jena. 
 
 1878. NicoLiNi. Un antico Economista Matematica (Ceva). 
 Giornale degli Econoniisti, vol. viii. fasc. 1. Oct. Padova. 8vo. 
 
 il879. Marshall (Alfred). The Pure Theory of Foreign Trade. 
 The Pure Theory of (Domestic) Values. Cambridge. 8vo. 
 Privately printed. 
 
 1826. Thiinen (Johann Heinrich von). Der isolirte Staat in 
 Beziehung auf Landwirthschaft und Nationalokonomie, oder 
 Untersuchungen iiber den Einfluss, den die Getreidepreise, der 
 Heichthum des Bodens und die Abgaben auf den Ackerbau 
 ausiiben. Hamburg. 8vo. viii, 290 pp. 
 
 1842. Thijnen (J. H. von). Der isolirte Staat, etc. Erster 
 Theil. Rostock. 8vo. xv, 391 pp. 
 
 1850. Thunen (J. H. von). Der isolirte Staat, etc. Zweiter 
 Theil. Erste Abtheilung. Der naturgemiisse Arbeitslohn und 
 dessen Yerhiiltniss zum Zinsfuss und zur Landrente. Rostock. 
 Svo. vi, 285 pp. 
 
 1863. ThIjnen (J. H. von). Der isolirte Staat. Zweiter Theil. 
 Zweite Abtheilung. Der naturgemussc Arbeitslohn, etc. 
 Rostock. 8vo. ix, 444 pp.
 
 APPENDIX II. 
 
 List of works and papers upon Economical Subjects, by the 
 author of the present book : — 
 
 1857. Comparison of the Land and Eailway Policy of New South 
 Wales. The Public Lands of New South Wales. Articles in 
 the Umpire newspaper, 7th April and 23rd June. Sydney, 
 New South Wales. 
 I8G2. Diagram, shewing all the Weekly Accounts of the Bank of 
 England, since the passing of the Bank Act of 1844, with the 
 Amount of Bank of England, Private, and Joint Stock Bank 
 Promissory Notes in Circulation during each week, and the 
 Bank Minimum B,ate of Discount. London. Sheet, 20 x 30 
 inches, coloured. 
 
 This Diagi-am represents to the eye all the useful results of 
 
 tables, containing about 113,000 figures. 
 
 1862. Diagram, shewing the Price of the English Funds, the 
 
 Price of W^heat, the Number of Bankruptcies, and the Ptate of 
 
 Discount, monthly, since 1731 ; so far as the same have been 
 
 ascertained. London. Sheet, 20 x 30 inches, coloured. 
 
 This Diagram is drawn from tables carefully compiled fur the 
 
 purpose, and containing more than 12,000 figures. 
 Explanatory Notes and References ai"e appended to each 
 Diagram. 
 18G2. (1) On the Study of Periodic Commercial Fluctuations. 
 With five diagrams. (2) Notice of a general Mathematical 
 Theory of Political Economy. Papers read in the F section of 
 the British Association at the Cambridge Meeting. Report. 
 Procecilings of Sections, pp. 157-8.
 
 312 Appendix II. 
 
 1863. A serious Fall in the Value of Gold Ascertained, and its 
 social effects set forth. With two diagrams. London : Edward 
 Stanford, Charing Cross. 8vo. 73 pp. 
 
 1865. The Coal Question; an Inquiry concerning the Progress of 
 the Nation, and the Probable Exhaustion of our Coal Mines. 
 London and Cambridge: Macmillan & Co. 8vo. xix, 349 pp. 
 
 18 0,5. On the Variation of Prices, and the Value of the Currency 
 since 1782. Paper read before the London Statistical Society, 
 May, 1865. Journal of the Statistical Society, vol. xxviii, 
 pp. 294-320. With four diagrams. 
 
 1866. On the frequent Axitumnal Pressure in the Money Market, 
 and the Action of the Bank of England. Paper read before the 
 Statistical Society, April, 1866. Journal of the Statistical 
 Society of London, vol. xxix, pp. 235-253. 
 
 1866. Brief Account of a General Mathematical Theory of Political 
 Economy. (Read at the British Association, 1862.) Journal 
 of the Statistical Society of London, vol. xxix, pp. 282-287. 
 
 1866. The Coal Question, &c. Second edition. London. 8vo, 
 xxvi 383 pp. 
 
 1866. An Introductory Lecture on the Importance of diffusing 
 a Knowledge of Political Economy. Delivered in Owens 
 College, Manchester, at the opening of the Session of Evening 
 Classes, on October 12. Manchester. 12mo. 35 pp. 
 
 1867. Science Lectures for the People. Lecture IX. On Coal : 
 its importance in manufactures and trade. Delivered in the 
 Carpenters' Hall, Manchester, January 16, 1867. (Science 
 Lectures, vol. i, pp. 128-140.) 
 
 1867. On the Analogy between the Post-office, Telegraphs, and 
 other systems of Conveyance of the United Kingdom, as regards 
 Government Control. Paper read before the Manchester Statis- 
 tical Society, April, 1867. Transactions, 1866-7, pp. 89-104. 
 
 1868. A Lecture on Trades' Societies: their Objects and Policy. 
 Delivered by request of the Trades Unionists' Political Asso- 
 ciation, March 31. Manchester. 8vo. 16 pp. 
 
 1868. Lecture on the Probable Exhaustion of our Coal Mines. 
 Boyal Institution of Great Britain. Friday Evening, March 13. 
 8vo. 7 pp.
 
 Ajypendix II. 313 
 
 1868. On the International Monetary Convention, and the Intro- 
 duction of an International Currency into this Kingdom. Paper 
 read before the Manchester Statistical Society, May 13. Trans- 
 actions, 1867-8, pp. 79-92. 
 
 1868. On the Condition of the Metallic Currency of the United 
 Kingdom, with reference to the Question of International 
 Coinage. Paper read before the Statistical Society of London, 
 November. Journal, &c., vol. xxxi, pp. 426-464, 
 
 1869, Letter on the Value of Grold. Economist newspaper, May 8. 
 Reprinted in the Journal of the' Statistical Society of London. 
 December. Vol. xxxii, p. 445, 
 
 1869. On the "Work of the Society in Connection with the 
 Questions of the Day. Inaugural Address read before the 
 Manchester Statistical Society, November 10, 1869. Transac- 
 tions, 1869-70, pp. 1-14. 
 
 1870. Opening Address of the President of Section F (Economic 
 Science and Statistics), of the British Association for the Ad- 
 vancement of Science, at the Fortieth Meeting, at Liverpool, 
 September, 1870. Report. Transactions of the Sections, 
 pp. 1781-87, Journal of the Statistical Society of London, 
 vol. xxxiii, pp. 309-326. 
 
 1870. On Industrial Partnerships, A Lecture delivered under 
 the auspices of the National Association for the Promotion of 
 Social Science, April 5, 1870, London: 1, Adam Street, Adelphi. 
 12mo. 39 pp. 
 
 1871. The Match Tax : a Problem in Finance. London. 8vo. 
 66 pp. 
 
 1871, The Theory of Political Economy. London and New York: 
 Macmillan & Co. 8vo. xvi, 267 pp. 
 
 1874, The Progress of the Mathematical Theory of Political 
 Economy, with an Explanation of the Principles of the Theory. 
 Paper read before the Manchester Statistical Society, November 
 11. Transactions, 1874-5, pp. 1-19, with a diagram, 
 
 1875. The Post-office Telegraphs and their Financial Results. 
 Fortnujhtly Review, December 1, vol. xviii. N.S. pp. 826-35. 
 
 1875. La Teorica dell' Economia Politica, esposta da W. Stanley 
 Jevons, Biblioteca dell' Economista. 3^ serie. Tomo ii, pp. 
 
 Y
 
 314 Appenduv II. 
 
 175—311. (Translated under the superintendence of Professor 
 Gerolamo Boccaixlo.) 
 
 1875. Money and the Mechanism of Exchange. (International 
 Scientific Series, vol. xvii.) London : H. S. King & Co. New 
 York : D. Appleton & Co. Post 8vo. xviii, 349 pp. 
 
 1876. La Monuaie et le M^canisme de I'Echange. Paris: Librairie 
 Germer Baillifere et Cie. (BibliothSque Scientifique Inter- 
 nationale, vol. XX.) Svo. viii, 288 pp. 
 
 1876. Geld und Geldverkehr. Leijizig : F. A. Brockhaus. (In- 
 ternationale Wissenschaftliche Bibliothek. xxi Band. 8vo. 
 xvi, 359 pp.) 
 
 1876. La Moneta ed il Meccanismo dello Scambio. Milano : 
 Fratelli Dumolard. (Biblioteca Scientifica Internazionale. Vol. 
 vi. 8vo. xxix, 319 pp.) 
 
 1876. On the United Kingdom Alliance and its Prospects of 
 Sviccess. Paper read before the Manchester Statistical Society, 
 March 8. Transactions, pp. 127-142. 
 
 1876. On the Frequent Autumnal Pressure in the Money Market, 
 and the Action of the Bank of England. Paper reprinted from 
 the Journal of the Statistical Society of London, 1866, in the 
 Transactions of the Manchester Statistical Society. Appendix, 
 pp. 17-41. 
 
 1876. The Future of Political Economy. Introductory Lecture 
 at the Opening of the Session, 1876-7, at University College, 
 London, Faculty of Arts and Laws. Fortnightly Review, 
 December, vol. xx, pp. 617-631. (See also App. I. 1877. 
 Jevons.) 
 
 1877. The Silver Question. A paper read by Hamilton A. Hill, 
 of Boston, before the American Social Science Association at 
 Saratoga, September 5. Boston: published for the Association 
 by A. Williams & Co. pp. 26-32. Reprinted in the London 
 Bankers' Magazine, December. 7 pp. 
 
 1878. Science Primers — Primer of Political Economy. London: 
 Macmillan & Co. 18mo. 134 pp. 
 
 1878. L'Economie Politique par W. Stanley Jevons, traduite 
 par Henry Gravcz, Ingenicur. Paris: Librairie Germer Bail- 
 liire et Cie. (Bibliothfeque Utile, vol. xliv.) 18mo. 184 pp.
 
 Appendix II. 315 
 
 1878. Money and the Mechanism of Exchange. London: C. 
 
 Kegan Paul & Co. Fourth edition. 
 1878. The Periodicity of Commercial Crises, and its Physical 
 
 Explanation. Paper read before the F Section of the British 
 
 Association at the Dublin Meeting, August 19. Report. 
 
 Transactions of Section F. p. 666. Published in the Journal 
 
 of the Statistical and Social Inquiry Society of Ireland, August, 
 
 1878. Vol. vii, pp. 334-342. 
 1878. Commercial Crises and Sunspots. Article printed in Nature 
 
 of November 14, vol. xix, pp. 33-37. 
 
 1878. Remarks on the Statistical Use of the Arithmometer. 
 Journal of the Statistical Society of London, December, vol. 
 xli, i^p. 597-601. 
 
 1879. Methods of Social Reform, No. II. A State Parcel Post, 
 Article in the Contemporary Review of January, vol. xxxiv, 
 pp. 209-229. 
 
 1879. Sunspots and Commercial Crises. Nature, April 24, vol. 
 xix pp. 588-590.
 
 BY THE SAME AUTHOR. 
 
 Works on Logic. 
 PKIMEE OF LOGIC. With lUustrations and Ques- 
 
 tions. New Edition. 18mo. Is. 
 
 ELEMENTAEY LESSONS IN LOGIC : DEDUC- 
 TIVE AND INDUCTIVE. With Copious Questions and 
 Examples, and a Vocabulary of Logical Terms. Seventh 
 Edition. Fcap. 8vo. 3s. Qd, 
 
 THE PEINCIPLES OF SCIENCE : a Treatise on 
 
 Logic and Scientific Method. Third Edition. Crown 8vo, 
 12s. 6d. 
 
 (The above three works form a consecutive course of logical 
 text-books.) 
 
 THE SUBSTITUTION OF SIMILAES THE 
 
 TRUE PRINCIPLE OF REASONING. Fcap. Bvo. 2s. 6d. 
 
 Works on Political Economy. 
 THE COAL QUESTION: an Inquiry Concerning 
 
 the Progress of the Nation, and the probable exhaustion of 
 our Coal Mines. (New Edition in preparation.) Bvo. 
 
 PEIMEE OF POLITICAL ECONOMY. 18mo. U. 
 
 Second Edition. 
 
 MACMILLAN AND CO., LONDON. 
 
 Elementaey Manual of the Pkinciples or Currency. 
 
 MONEY AND THE MECHANISM OF EX- 
 CHANGE. Fourth Edition. Crown 8vo. 5s. (International 
 Scientific Series.) 
 
 C. KEGAN PAUL AND CO.
 
 Bedford Street, Strand, London, W.C. 
 Attgnsf, 1879. 
 
 MacmillaiV &- Co.'s Catalogue of Works 
 in the Departments of History^ Biography^ 
 Travels^ Critical and Literary Essays, 
 Politics, Political and Social Economy^ 
 Law, etc.; a?id Works comiected with Lan- 
 guage. 
 
 HISTORY, BIOGRAPHY, TRAVELS, (S:c. 
 
 Albemarle.— FIFTY YEARS OF MY LIFE. By George 
 Thomas, Earl of Albemarle. With Steel Portrait of tlie first Earl 
 of Albemarle, engraved by Jeens. Third and Cheaper Edition. 
 Crown 8vo. "js. 6d. 
 ^' The book is one of the most amusing of its class. . . . These remi- 
 niscences have the charrn a?id flavour of personal experience, and they 
 bring us into direct contact with thepersons they describe." — Edinburgh 
 Review. 
 
 Anderson.— MANDALAY TO MOMIEN ; a Narrative of the 
 Two Expeditions to Western China, of 1868 and 1875, under 
 Colonel E. B. Sladen and Colonel Horace Browne. By Dr. 
 Anderson, F.R. S.E., Medical and Scientific Officer to the Ex- 
 peditions. With numerous Maps and Illustrations. 8vo. 21.'. 
 " /4 handsome, well-timed, entertaining, and instructive volume." — 
 Academy. 
 
 "^ pleasant, useful, carefully-writteny and impo7-tant work." — 
 Athen^um. 
 
 Appleton. — Works by T. G. Appleton :— 
 A NILE JOURNAL. Illustrated by Eugene Benson. Crown 
 
 8vo. 6s. 
 SYRIAN SUNSHINE. Crown 8vo. 6j. 
 
 Arnold. — ESSAYS IN CRITICISM. By Matthew Arnold. 
 New Edition, Revised and Enlarged. Crown Svo. <)s. 
 
 Atkinson. — an ART TOUR TO NORTHERN CAPITALS 
 OF EUROPE, including Descriptions of the Towns, the Museums, 
 and other Art Treasures of Copenhagen, Christiania, Stockholm, 
 
 5,000.8.79. A
 
 2 ^f MCMILLAN'S CATALOGUE OF WORKS IN 
 
 Abo, Ilelsint^i'ors, Wihorg, St. Petersburg, Moscow, and Kief. 
 By (. Beavini;i(jn Atkinson. 8vd. i2j. 
 " Allhoii^h the main piirbose of the hook is strictly kept in view, and we 
 n<n)er Jorget for long that 7i)e are travelling with a student and connoisseur, 
 Mr. Atkinson gives variety to his narralii'e by glimpses of scenery and 
 brief allunons to history and manners juhich are always wdcoine when 
 thev occur, and are H'-ver 7vordy or overdone. We have seldom met with 
 a book in which what is principal and what is accessory have been kept in 
 better proportion to each other." — Saturday Review. 
 
 Bailey. —THE SUCCESSION TO THE ENGLISH CROWN. 
 
 A liistor'cal Sketch. By A. Bailey, M.A., Banister-at-Law. 
 Crown Svo. "js. 6d. 
 
 Baker (Sir Samuel W.)— Works by Sir Samuel Baker, 
 Pacha, M.A., F.R.G.S.:— 
 
 ISMATLIA : A Narrative of the Expedition to Central Africa for 
 
 tlie Suppression of the Slave Trade, organised by Ismail, Khedive 
 
 of Egypt. With Portraits, Map, and fifty full-page Illustrations 
 
 by ZwECKER and Durand. New and Cheaper Edition. With 
 
 New Preface. Crown Svo. 6s. 
 
 "A book which will be read with very great interest." — Times. " Well 
 
 written and full of remarkable adventures." — Pall Mall Gazette. 
 
 ^^ Adds anotlier thrilUnj chapter to the history of African adventure." — 
 
 Daily News. '^ A'eads more like a romance . . . . incomparably more 
 
 entertaining tha7t books of African travel usually are." — Morning Post. 
 
 THE ALBERT N'YANZA Great Basin of the Nile, and Explora- 
 tion of the Nile Sources. Fifih Edition. Maps and Illustrations. 
 Crown Svo. ds. 
 " Charmingly 'Mritten ;" says the SPECTATOR, "full, as might be 
 expected, of incident, and free from that wearisome reiteration of useless 
 facts which is the drawback to almost all books of African travel." 
 
 THE NILE TRIBUTARIES OF ABYSSINIA, and the Sword 
 
 Hunters of the Hamran Arabs. With Maps and Illustrations. 
 
 Sixtli Edition. Crown Svo. 6^. 
 
 7'he Times says : "/t adds much to our itiformation respecting Egyptian 
 
 Abyssinia and th^ different races that spread over it. It contains, more- 
 
 over, some notable instances of English daring and enterprising skill ; 
 
 it abounds in animated tales of exploits dear to the heart of the British 
 
 sportsman ; and it will attract even the least studious reader, as the author 
 
 tells a story well, and can describe nature with uncommon power." 
 
 Bancro't — the HISTORY OF THE UNITED STATES 
 OF AMERICA, FROM THE DISCOVERY OF THE CON- 
 TINENT. By George Bancroft. New and thoroughly Re- 
 vised Edition. Six Vols. Crown Svo. 54J.
 
 HrSTORY, BIOGRAPHY, TRAVELS, ETC. 3 
 
 Barker (Lady). — Woiks by Lady Barker :— 
 
 A YEAR'S HOUSEKEEPING IN SOUTH AFRICA. With 
 Illustrations. New and Cheaper Edition. Crown 8vo, 6s, 
 
 " We have to thank Lady Barker for a very amusing book, over which 
 we have spent many a delightful hour, and of which we ivill not take 
 leave without alluding to the ineffably droll illustrations which ad I so very 
 much to the enjoytnent of her clear a)id sparkling descriptions,''' — MoRNiNG 
 Post. 
 
 Beesly.— STORIES from the history of ROME. By 
 Mrs. Beesi.y. Extra fcap. 8vo. 2s. 6d. 
 " A little book for which, every cultivated and intelligent jnother will be 
 grateful for. " — ExAM I .\ ER. 
 
 Bismarck_IN THE FRANCO-GERMAN WAR. An Authorized 
 Translation from the German of Dr. MoRiTZ BuscH, Two Vol;. 
 Crown 8vo. \%s. 
 The Times says : — " The publication of Bismarck'' s after-dinner talk, 
 whether discreet or not, zuill be of priceless biographical value, and English- 
 men, at least, will not be disposed to quarrel loith Dr. Busch for giving a 
 picture as true to life as Bosiuell 's ' Johnson ' of the foremost practical 
 genius thai Gennany has produced since Frederick the Greats 
 
 Blackburne.— BIOGRAPHY OF THE RIGHT HON, 
 FRANCIS BLACKBURNE, Late Lord Chancellor of Ireland. 
 Chiefly in connexion with his Public and Political Career. By his 
 Son, Edward Blackburne, Q.C. With Portrait Engraved by 
 Jeens. 8vo. \2S. 
 
 Blanford (W. T.)— GEOLOGY AND ZOOLOGY OF 
 ABYSSINIA. By W. T. Blanford. 8vo. 2\s. 
 
 Bronte. — CHARLOTTE BRONTE. A Monograph. By T, 
 Wemyss Reid. With Illustrations. Third Edition. Crown 
 8vo. 6j. 
 
 Mr. Reid's little volume, which is based largely on letters, hitherto 
 unpublished, from Charlotte Bronte to her school f, How and life-long 
 friend. Miss Ellen A'ussey, is inea7tt to be a companion, and not a rival, 
 to Mrs. GaskeWs well-knoiun '■'Life." To speak of the advantage rf 
 making biography autobiographical by the liberal use of correspondence has 
 she was by nature {as Mr. Reid puts ij^ "a hatpy and hii^h-spirited girl, 
 and that roen to the very last she had the /acuity of overcoming her 
 sorroivs by means of that steadfast courage 'which 7U is her most precit7cs 
 Possession, and to 7vhich she luas indebted for her successive victories over 
 trials and disappointments of no ordinary character." 
 
 The book is illustrated by a Portrait of the Rev. Patrick Bronte, seva-al 
 Views of Haworth and its neighbourhood, and a facsimile of one of the 
 most characteristic of C/mrlotte's letters. 
 
 A 2
 
 4 M ACM ILL AN' S CATALOGUE OF WORKS IN 
 
 Brooke.— THE RAJA OF SARAWAK: an Account of Sir 
 
 lames B-iooke, K. C.B., LL. D. Given chiefly through Letters 
 
 or Journals. By Gertrude L. Jacob. With Portrait and 
 
 Maps. Two Vols. 8vo. 25.f. 
 
 " They wJio read Miss yacoUs book — and all should read it: all who 
 
 are under the delusion that in our time there is no scope for heroism, and 
 
 ■no place for romantic adventure, end no f lace for enterprise and ambition 
 
 —will see how incident is crowded upon incidetit, and struggle upon 
 
 yiruggle, till in the very abundance of materials that come to her hand 
 
 ihe authoress can scarcely stop to give sufficient distiiutness to her 
 
 ivonderjtd narrative. " — ACADEMY. 
 
 Brooke. — RECOLLECTIONS OF THE IRISH CHURCH, 
 By Richard S. Brooke, D.D., late Rector of Wyton, Hunts. 
 Crown 8vo. 4J-. 6d. 
 
 Bryce. — Works by James Bryce, D.C.L., Regius Professor of 
 Civil Law, Oxford : — 
 
 THE HOLY ROMAN EMPIRE. Sixth Edition, Revised and 
 Enlarged. Crown 8vo. "js. 6d. 
 
 " /t exactly sjipplies a want: it affords a key to much which men 
 read of in their books as isolated facts, but of which they have hitherto 
 had no connected exposition set before ^^^;/?."— ^Saturday Review. 
 
 TRANSCAUCASIA AND ARARAT: being Notes of a Vacation 
 Tour in the Autumn of 1876. With an Illustration and Map. 
 Third Edition. Crown 8vo. 9J. 
 "Mr. Bryce has luritten a lively and at the same time an instructive 
 description of the tour he made last year in and about the Caucasus, When 
 well-informed a jurist travels into regions seldom visited^ and even 
 walks tip a mountain so rarely scaled as Ararat, he is justified in think- 
 ing that the impressions he brings home are worthy of being co?nmunicated 
 to the zvorld at large, especially when a terrible war is casting a lurid glow 
 over the countries he has lately surveyed" — AtheNj^um. 
 
 Burgoyne. — POLITICAL AND MILITARY EPISODES 
 DURING THE FIRST HALF OF THE REIGN OF 
 GEORGE III. Derived from the Life and Correspondence of 
 the Right Hon. J. Burgoyne, Lieut. -General in his Majesty's 
 Army, and M.P. for Preston. By E. B. de Fonblanque. With 
 Portrait, Heliotype Plate, and Maps. 8vo. i6j-. 
 
 Burke. — EDMUND BURKE, a Historical Study. By JOHN 
 MoKLEY, B.A., Oxon. Crown 8vo. Is. dd. 
 " The style is terse and incisive, and brilliant with epigram, and 
 foint. lis sustained potver of reasoning, its wide sweep 0/ observation 
 and reflection, its elevated ethical and social tone, stamp it as a work of 
 high excellence.''' — Saturday Review.
 
 HISTORY, BIOGRAPHY, TRAVELS, ETC. 5 
 
 Burrows. — WORTHIES OF ALL SOULS : Four Centuries cf 
 English History. Illustrated from the College Archives. By 
 Montagu Burrows, Chichele Professor of Modern History at 
 Oxford, Fellow of All Souls. 8vo. I4r. 
 "^ most amusing as zvell as a most instructive book. — Guardian. 
 
 Campbell. — LOG-LETTERS FROM THE "CHALLENGER." 
 By Lord George Campbell, With Map. Fifth and cheaper 
 Edition. Crown 8vo. 6j. 
 
 "yi delightful book, which we heartily commend to the general reader." 
 — Saturday Review. 
 
 " We do not hesitate to say that anything so fresh, so picturesque, so 
 generally delightful, as thtse log-letters has not appeared atnong books of 
 travel for a long time.''' — Examiner. 
 
 ^' A more lively and amusing record of travel we have not had the 
 fortune to read for some time. The whole book is pervaded by a spirit of 
 life, animation, and fun." — STANDARD. 
 
 Campbell. — my circular notes : Extracts from journals ; 
 Letters sent Home ; Geological and other Notes, written while 
 Travelling Westwards round the World, from July 6th, 1874, to 
 July 6th, 1875. ^y J- F- Campbell, Author of "Frost and 
 Fire." Cheaper Issue. Crown 8vo. ds. 
 " We have read numbers of books of travel, but we can call to mind 
 few that have given us more genuine pleasure than this. A more agree- 
 able style of narrative tJian his it is hardly possible to conceive. We seem 
 to be accompanying him in his trip round the world, so life-like is his 
 description of the countries he visited." — Lanp AND Water, 
 
 Campbell, — TURKS and greeks. Notes of a recent Ex- 
 cursion. By the Hon. Dudley Campbell, M.A. With Coloured 
 Map. Crown 8vo. 3^. dd. 
 
 CarStares. — WILLIAM CARSTARES : a Character and Career 
 of the Revolutionary Epoch {1649— 1715), By Robert Story, 
 Minister of Rosneath, 8vo. \zs. 
 
 Chatterton : A BIOGRAPHICAL STUDY. By Daniel 
 Wilson, LL.D., Professor of Historj' and English Literature in 
 University College, Toronto. Crown 8vo. ds. 6d. 
 
 Chatterton: a STORY OF THE YEAR 1770. By Professor 
 Masson, LL.D. Crown Svo. 5 J. 
 
 Clark.— MEMORIALS FROM JOURNALS AND LETTERS 
 OF SAMUEL CLARK, M.A., formerly Principal of the 
 National Society's Training College, Battersea. Edited with 
 Introduction by his Wife. With Portrait. Crown Svo, 7.^.6./.
 
 6 MACMILLAN'S CATALOGUE OF WORKS IN 
 
 Combe.— THE LTFE of GEORGE COMBE, Author of "The 
 Constitution of Man." By Charles Gibbon. With Three 
 Portraits engraved by Jeens. Two Vols. 8vo. 325. 
 "A graphic and interestmg account of the long life and indefaHgabU 
 
 labours of a very remarkable man." — Scotsman. 
 
 Cooper. — ATHENE CANTABRIGIENSES. By Charles 
 Henry Cooper, F.S.A., and Thompson Cooper, F.S.A. 
 Vol. I. 8vo., 1500—85, i8j-. ; Vol. II., 1586— 1609, i8j-. 
 
 Correggio.— ANTONIO ALLEGRI da CORREGGIO. From 
 
 the German of Dr. Julius Meyer, Director of the Royal Gallery, 
 Berlin. Edited, with an Introduction, by Mrs. Heaton. Con- 
 taining Twenty Woodbury-type Illustrations. Royal 8vo. Cloth 
 elegant, '^is. 6d. 
 
 Cox (G. V.)— RECOLLECTIONS OF OXFORD. By G. 
 V. Cox, M.A., New College, late Esquire Bedel and Coroner 
 in the University of Oxford. Cheaper Edition. Crown 8vo. 6j. 
 
 Cunynghame (Sir A. T.) — MY COMMAND IN SOUTH 
 AFRICA, 1874 — 78. Comprising Experiences of Travel in the 
 Colonies of South Africa and the Independent States. By Sir 
 Arthur Thurlovv Cunynghame, G.C.B., then Lieutenant- 
 Governor and Commander of the Forces in South Africa. Third 
 Edition. 8vo. 123-. dd. 
 The Times says : — "// is a volume of great interest, .... full of 
 incidents "uhich vividly illustrate the condition of the Colonies and the 
 character and habits of the natives It contains valuable illus- 
 trations of Cape warfare, and at the present moment it cannot fail to 
 com?7iand zuiUe-spread attention." 
 
 " Daily News." — the DAILY NEWS' CORRESPOND- 
 ENCE of the War between Germany and France, 1870 — i. Edited 
 with Notes and Comments. New Edition. Complete in One 
 Volume. With Maps and Plans. Crown 8vo. 6j. 
 
 THE DAILY NEWS' CORRESPONDENCE of the War between 
 Russia and Turkey, to the fall of Kars. Including the letters of 
 Mr. Archibald Forbes, Mr. J. E. McGahan, and other Special 
 Correspondents in Europe and Asia, Second Edition, enlarged. 
 Cheaper Edition. Crown 8vo. 6^. 
 
 FROM THE FALL OF KARS TO THE CONCLUSION OF 
 PEACE. Cheaper Edition. Crown 8vo. 6s. 
 
 Davidson. — the LIFE OF a SCOTTISH PROBATIONER ; 
 
 being a Memoir of Thomas Davidson, with his Poems and 
 Letters. By James Brown, Minister of St. James's Street 
 Churcii, Paisley. Second Edition, revised and enlarged, with 
 Portrait. Crown 8vo. 7^. 6d.
 
 HISTORY, BIOGRAPHY, TRAVELS, ETC. 7 
 
 Deas. — THE RIVER CLYDE. An Historical Description of the 
 Rise and Progress of the Harbour of Glasf;OW, and of the Im- 
 provement of the River from (jlasgovv to Port Glasgow. By J. 
 Deas, M. Inst. C.E. 8vo. los. 6 J. 
 
 Denison.— A HISTORY OF CAVALRY FROM THE EAR- 
 LIEST TIMES. Wiih Lessons for the Future. Py Lieut. -Col. 
 George Denison, Commanding the Goveinor-General's Body 
 Guard, Canada, Author of " Modern Cavalry." With Maps and 
 Plans, 8vo. i2>s. 
 
 Dilke. — GREATER BRITAIN. A Record of Travel in English- 
 speaking Countries during 1866-7. (America, Australia, India.) 
 By Sir Charles Wentworth Dilke, M.P. Sixth Edition. 
 Crown 8vo. 6s. 
 " Many of the subjects discussed in these pages" savs the Daily News, 
 " are of the widest interest, and such as no ?nan who cares for the Juture 
 of his race and of the world can afford to treat with indifference." 
 
 Doyle. — HISTORY OF AMERICA. By J. A. Doyle. With 
 Maps. i8mo. 4J'. 6d. 
 " Mr. Doyle^s style ?j clear and simple, his facts are accurately stated, 
 and his book is meritoriously free /ro7n prejudice on questions zvkere 
 partisanship runs high amongst us." — Saturday Review. 
 
 Drummond of Hawthornden : THE STORY OF HIS 
 LIFE AND WRITINGS. By Professor Masson. With Por- 
 trait and Vignette engraved by C. H. Jeens. Crown 8vo. loj. 6d. 
 
 Duff. — Worlss by M. E. Grant-Duff, M.P., late Under Secretary 
 of State for India : — 
 
 NOTES OF AN INDIAN JOURNEY. W^ith Map. 8vo. \os. 6d. 
 
 *' These notes are full of pleasant rcvia-ks and illustrations, borrowed 
 from every kind of source." — Satukd.\y Review. 
 
 MISCELLANIES POLITICAL AND LITERARY. Svo. \os. bd. 
 
 Eadie. — life of JOHN EADIE, D.D., LL.D. By James 
 Brown, D.D., Author ot " The Life of a Scottish Probationer." 
 With Portrait. Second Edition. Crown 8vo. 7^-. dd. 
 *' An ably wtitten and characteristic biography." — Times. 
 
 Elliott. — LIFE OF HENRY VENN ELLIOTT, of Brighton. 
 By JosiAH Bateman, M.A. With Portrait, engraved by Jeens. 
 Extra fcap. Svo. Third and Cheaper Edition. 6j. 
 
 Elze. — ESSAYS ON SHAKESPEARE. By Dr. Karl Elze, 
 Translated with the Author's sanction by L. Dora Schmitz. 
 Svo. \2S. 
 "A more desirable contribution to criticism has not recently been made." 
 
 — Athen^um.
 
 8 MACMILLAN'S CATALOGUE OF WORKS IN 
 
 English Men of Letters. Edited by John Morley. a 
 Series of Short Books to tell people what is best worth knowing 
 as to the Life, Character, and Works of some of the great 
 English Writers. In crown 8vo. Price 2s. 6d. each. 
 
 I. DR. JOHNSON. By Leslie Stephen. 
 
 ' ' The neio sei-ies opens zv.'ll with Air. Leslie Stephen's sketch of Dr. 
 yohnson. It could hardly have been done better ; and it will convey to 
 the readers for whom it is ititendcd a jiuter estimate of yohnson than 
 either of the. two essays of Lord Macaulay ." — Pall Mall Gazette. 
 
 IL SIR WALTER SCOTT. By R. H. Hutton. 
 " The tone of the volume is excellent throitghout." — Athen^UM. 
 * ' We could 7iot wish for a more suggestive introduction to Scott and 
 his poems and novels." — Examiner. 
 
 IIL GIBBON. By J. C. Morison. 
 
 " As a clear, thought ftd, and attractive record of the life and works of 
 the greatest among the world's historians, it deserves the highest praise," — 
 Examiner. 
 
 IV. SHELLEY. By J. A. Symonds. 
 
 " The lovers of this great poet are to be congratulated on having at 
 their co7iitnand so fresh, clear, and intelligent a presentment of the subject, 
 ■written by a man of adequate and wide culture." — Athen/EUM. 
 
 V. HUME. By Professor Huxley. 
 
 " It viay fairly be said that no one 7107a living could have expounded 
 IIu7ne with more sy7iipathy or with equal perspicuity." — AtheNj*;um. 
 
 VL GOLDSMITH. By William Black. 
 
 " Air. Black brings a fine sympathy and taste to bear in his criticism 
 of Goldsmith's writings as well as i7t his sketch of the incidents of his life." 
 ATHEN/EUM. 
 
 VIL DEFOE. By W. Minto. 
 
 ^' Air. AIi7?to's book is careful and accurate in all that is stated, and 
 faithful in all that it suggests. It ■mill repay reading mo7-e than once." 
 -Athen.^um. 
 
 VIII. BURNS. By Principal Shairp, Professor of Poetry in the 
 University of Oxford. 
 
 *' It is impossible to desire fairer criticis7?t than Principal Shairp' s 
 
 }n Burns' s poetry None of the series has given a t7-uer estit?iate 
 
 either 0/ character or of geriius than /his little volu77ie and all 
 
 7vho 1-ead it will be tho7-oughly grateful to the author for this monu7nent 
 to the ge7iius of Scotland's greatest poet." — SPECTATOR. 
 
 IX. SPENSER. By the Very Rev. the Dean of St. Paul's. 
 "Dr. Church is master of his subject, and writes always with good 
 
 taste." — Academy. 
 
 X. THACKERAY. By Anthony Trollope. 
 
 ' ' Air. Trollope' s sketch is excellently adapted to fufil the purpose op 
 the Scries in which it appears." — Athen^um.
 
 HISTORY, BIOGRAPHY, TRAVELS, ETC. 9 
 
 English Men of Letters.— ^^;;//;,?/^;/. 
 JiURKE. Ey John Morlkv. )r,r , , 
 
 MILTON. By Mark Pattisox. \^{Nearly ready. 
 
 Others in preparation. 
 
 Eton College, History of. By H. C. Maxwell Lyte, 
 M.A. With numerous Illustrations by Professor Delamotte, 
 Coloured Plates, and a Steel Portrait of the Founder, engraved 
 by C. II. Jeens. New and cheaper Issue, with Corrections. 
 Medium 8vo. Cloth elegant, zis. 
 " Hitherto no account of the College, with all its associations, has 
 
 appeared which can compare either in comt'leteness or in interest with 
 
 this. . . . It is indeed a book worthy of the ancient renoivn oj King 
 
 Henry's College.''^ — Daily News. 
 
 " We are at length presented zvith a zvork on England's greatest public 
 
 school, worthy of the subject of luhich it treats. . . . A really valuable and 
 
 authentic history of Eton College." — GUARDIAN. 
 
 European History, Narrated in a Series of Historical 
 
 Selections from the best Authorities. Edited and arranged by 
 
 E. M. Sewell and C. M. Yonge. First Series, crown 8vo, 6s. ; 
 
 Second Series, 1088-1228, crown 8vo. 6s. Third Edition. 
 
 '" IVe know of scarcely anything," says the GUARDIAN, of this volume, 
 
 "which is so likely to raise to a higher level the average standard of 
 
 English education." 
 
 Faraday. — MICHAEL FARADAY. By J. H. Gladstone, 
 Ph.D., F.R.S. Second Edition, with Portrait engraved by Jeens 
 from a photograph by J. Watkins. Crown 8vo. 4?. 6d. 
 PORTRAIT. Artist's Proof, ^s. 
 
 Forbes.— LIFE and letters of JAMES david 
 
 FORBES, F.R.S., late Principal of the United College in the 
 University of St. Andrews. By J. C. Shairp, LL.D., Principal 
 of the United College in the University of St. Andrews ; P. G. 
 Tait, M.A., Professor of Natural Philosophy in the University 
 of Edinburgh; and A. Adams-Reilly, F.R.G.S. 8vo, with 
 Portraits, Map, and Illustrations, \6s. 
 
 Freeman. — Works by Edward A. Freeman, D.C.L.,LL.D. : — 
 HISTORICAL ESSAYS. Third Edition. 8vo. ioj. 6d. 
 Contents:—/. '■'■The Mythical and Romantic Elements in Early 
 En'-'lish History;" II. '''' The Continuity of English History;" IJl. 
 **The Relations betzveen the Croivns of England and Scotland ;"^ IV. 
 "St. Thomas of Canterbury and his Biograthers ;" V. " The Reign oJ 
 Edward the Third:" VI. "The Holy Roman Empire;" VII. "The 
 Franks and the Gauls;" VIII. "The Early Sieges of Paris;" IX. 
 "Frederick the First, King of Italy ;" X. "The Emperor Frede)-tck the 
 Second;" XI. "Charles the Bold ;" XII. " Presidential Government.
 
 lo MACMILLAN'S CATALOGUE OF WORKS IN 
 
 Fre e m an — continued. 
 
 A SECOND SERIES OF HISTORICAL ESSAYS. 8vo. 
 \Os. bd. 
 
 The principal Essays are: — "Ancient Greece and Medicroal Italy:" 
 "Mr. Gladstone's IIo?ner and the Homeric As;es :''^ ''''The Historians 
 of Athens:'" *' The Athenian Democracy :" '* Alexander the Great:" 
 ^'Greece duting the Mcuedoniati Period :" ^^Alotnmsens History of Rome :" 
 ** Lucius Cornelius Sulla :" '* The Flavian Cmsars." 
 
 HISTORICAL ESSAYS. Third Series. [/« the press. 
 
 COMPARATIVE POLITICS.— Lectures at the Royal Institution. 
 To which is added the " Unity of History," the Rede Lecture at 
 Cambridge, 1872. 8vo. 14^-. 
 
 THE HISTORY AND CONQUESTS OF THE SARACENS. 
 Six Lectures. Third Edition, with New Preface. Crown 8vo. 
 IS. 6d. 
 
 HISTORICAL AND ARCHITECTURAL SKETCHES: 
 
 chiefly Italian. With Illustrations by the Author. Crown 8vo. 
 
 lOi-. 6d. 
 
 " LIr. Fieetnan may here be said to give us a series of ''notes on the 
 
 spot ' in illustration 0/ the intimate relations of History afid Architecture, 
 
 and this is done in so mastei ly a manner — there is so much freshness, so 
 
 much kuoiL'ledge so admirably condensed, that zve are alniust tempted to 
 
 say that lue prefer these sketches to his more elaborate studies." — NoNCON- 
 
 FORiMIbT. 
 
 HISTORY OF FEDERAL GOVERNMENT, from the Foun- 
 dation of the Achaian League to the Disruption of the United 
 States. Vol. I. General Introduction. History of the Greek 
 Federations. 8vo. 21s. 
 
 OLD ENGLISH HISTORY. \M\\.\i Five Coloured Maps. Fourth 
 Edition. Extra fcap. 8vo., half-bound. 6^. 
 
 " The book indeed is full of instruction and interest to students oj all 
 ages, and he must be a well-info> med man indeed who will not rise 
 from its perusal with clearer and more accurate ideas of a too much 
 neglected portion of English history." — Spectator. 
 
 HISTORY OF THE CATHEDRAL CHURCH OF WELLS, 
 
 as illustrating the History of the Cathedral Churches of the Old 
 
 Foundation. Crown 8vo. 3^. dd. 
 
 " The history assumes in Mr. Freeman^ s hands a significance, and, we 
 
 may add, a practical value as suggestive of %vhat a cathedral ought to be, 
 
 ivhich make it well worthy of mention." — SPECTATOR. 
 
 TPIE GROWTH OF THE ENGLISH CONSTITUTION 
 FROM THE EARLIEST TIMES. Crown 8vo. 55. Third 
 Edition, revised.
 
 HISTORY, BIOGRAPHY, TRAVELS, ETC. ii 
 
 F r e e m an — continued. 
 GENERAL SKETCH OF EUROPEAN HISTORY. Being 
 Vol. I. of a Historical Course for Schools edited by E. A. 
 Freeman. New Edition, enlarged with Maps, Chroaoloyical 
 Table, Index, &c. i8mo. 3^. dd. 
 " Ji supplies the great want of a good foundation for historical teach- 
 ing. The scheme is an excellent one, and this instalment has been 
 accepted in a way that promises much for the volumes that are yet 
 to appear." — EDUCATIONAL Times. 
 
 THE OTTOMAN POWER IN EUROPE : its Nature, its Growth, 
 and its Decline. With Three Coloured Maps. Crown 8vo. 7^. 6d. 
 
 Galileo. — THE private life of GALILEO. Compiled 
 principally from his Correspondence and that of his eldest 
 daughter. Sister Maria Celeste, Nun in the Franciscan Convent of 
 S. Matthew in Arcetri. With Portrait. Crown 8vo. "js. bd. 
 
 Geddes. — tpie problem of the homeric poems. 
 
 By W. D. Geddes, LL. D., Professor of Greek in the University 
 of Aberdeen. 8vo. 14s. 
 
 Gladstone — Works by the Right Hon.W. E. Gladstone, M.P. :— 
 JUVENTUS MUNUl. The Gods and Men ol the Heroic Age. 
 
 Crown 8vo. cloth. With Map. io.r. 6d. Second Edition. 
 "Seldom," says the Athen^um, "out of the great poetns themselves, 
 
 have these Divinities looked so majestic and respectable. To read these 
 
 brilliant details is like standing on the Olympian threshold and gazing at 
 
 the ineffable brightness within." 
 
 HOMERIC SYNCHRONISM. An inquiry into the Time and 
 
 Place of Homer. Crown 8vo. 6^-. 
 " // is impossible not to admire the immense range of thought and 
 inquiry which the author has displayed." — British Quarterly 
 Review. 
 
 Goethe and Mendelssohn (1821— 1831). Translated from the 
 
 German of Dr. Karl Mendelssohn, Son of the Composer, by 
 M. E. Von Glehn. From the Private Diaries and Home 
 Letters of Mendelssohn, with Poems and Letters of Goethe never 
 before printed. Also with two New and Original Portiaits, Fac- 
 similes, and Appendix of Twenty Letters hitherto unpublished. 
 Crown 8vo. ^s. Second Edition, enlarged. 
 «' , . , Every page is full of interest, not mo-ely to the mtisi- 
 
 cian, but to the general reader. The book is a very charjning one, on 
 
 a topic of deep and lasting interest." — Standard.
 
 12 MACMILLAN'S CATALOGUE OF WORKS IN 
 
 Goldsmid. — TELEGRAPH AND TRAVEL. A Narrative of 
 the Formation and Development of Telegraphic Communication 
 between England and India, under the orders of Her Majesty's 
 Government, with incidental Notices of the Countries ti'aversed by 
 the Lines. By Colonel Sir Frederic Goldsmid, C.B., K.C.S.I., 
 late Director of the Government Indo-European Telegraph. With 
 numerous Illustrations and Maps. 8vo, 21s. 
 " The ?nerit of the work is a total absence of exaggeration, which does 
 
 not, hozvruer, preclude a vividness and vigour of style not always character^ 
 
 istic of similar narratives." — STANDARD. 
 
 Gordon.— LAST LETTERS FROM EGYPT, to which are added 
 
 Letters from the Cape. By Lady Duff Gordon. With a 
 
 Memoir by her Daughter, Mrs. Ross, and Portrait engraved by 
 
 Jeens. Second Edition. Crown 8vo. 9^. 
 
 " The intending tourist who wishes to acquaint himself zuith the country 
 
 he is about to visit, stands embarrassed amidst the riches presented for his 
 
 choice, and in the end probably rests contented with the sober nsefidness of 
 
 Murray, He iv-ill not, hotvever, if he is well advised, grudge a place in 
 
 his portmanteau to this book." — Times. 
 
 Gray. — china. A History of the Laws, Manners, and Customs 
 of the People. By the Venerable John Henry Gray. LL.D., 
 Archdeacon of Hong Kong, formerly H. B. M. Consular Chaplain 
 at Canton. Edited by W. Gow Gregor. With 150 Full-page Illustra- 
 tions, being Facsimiles of Drawings by a Chinese Artist. 2 Vols, 
 Demy 8vo. 32J. 
 ^^ Its pages contain the most truthful and vivid picture of Chinese life 
 
 wliich has ever been published." — Athen^UM. 
 
 " 77^1? only elaborate and valuable book we have had for many years 
 
 treating generally of the people of the Celestial Empire." — ACADEMY. 
 
 Green. — Works by John Richard Green: — 
 
 , HISTORY OF THE ENGLISH PEOPLE. Vol. I.— Early 
 
 England — Foreign Kings — The Charter — The Parliament. With 
 
 8 Coloured Maps. 8vo. 16s. Vol. II. — The Monarchy, 
 
 1461 — 1540; the Restoration, 1540 — 1603. Svo. 16^. Vol.111. 
 
 — Puritan England, 1603 — 1660; thCj Revolution, 1660 — 1688, 
 
 With 4 Maps. 8vo. i6s. [Vol. IV. in the press. 
 
 "Mr. Green has done a work which probably no one but himself could 
 
 have done. He has read and assimilated the residts of all the labours of 
 
 students during the last half centuty in the field of English history, and 
 
 has given them a fresh meaning by his 07un independent stJidy. He has 
 
 fused together by the force of sympathetic imagination all that he has so 
 
 collected, and has ^iven us a vivid and forcible sketch of the march of 
 
 English histoty. His hook, both in its aims and its accot?iplishments, 
 
 rises far beyond any of a similar kind, and it will give the colouring to the 
 
 popular view to English histoiy for some time to come." — Examiner.
 
 HISTORY, BIOGRAPHY, TRAVELS, ETC. 13 
 
 Green . — continued. 
 
 A SHORT HISTORY OF THE ENGLISH PEOPLE. With 
 Coloured Maps, Genealogical Tables, and Chronological Annals. 
 \\ Crown 8vo. 8^. 6^/. Sixtyfir.it Thousand. 
 
 " To say tliat Mr. Grwn's book is better than those which have pre- 
 ceded it, 7vould be to convey a vay inadequate impression of its merits. It 
 stands alone as the one general history of the coimtry, for the sake of 
 which all others, if young and old are wise, 'will be speedily and surely set 
 aside." 
 
 STRAY STUDIES FROM ENGLAND AND ITALY. Crown 
 8vo. Sj. 6d. Containing : Lambeth and the Archbishops — The 
 Florence of Dante — Venice and Rome — Early History of Oxford 
 — The District Visitor — Capri — Hotels in the Clouds — Sketches 
 in Sunshine, &'c. 
 
 " One and all of the papers are eminently readable.'''' — Athen^UM. 
 
 Guest. — LECTURES ON THE HISTORY OF ENGLAND. 
 By M. J. Guest. With Maps. Crown Svo. ds. 
 
 Hamerton. — Works by p. G. Hamerton:— 
 THE INTELLECTUAL LIFE. With a Portrait of Leonardo da 
 Vinci, etched by Leopold Flameng. Second Edition. Crown 
 \os. i)d. Svo. 
 " "[Ve have read the whole book with great pleasure, and we can re- 
 commend it strongly to all who can appreciate grave reflections on a very 
 important subject, excellently illustrated from the resources of a mind 
 stored with much 7-eading and much keen obseivation of real life.'''' — 
 Saturday Review. 
 
 THOUGHTS ABOUT ART. New Edition, revised, with an 
 
 Introduction. Crown Svo. Sj. 6d. 
 ".(4 manual of sound and thorough criticism on artr — Standard. 
 
 Hill. — THE RECORDER OF BIRMINGHAM. A Memoir of 
 Matthew Davenport Hill, with Selections from his Correspondence. 
 By his Daughters Rosamond and Florence Davenport-Hill. 
 With Portrait engraved by C. H. Jeens. Svo. \hs. 
 
 Hill.— WHAT WE SAW IN AUSTRALIA. By Rosamond 
 and Florence Hill, Crown Svo. io.v. bd. 
 '* May be recommended as an interesting and truthful picture cf the 
 condition of those lands which are so distant and yet so jnuch like home." 
 — Saturday Review,
 
 U MACMTLLAN'S CATALOGUE OF WORKS IN 
 
 Hodgson. — MEMOIR OF REV. FRANCIS HODGSON, 
 B. D., Scholar, I'oet, and Divine. By his Son, the Rev. James 
 T. Hodgson, M.A. Con'.aining numerous letters from Lord 
 Byron and others. With Portrait engraved by Jeens. Two 
 Vols. Crown 8vo. i8f. 
 " A book that has added so much of a healthy vaiure to our kno'ddrdge 
 
 of Byron, and that contains so rich a store of delightful correspondence.''' 
 
 — A'l'HENiEU.M. 
 
 Hole. — A GENEALOGICAL STEMMA OF THE KING.S 
 OF ENGLAND AND FRANCE. By the Rev. C. Hole, 
 M.A., Trinity College, Cambridge. On Sheet, is. 
 
 A BRIEF BIOGRAPHICAL DICTIONARY. Compiled and 
 Arranged by the Rev. CHARLES Hole, M.A. Second Edition. 
 iSmo. 4s. 6d. 
 
 Hooker and Ball. — marocco and THE GREAT 
 
 ATLAS: journal of a Tour in. By Sir Joseph D. Hooker, 
 K.C.S.I., C.B., F.R.S., &c., and John Ball, F.R.S. With an 
 Appendix, including a Sketch of the Geology of Marocco, by 
 G. Maw, F.L.S., F.G.S. With Illustrations "and Map. 8vo. 21s. 
 
 Hozier (H. M.) — Works by Captain Henry M. Hozier, 
 late Assistant Military Secretary to Lord Napier of Magdala : — 
 
 THE SEVEN WEEKS' WAR ; Its Antecedents and Incidents. 
 
 AWc and Cheaper Edition. With New Preface, Maps, and Plans. 
 
 Crown 8vo. 6j-. 
 
 " All that Air. Hozier saw of the great events of the -war — and he saw 
 
 a large share of them — he describes in clear and vivid language^" — 
 
 Saturday Review. 
 
 THE INVASIONS OF ENGLAND : a History of the Past, with 
 Lessons for the Future. Two Vols. 8vo. 28^. 
 
 The Pall Mall Gazette says : — "'As to all invasions executed, or 
 deliberately projected but not caj-j-ied out, front the latiding of fulius 
 Ccesar to the raising of the Boulogne cainp. Captain Hozier furnishes 
 copious and most interesting particulars. " 
 
 Hiibner. — a RAMBLE ROUND THE WORLD IN 1871. By 
 
 M. Le Baron Hijbner, formerly Ambassador and Minister. 
 
 Translated by Lady Herbert. New and Cheaper Edition. 
 
 With numerous Illustrations. Crown 8vo. 6s. 
 
 " It is difficult to do ample justice to this pleasant narrative of travel 
 
 . ... it does not contain a single dull paragraph" — MORNiNG PoST. 
 
 Hughes. — Works by Thomas Hughes, Q.C, Author of "Tom 
 Brown's School Days." 
 ALFRED THE GREAT. New Edition. Crown 8vo. dr.
 
 HISTORY, BIOGRAPHY, TRAVELS, ETC. 15 
 
 H U ghe S . — continued. 
 
 MEMOIR OF A BROTHER. With Portrait of George Hughes, 
 after Watts. Enj^raved by Jeens. Crown 8vo. 5^. Sixth 
 Edition. 
 " The hoy ivho can read this hook unthoiit dei'iving from it some addi- 
 tional impulse loivards honouriihle, manly, and independent conduct, has 
 no ^ood stuff in him." — Daily News. 
 
 Hunt. — HISTORY OF ITALY. By the Rev. W. Hunt, M.A. 
 
 Being the Fourth Volume of the Historical Course for Schools. 
 
 Edited by Edward A. Freeman, U. C.L. iSmo. 3^-. 
 " Mr. Hunt i^ives us a most compact but very readable little book, con- 
 taining in small compass a very complete outline of a complicated and 
 perplexing subject. It is a book which may be safely recommended to 
 others besides schoolboys." — ^JOHN BuLL. 
 
 Irving.— THE ANNALS OF OUR TIME. A Diurnal of Events, 
 Social and Political, Home and Foreign, from the Accession of 
 Queen Victoria to the Peace of Versailles. By Joseph Irving. 
 fourth Edition. 8vo. half-bound, lbs. 
 
 ANNALS OF OUR TIME. Supplement. From Feb. 28, 1871, 
 to March 19, 1874. 8vo. ^. 6d. 
 
 ANNALS OF OUR TLME. Second Supplement. From March, 
 
 1874, to the Occupation of Cypru-;. 8vo. 45. 6d. 
 " IVe have bejore us a trusty and ready guide to the events of the 
 past thirty years, available equally for the statesman, the politician, the 
 public writer, and the general reader." — Times. 
 
 James. — Works by Henry James, Jun. FRENCH POETS AND 
 NOVELISTS. Crown 8vo. %s. 61. 
 Contents: — Alfred de Musset ; Thcophile Cauli^r ; Bauddaire ; 
 Honore de Balzac ; George San I ; The Two Amperes ; Turgenieff, &'c. 
 
 Johnson's Lives of the Poets. — The Six Chief 
 
 Lives — Milton, Dryden, Swift, Addison, Pope, Gray. With 
 Macaulay's " Life of Johnson." Edited, with Preface, by 
 Matthew Arnold. Crown Svo. 6s. 
 
 Killen.— ECCLESIASTICAL HISTORY OF IRELAND, from 
 the Earliest Date to the Present Time, liy W. D. Killen, D. D., 
 President of Assembly's College, Belfast, and Professor of Eccle- 
 siastical History. Two Vols. 8vo. 25^. 
 " Those who have the leisure will do well to read these two volumes. 
 
 They are full of intei-est, and are the result of great research. . . . We 
 
 have no hesitation in recjmmending the work to all who wish to improve 
 
 their acquaintance wi^h Irish history." — Spectator.
 
 1 6 MACMILLAN'S CATALOGUE OF WORKS IN 
 
 Kingsley (Charles). — Works by the Rev. Charles Kingsi.ey, 
 M.A., Rector of Eversley find Canon of Westminster. (For 
 other Works by the same Author, see Theological and Belles 
 Lettres Catalogues. ) 
 
 ON THE ANCIEN REGIME as it existed on the Continent before 
 the French Revolution. Three Lectures delivered at the 
 Royal Institution. Crown 8vo. 6^. 
 
 AT LAST : A CHRISTMAS in the WEST INDIES. With nearly 
 Fifty Illustrations. Fifth Edition. Crown 8vo. 6^. 
 
 Mr. Kin'^sley's dream of forty years was at last fulfilled, when he 
 started on a Christmas expedition to the West Indies, for the purpose of 
 beccmittg pasonally acquainted with the scenes which he. has so vividly 
 described in " IVest-vard Ho !" These tzuo volumes are the journal of his 
 voyage. Records of natural Jiistory, sketches of tropical landscape, chapters 
 on education, vinos of society, all find their place. " We can only say 
 that Mr. Ringsleys account of a ' Christmas in the West Indies ' is in 
 every way zuorthy to be classed among his happiest productions." — 
 Standard. 
 
 THE ROMAN AND THE TEUTON. A Series of Lectures 
 delivered before the University of Cambrida:e. New and Cheaper 
 Edition, with Preface by Professor Ma.x Muller. Crown 8vo. 6j. 
 
 PLAYS AND PURITANS, and other Historical Essays. With 
 Portrait of Sir Walter Raleigh. New Edition. Crown 8vo. ds. 
 
 In addition to the Essay mentioned in the title, this volume contains 
 other two — one on "Sir Walter Raleigh and his Time," and one on 
 Froude^s " History of England. " 
 
 Kingsley (Henry). — TALES OF OLD TRAVEL. Re- 
 narrated by Henry Kingsley, F.R.G.S. With Eight Illus- 
 trations by HuARD. Fifth Edition. Crown 8vo. 5^. 
 " We kno'cu no better book for those luho want knowledge or seek to 
 refresh it. As for the ' sensational,^ most novels are tat)ie compared with 
 these narratives." — Athen^UM. 
 
 Lang. — CYPRUS : Its Histoiy, its Present Resources and Future 
 
 Prospects. By R. Hamilton Lang, late H.M. Consul for the 
 
 Island of Cyprus. With Two Illustrations and Four Maps. 8vo. 14^. 
 
 " The fair and impartial account of her past and present to be found in 
 
 these pages has an tindoublcd claim on the attention of all intelligent 
 
 readers.''' — Morning Post. 
 
 LaoCOOn. — Translated from the Text of Lessing, with Preface and 
 Notes by the Right Hon. SiR Robert J. Phillimore, D.C.L. 
 With Photographs. 8vo. 12s.
 
 HISTORY, BIOGRAPHY, TRAVELS, ETC. 17 
 Leonardo da Vinci and his Works. — Consisting of a 
 
 Life of Leonardo Da Vinci, by Mrs. Charles \V. Heaton, 
 
 Author of "Albrecht Diirer of Niirnberg," &c., an Essay on his 
 
 Scientific and Literary Works by Charles Christopher 
 
 Black, M. A., and an account of his more important Paintings 
 
 and Drawings. Illustrated with Permanent Photographs. Royal 
 
 8vo, cloth, extra gilt. 31^. 6d. 
 
 " A beautiful volume, both without and within. Messrs. Macmillan 
 
 are conspicuous among publishers for the choice binding and printing of 
 
 their books, and this is got up in their best style. . . . JVo English 
 
 publication that we know of has so thoroughly and attractively collected 
 
 together all that is known of Leonardo." — Times. 
 
 Liechtenstein,— HOLLAND HOUSE. By Princess Marie 
 
 Liechtenstein. With Five Steel Engravings by C. H. Jeens, 
 
 after Paintings by Watts and other celebrated Artists, and 
 
 numerous Illustrations drawn by Professor P. H. Delamotte, and 
 
 engraved on Wood by J. D. Cooper, W. Palmer, and Jewitt & 
 
 Co. Third and Cheaper Edition. Medium 8vo. cloth elegant. 
 
 1 6 J. 
 
 Also, an Edition containing, in addition to the above, about 40 
 
 Illustrations by the Woodbury-type process, and India Proofs of 
 
 the Steel Engravings. Two vols, medium 4to. half morocco 
 
 elegant. 4/. 4s'. 
 
 " When every strictly just exception shall have been taken, she may be 
 
 conscientiously congratulated by the most scrupulous critic on the produ^- 
 
 tion of a useful, agj-eeable, beautifully -illustrated, and attj-cutive book." — 
 
 Times. ^^ It would take up more room than we can spare to enumerate 
 
 all the interesting suggestions and notes which are to be found in these 
 
 volumes The woodcuts are admirable, and some of the autographs 
 
 are very interesting." — Pall Mall Gazette. 
 
 Lloyd. — THE AGE OF PERICLES. A History of the Arts and 
 Politics of Greece from the Persian to the Peloponnesian War. 
 By W. Wat kiss Lloyd. Two Vols. 8vo. 21s. 
 " No such account of Greek art of the best period has yet been brought 
 
 together in an English work Mr. Lloyd has produced a book op 
 
 unusu^ excellence and interest." — Pall Mall Gazette. 
 
 Macarthur. — HISTORY OF SCOTLAND, By Margaret 
 
 Macarthur. Being the Third Volume of the Historical Course 
 
 for Schools, Edited by Edward A. Freeman, D.C.L. Second 
 
 Edition. i8mo. 2s. 
 
 '^ It is an excellent summary, unimpeachable as io facts, and putting 
 
 them in the clearest and most impartial light attainable." — GUARDIAN. 
 
 " No previous History oj Scotland of the same bulk is anything like so 
 
 trustworthy, or deserves to be so extensively used as a text-book." — Globe. 
 
 B
 
 1 8 MACMILLAN'S CATALOGUE OF WORKS IN 
 
 Macmillan (Rev. Hugh). — For other Works by same Author, 
 see Theological and Scientific Catalogues. 
 
 HOLIDAYS ON HIGH LANDS ; or, Rambles and Incidents in 
 
 search of Alpine Plants. Second Edition, revised and enlarged. 
 
 Globe 8vo. cloth. 6^. 
 
 "Botanical knowledge is blended with a love of nature, a pious en- 
 
 thusiasm, a7td a rich felicity of diction not to be met with iii any works 
 
 of kindred character, if we except those of Hugh Miller." — TELEGRAPH. 
 
 *^ Mr. Macmillan's glowing pictures of Scandinavian scenery" — - 
 
 Saturday Review. 
 
 Macready. — macready'S reminiscences and se- 
 lections FROM HIS diaries AND LETTERS. Edited 
 by Sir F. Pollock, Bart., one of his Executors. With Four 
 Portraits engraved by Jeens. New and Cheaper Edition. Crown 
 8vo. 7^'. 6(7'. 
 " jfls a careful and for the most part just estimate of the stage during 
 a very brilliant pet tod, the attraction of these volumes can scarcely be 
 surpassed. .... Readers who have no s-pecial interest in theatrical 
 matters, but enjoy miscellaneous gossip, will be allured f-om page to page, 
 attracted by familiar names and by observations upon popular actors and 
 authors. " — Spectator. 
 
 Mahaffy. — Works by the Rev. J. P. Mahaffy, M.A., Fellow of 
 Trinity College, Dublin : — 
 SOCIAL LIFE IN GREECE FROM HOMER TO MENAN- 
 DER. Third Edition, revised and enlarged, with a new chapter 
 on Greek Art. Crown 8vo. gr. 
 " It should be in the hands of all who desire thoroughly to understand 
 and to enjoy Gt-eek literature, and to get an intelligent idea of the old Greek 
 life, political, social, a )td religious." — GUARDIAN. 
 
 RAMBLES AND STUDIES IN GREECE. With Illustrations. 
 Crown Svo. \os. 6d. New and enlarged Edition, with Map and 
 Illustrations 
 "yi singularly instructive and agreeable volutne.^^ — AtheN/^UM. 
 
 " Maori." — SPORT AND WORK ON THE NEPAUL FRON- 
 TIER ; or, Twelve Years' Sporting Reminiscences of an Indigo 
 Planter. By "Maori." With Illustrations. Svo. 14^. 
 
 Margary. — THE JOURNEY OF AUGUSTUS RAYMOND 
 MARGARY FROM SHANGHAE TO BHAMO AND BACK 
 TO MANWYNE. From his Journals and Letters, with a brief 
 Biographical Preface, a concluding chapter by Sir Rutherford 
 Alcock, K.C.B., and a Steel Portrait engraved by Jeens, and 
 Map. Svo. \os. 6d. 
 " There is a manliness, a cheerful spirit, an inherent vigour which 
 
 was never overcome by sickness or debility, a tact which conquered the
 
 HISTORY, BIOGRAPHY, TRAVELS, ETC. 19 
 
 prejudices of a strange and suspicious population, a quiet self-reliance, 
 always combined ivith deep religious feeling, unalloyed by either priggish- 
 ness, cant, or superstition, that ought to commend this volume to readers 
 sitting quietly at home who feel any pride in the high estimation accorded 
 to men of their race at Yarkand or at Khiva, in the heart of Africa, or 
 on the shores of Lake Seri-kul." — Saturday Review. 
 
 Markham.— NORTHWARD HO ! By Captain Albert H. 
 Markham, R.N., Author of "The Great Frozen Sea," &c. 
 Including a Narrative of Captain Phipp^'s Expedition, by a Mid- 
 shipman. With Illustrations. Crown 8vo. los. 6d. 
 
 Martin.— THE HISTORY OF LLOYD'S, AND OF MARINE 
 INSURANCE IN GREAT BRITAIN. With an Appendix 
 containing Statistics relating to Marine Insurance. By Frederick 
 Martin, Author of "The Statesman's Year Book." 8vo. 14J. 
 
 Martineau.— BIOGRAPHICAL SKETCHES, 1852— 1875. 
 By Harriet Martineau. With Additional Sketches, and Auto- 
 biographical Sketch. Fifth Edition. Crown 8vo. 6s. 
 " Miss Martineau' s large literary powers and her fine intellectual 
 
 training make these little sketches more instructive, and constitute them 
 
 more genuinely 7vorks of art, than many more ambitious and diffuse 
 
 biographies."— YoKyiHGUTWi Review. 
 
 MasSOn (David).— For other Works by same Author, see Philo- 
 sophical and Belles Lettres Catalogues. 
 CHATTERTON : A Story of the Year 1770. By David Masson, 
 LL.D., Professor of Rhetoric and English Literature in the Uni- 
 vei"sity of Edinburgh. Crown 8vo. 5^. 
 
 THE THREE DEVILS : Luther's, Goethe's, and Milton's ; and 
 
 other Essays. Crown 8vo. 5^. 
 WORDSWORTH, SHELLEY, AND KEATS; and other 
 
 Essays. Crown 8vo. 5^. 
 
 Mathews.— LIFE OF CHARLES J. MATHEWS. Chiefly 
 Autobiographical. With Selections from his Correspondence and 
 Speeches. Edited by Charles Dickens. 
 " The book is a charming one from first to last, and Mr. Dickens 
 
 deserves a full measure of credit for the care and discrimination he has 
 
 exercised in the business of editing." — GLOBE. 
 
 Maurice. — the friendship of books ; and OTHER 
 LECTURES. By the Rev. Y. D. Maurice. lidited with Pre- 
 face, by Thomas Hughes, Q.C. Ciowti 8vo. 105. td. 
 " The high, pure, sympathetic, and truly charitable nature of Mr. 
 Maurice is delightfully visible throughout these lectures, which are ex- 
 cellently adapted to spread a love of literature amongst the people." — 
 Daily News.
 
 20 MACMILLAN'S CATALOGUE OF WORKS IN 
 
 Mayor (J. E. B.)_WORKS edited by John E. B. Mayor, 
 M.A., Kennedy Professor of Latin at Cambridge : — 
 
 CAMBRIDGE IN THE SEVENTEENTH CENTURY. Part II. 
 Autobiography of Matthew Robinson. Fcap. 8vo. 5^. ()d. 
 
 LIFE OF BISHOP BEDELL. By his Son. Fcap. 8vo. 3^. bd. 
 
 Melbourne. — MEMOIRS OF THE RT. HON. WILLIAM, 
 
 SECOND VISCOUNT MELBOURNE. By W. M. Torrens, 
 
 M. P. With Portrait after Sir. T. Lawrence. Second Edition. 
 
 2 Vols. 8vo, 'i'^s. 
 
 " As might be expected, he has produced a book which will command 
 
 and reivard attention. It contains a great deal of valuable matter and 
 
 a great deal of animated, elegant writing." — Quarterly Review. 
 
 Mendelssohn.— LETTERS AND RECOLLECTIONS. By 
 
 Ferdinand Hiller. Translated by M. E. Von Glehn. With 
 Portrait from a Drawing by Karl Muller, never before pub- 
 lished. Second Edition. Crown 8vo. 7^. dd. 
 " This is a very interesting addition to our knowledge of the great 
 German composer. It reveals him to us under a new light, as the warm' 
 hearted comrade, the musician whose soul was in his work, and the home' 
 loving, domestic man." — Standard. 
 
 Merewether.— BY SEA AND BY LAND. Being a Trip 
 
 through Egypt, India, Ceylon, Australia, New Zealand, and 
 America — all Round the World. By Henry Alworth Mere- 
 wether, one of Her Majesty's Counsel. Crown 8vo. 8j. 6d. 
 
 Michael Angelo Buonarotti ; Sculptor, Painter, Architect. 
 
 The Story of his Life and Labours. By C. C. Black, M.A. 
 
 Illustrated by 20 Permanent Photographs. Royal 8vo. cloth 
 
 elegant, 31J. 61a?'. 
 
 ' ' The story of Michael Angelo s life remains interesting whatever be the 
 
 manner of telling it, and supported as it is by this beautiful series of photo • 
 
 {graphs, the volume must take rank among the most splendid of Christmas 
 
 books, fitted to sa-ve and to outlive the season" — Pall Mall Gazette. 
 
 Michelet — A SUMMARY OF MODERN HISTORY. Trans- 
 lated from the French of M. Michelet, and continued to the 
 present time by M. C. M. Simpson. Globe 8vo. 4?. tcC. 
 
 Milton. — LIFE OF JOHN MILTON. Narrated in connection 
 with the Political, Ecclesiastical, and Literary History of his Time. 
 By David Masson, M.A., LL.D., Professor of Rhetoric and 
 English Literature in the University of Edinburgh. With Portraits. 
 Vol. L i8j. Vol. II., 1638— 1643. 8vo. 16^. Vol. III. 
 1643 — 1649. 8vo. \%s. Vols. IV. and V. 1649— 1660. 32J. 
 Vol. VI. in the press. 
 This 7uork is not only a Biography, but also a continuous Political, Eccle- 
 siastical, and Literary History of England through Milton's whole time.
 
 HISTORY, BIOGRAPHY, TRAVELS, ETC. 
 
 Mitford (A. B.)— tales OF OLD japan. By A. B. 
 
 MiTFORD, Second Secretary to the British Legation in Japan. 
 
 With upwards of 30 Illustrations, drawn and cut on Wood by 
 
 Japanese Artists. New and Cheaper Edition. Crown 8vo. 6s. 
 
 " These very original volumes will always be inieresling as memorials 
 
 of a most exceptional society, vjhile regarded simply as tales, they are 
 
 sparkling, sensational, and dramatic, a7td the origittality of their idea 
 
 and the quaintness of their language give them a most captivating 
 
 piquancy. The illustrations are extremely interesting, and for the 
 
 curious in such matters have a special and particular value." — Pall 
 
 Mall Gazette. 
 
 Monteiro.— ANGOLA AND THE RIVER CONGO. By 
 Joachim Monteiro. With numerous Illustrations from Sketches 
 taken on the spot, and a Map. Two Vols, crown 8vo, 2is. 
 " Gives the first detailed account of a part of tropical Africa 'which is 
 
 httle known to Englishmen The ranarks on the geography and 
 
 zoology of the country and the manners and customs of the various races 
 inhabiting it, are extremely curious and interesting." — Saturday Re- 
 view. ' ' Eull of valuable information and much picturesque description. " 
 Pall Mall Gazette. 
 
 Morison.— THE LIFE AND TIMES OF SAINT BERNARD, 
 Abbot of Clairvaux. By James Cotter Morison, M.A. New 
 Edition. Crown 8vo. 6^. 
 
 Moseley. — NOTES BY A NATURALIST ON THE CHAL- 
 LENGER: being an Account of various Observations made 
 during the Voyage of H.M.S. Challenger, Round the World, 
 in 1872-76. By H. N. Moseley, F.R.S., Member of the 
 Scientific Staff of the Challenger. 8vo, with Maps, Coloured Plates, 
 and Woodcuts. 2U. 
 
 Murray. — ROUND ABOUT FRANCE. By E. C. Grenville 
 Murray. Crown 8vo. ']s. 6d. 
 " These short essays area perfect mine of information as to the present 
 condition and future prospects of political parties in France. . . . It is 
 at once extremely interesting and exceptionally instructive on a subject on 
 which few English people are well informed." — Scotsman. 
 
 Napier. — MACVEY NAPIER'S SELECTED CORRES- 
 PONDENCE. Edited by his Son, Macvey Napier. 8vo, 14J. 
 " This exceedingly interesting work. . . . Mr. Napier has certainly been 
 7i'ell advised in admitting the general public to the knowledge of a volume 
 which is hardly to be surpassed in point of interest among recent publica- 
 tions." — Examiner.
 
 22 MACMILLAN'S CATALOGUE OF WORKS IN 
 
 Napoleon.— THE HISTORY OF NAPOLEON I. By P. 
 
 Lanfrey. a Translation with the sanction of the Author. Vols. 
 
 I. II. and III. 8vo. price I2s. each. \Vol. IV. in the press. 
 
 The Fall Mall Gazette says it is "one of the most striking 
 pieces of historical composition of which France has to boast," and the 
 Saturday Review calls it ^^ an excellent translation of a work oti every 
 ground deserving to be trattslated. It is unqitestionably and immeasurably 
 the best that has been produced. It is in/act the only work to which we 
 can turn for ayt accurate and trustworthy narrative of that extraordinary 
 career. . . . The book is the best and indeed the only trustworthy history 
 of Napoleon which has been written." 
 
 Nichol. — TABLES OF EUROPEAN LITERATURE AND 
 HISTORY, a.d. 200—1876. By J. NiCHOL, LL.D., Professor 
 of English Language and Literature, Glasgow. 4to. 6s. 6d. 
 TABLES OF ANCIENT LITERATURE AND HISTORY, 
 B.C. 1500— A.D. 200. By the same Author. 4to. 45-. 6a'. 
 
 Oliphant (Mrs.). — THE MAKERS OF FLORENCE : Dante 
 Giotto, Savonarola, and their City. By Mrs. Oliphant. With 
 numerous Illustrations from drawings by Professor Delamotte, 
 and portrait of Savonarola, engraved by Jeens. Second Edition. 
 Medium 8vo. Cloth extra. 21^. 
 '• Mrs. Oliphant has made a beautiful addition to the mass of literature 
 
 already piled round the records of the Tuscan capital." — Times. 
 
 " We are gi-ateful to Mrs. Oliphant for her eloquent and beautiful 
 
 sketches of Dante, Fra Angelico, arid Savonarola. They are picturesque, 
 
 full of life, and rich in detail, and they are charmingly illustrated by the 
 
 art of the engraver." — SPECTATOR. 
 
 Oliphant.— THE DUKE AND THE SCHOLAR; and other 
 Essays. By T. L. Kington Oliphant. 8vo. ^s. 6d. 
 '* This volume contains one of the most beautiful biop-aphical essays we 
 have seen since Alacaulay^s days." — Standard. 
 
 Otte. — SCANDINAVIAN HISTORY. By E. C. Otte, With 
 Maps. Extra fcap. 8vo. 6.i-. 
 " We have peculiar pleasure in recommending this intelligent risume 
 of Northertt history as a book essential to every Fnglish?>ian who interests 
 himself in Scandinavia."— Spectator. 
 
 Owens College Essays and Addresses. — By Pro- 
 fessors and Lecturers of Owens College, Manchester. 
 Published in Commemoration of the Opening of the New College 
 Buildings, October 7th, 1873. 8vo. 14s. 
 
 Palgrave (R. F. D.)— the HOUSE OF COMMONS ; 
 Ilhistrations of its Plistory and Practice. By Reginald F. D. 
 Pai,(;rave, Clerk Assistant of the House of Commons. New 
 and Revised Edition. Crown 8vu. 2s. 6d.
 
 Mrs TORY, BIOGRAPHY, TRAVELS, ETC. 23 
 Palgrave (Sir F.) — history OF Normandy and 
 
 OF ENGLAND. By Sir Francis Palgrave, Deputy Keeper 
 of Her Majesty's Public Records. Completing the History to the 
 Death of William Rufus. 4 Vols. Svo. 4/. 45-. 
 
 Palgrave (W. G.) — A NARRATIVE OF A YEAR'S 
 JOURNEY THROUGH CENTRAL AND EASTERN 
 ARABIA, 1862-3. By William Gifford Palgrave, late of 
 the Eighth Regiment Bombay N. I. Sixth Edition. With Maps, 
 Plans, and Portrait of Author, engraved on steel by Jeens. Crown 
 Svo. 6s, 
 *^ He kas not only written one of the best books on the Arabs and one 
 
 of the best books on Arabia, but he has done so in a manner that viiist 
 
 command the respect no less than the admiration of his fellow-country 
 
 men." — Fortnightly Review. 
 
 ESSAYS ON EASTERN QUEStlONS. By W. Gifford 
 Palgrave. Svo. los. 6d. 
 
 " These essays are full of anecdote and interest. The book is decidedly 
 a valuable addition to the stock of literature on which meti must 
 base their opinion of the difficult social and political problems sug- 
 gested by the designs of Russia, the capacity of Mahometans Jor 
 sovereignty, and the ' good government and retention of Jndia." — 
 Saturday Review. 
 
 DUTCH GUIANA. With Maps and Plans. Svo. 9^. 
 
 "His pages are nearly exhaustive as far as facts and statistics go, 
 while they are lightened by graphic social sketches as well as sparkling 
 descriptions of scenery.'" — Saturday Review. 
 
 Patteson, — life and letters of john coleridge 
 
 PATTESON, D.D., Missionary Bishop of the Melanesian Islands. 
 
 By Charlotte M. Yonge, Author of " The Heir of Redclyffe." 
 
 With Portraits after RICHMOND and from Photograph, engraved by 
 
 Jeens. With Map. Fifth Edition. Two Vols. Crown Svo, \2.s. 
 
 ^^ Miss Yotige's work is in one respect a model biography. It is made 
 
 up almost entirely of Patteson' s own letters. Aware that he had left his 
 
 home once and for all, his correspondence took the for in of a diajy, and 
 
 as we read on we come to know the mati, and to love him almost as if we 
 
 had seen him." — AtheN/EUM. "Such a life, with its grand lessons of 
 
 unselfishness, is a blessing and an honour to the age in which it is lived ; 
 
 the biography cannot be studied without pleasure and profit, and indeed 
 
 we should think Utile of the man who did not rise from the study of it 
 
 better and wiser. Neither the Church nor the nation which produces 
 
 such sons need ever despair of its future." — Saturday Review. 
 
 Pauli. — PICTURES OF OLD ENGLAND. By Dr. Reinhold 
 Pauli. Translated, with the approval of the Author, by E. C. 
 Ottf.. Cheaper Edition. Crown Svo. 6^.
 
 24 MACMILLAN'S CATALOGUE OF WORKS TN 
 
 Payne. — a history of EUROPEAN COLONIES. By 
 E. J. Payne, M.A. With Maps. i8mo. 45-. (id. 
 The Times says : — " We have seldom met with a historian capable oj 
 forming a more comprehensive, far-seeing, and unprejudiced estimate of 
 events and peoples, and we can commend this little work as one certain to 
 prove of the highest interest to all thoughtful readers^ 
 
 Persia. — eastern Persia. An Account of the Journeys of 
 the Persian Boundary Commission, 1870-1-2. — Vol. I. The Geo- 
 graphy, with Narratives by Majors St. John, Lovett, and Euan 
 Smith, and an Introduction by Major-General Sir Frederic 
 GOLDSMID, C.B., K.C.S.I., British Commissioner and Arbitrator. 
 With Maps and Illustrations. — Vol. II. The Zoology and Geology, 
 By W. T. Blanford, A.R.S.M., F.R.S. With Coloured lUus- 
 trations. Two Vols. 8vo. 42J. 
 " The volumes largely increase our store of information about 
 
 countries with which Englishmen ought to be familiar 
 
 They throw into the shade all that hitherto has appeared in our tongue 
 respecting the local features of Persia, its scenery, its resources, even its 
 social condition. Thev contain also abundant evidence of English 
 endurance, daring, and spirit." — Times. 
 
 Prichard. — the administration of INDIA. From 
 1859 to 1868. The First Ten Years of Administration under the 
 Crown. By I. T. Prichard, Barrister-at-Law. Two Vols. 
 Demy Svo. With Map. 2\s. 
 
 Raphael.— RAPHAEL OF URBINO AND HIS FATHER 
 GIOVANNI SANTI. By J. D. Passavant, formerly Director 
 of the Museum at Frankfort. With Twenty Permanent Photo- 
 graphs.- Royal Svo. Handsomely bound. 31^. 6^^. 
 
 The Saturday Review says of them, " We have seen not a fezo 
 elegant specimens of Mr. Woodbury's new process, but we have seen 
 none that equal these. " 
 
 Reynolds. — SIR JOSHUA REYNOLDS AS A PORTRAIT 
 PAINTER. AN ESSAY. By J. Churton Collins, B.A. 
 Balliol College, O.xford. Illustrated by a Series of Portraits of 
 distinguished Beauties of the Court of George III. ; reproduced 
 in Autotype from Proof Impressions of the celebrated Engravings, 
 by Valentine Green, Thomas Watson, F. R. Smith, E. 
 Fisher, and others. Folio half-morocco. £<^ '^s. 
 
 Rogers (James E. Thorold). — HISTORICAL GLEAN- 
 INGS : A Series of Sketches. Montague, Walpole, Adam Smith, 
 Cobbett. By Prof. Rogers. Crown 8vo. 4?. (>d. Second Series, 
 Wiklif, Laud, Wilkes, and Home Tooke. Crown Svo. bs.
 
 HISTORY, BIOGRAPHY, TRAVELS, ETC. 25 
 Routledge. — chapters in the history of popular 
 
 PROGRESS IN ENGLAND, chiefly in Relation to the Freedom 
 of the Press and Trial by Jury, 1660 — 1820. With application to 
 later years. By J. Routledge. 8vo. i6j. 
 " The volume abounds in facts and information, almost ahvays useful 
 and often curivus." — Times. 
 
 Rumford. — COUNT RUMFORD'S complete WORKS, 
 with Memoir, and Notices of his Daughter. By George Ellis. 
 Five Vols. 8vo. 4/. 14^-. 6d. 
 
 Seeley (Professor). — LECTURES AND ESSAYS. By 
 J. R. Seeley, M.A. Professor of Modem History in the 
 University of Cambridge. 8vo. los. 6d. 
 Contents : — Roman Iinperialism : i. The Great Roman Revolu- 
 tion; 2. The Proximate Cause* of the Fall of the Roman Empire ; 
 The Later Empire. — Aliltott's Political Opinions — Milton's Poetry 
 — Elementary Principles in Art — Liberal Education in Universities 
 — English in Schools — The Church as a Teacher of Morality — The 
 Teaching of Politics : an Inaugural Lecture delivered at Cambridge. 
 
 Shelburne.— LIFE OF William, earl of shelburne, 
 
 AFTERWARDS FIRST MARQUIS OF LANSDOWNE. 
 
 With Extracts from his Papers and Correspondence. By Lord 
 
 Edmond Fitzmaurice. In Three Vols. 8vo. VoL I. 1737 — 
 
 1766, I2J-. ; Vol.dl. 1766— 1776, \zs. ; Vol. III. 1776 — 1805. xds. 
 
 "Lord Edtnond Fitzmaurice has succeeded in placing before us a 
 
 wealth of new matter, -which, while casting valuable and much-needed 
 
 light on several obscure passages in the political history of a hundred 
 
 years ago, has enabled us for the first time to form a clear and consistent 
 
 idea of his ancestor.'' — Spectator. 
 
 Sime. — history of Germany, By james Sime, m.a. 
 
 i8mo. 3J'. Being Vol. V. of the Historical Course for Schools 
 Edited by Edward A. Freeman, D.C.L. 
 " This is a remarkably clear and impressive History of Germany. Its 
 great rodents are wisely kept as central figures , and the smaller events are 
 carefully kept not only subordinate and subservient, but most skilfully 
 woven into the texture of the historical tapestry presented to the eye." — 
 Standard. 
 
 Squier. — PERU : INCIDENTS OF TRAVEL AND EX- 
 PLORATION in the land of the INCAS. By E. G. 
 Squier, M.A., F.S.A., late U.S. Commissioner to Peru. With 
 300 Illustrations. . Second Edition. 8vo. 2ls. 
 The Times says : — " No more solid and trustzvorthy contribution haa 
 been made to an accu7-ate knaiuledge of what are among the most wonderful 
 ruins in the world. The work is really what its title implies. While of 
 the greatest importance as a contribution to Pei uvian archceology, it is also a 
 thoroughly entertaining and instructive narrative of travel. Mot the least 
 ifnportant feature must beconsidered the numei'oui well executed illustrations ."
 
 26 MACMILLAN'S CATALOGUE OF WORKS IN 
 
 Strangford. — EGYPTIAN S?IRINES AND SYRIAN SEPUL- 
 CHRES, including a Visit to Palmyra. By Emily A. Beaufort 
 (Viscountess Strangford), Author of " The Eastern Shores of 
 the Adriatic." New Edition. Crown 8vo. "Js. 6d. 
 
 Tait.— AN ANALYSIS OF ENGLISH HISTORY, based upon 
 Green's "Short History of the English People." By C. W. A. 
 Tait, M.A., Assistant Master, Clifton College. Crown 8vo. 
 35. 6d. 
 
 Thomas.— TFIE LIFE OF JOHN THOMAS, Surgeon of the 
 "Earl of Oxford" East Indiaman, and First Baptist Missionary to 
 Bengal. By C. B. Lewis, Baptist Missionary. 8vo. los. 6d. 
 
 Thompson. — HISTORY OF ENGLAND. By Edith Thomp- 
 
 SON. Being Vol. II. of the Historical Course for Schools, Edited 
 
 by Edward A. Freeman, D. C.L. New Edition, revised and 
 
 enlarged, with Maps. iSmo. 2s. 6d. 
 
 ^^ Freedom from prejudice, simplicity of style, and accuracy of state- 
 
 ment, are the characttristics of this volume. It is a tritstzvortky text-book, 
 
 and likely to be generally serviceable in schools." — Pall Mall Gazette. 
 
 *' In its great accuracy and correctness of detail it stands far ahead of the 
 
 general nin of school 7nanuals. Its arrangement, too, is clear, and its 
 
 style simple and straightjorward." — Saturday Review. 
 
 Todhunter. — THE CONFLICT OF STUDIES ; AND 
 OTPIER ESSAYS ON SUBJECTS CONNECTED WITH 
 EDUCATION. By Isaac Todhunter, M.A., F.R.S., late 
 Fellow and Principal Mathematical Lecturer 01 St. John's College, 
 Cambridge. 8vo. loj. 6d. 
 Contents : — 1. The Conflict of Studies. II. Competitive Exa- 
 minations. III. Private Study of Mathematics. IV. Academical 
 Reform. V. Elementary Geometry. VI, The Mathematical Tripos. 
 
 Trench (Archbishop). — For other Works by the same Author, 
 
 see Theological and Belles Lettres Catalogues, and 
 
 page 30 of this Catalogue. 
 GUSTAVUS ADOLPHUS IN GERMANY, and other Lectures 
 
 on the Thirty Years' War. Second Edition, revised and enlarged. 
 
 Fcap. Svo. 4-;. 
 PLUTARCH, HIS LIFE, HIS LIVES, AND PIIS MORALS. 
 
 Five Lectures. Second Edition, enlarged. Fcap. Svo. 3^^. ()d. 
 LECTURES ON MEDIEVAL CHURCH HISTORY. Being 
 
 the substance of Lectures delivered in Queen's College, London. 
 
 Second Edition, revised. Svo. 12s. 
 
 Trench (Maria). — THE LIFE OF ST. TERESA. By Marta 
 Trench. With Portrait engraved by Jeens. Crown Svo, cloth 
 extra. 8j. 6d. 
 "A book of rare interest." — John Bull.
 
 HISTORY, BIOGRAPHY, TRAVELS, ETC. 27 
 
 Trench (Mrs. R.)— REMAINS OF THE LATE MRS. 
 RICHARD TRENCH. Being Selections from her Journals, 
 Letters, and other Papers. Edited by Archbishop Trench. 
 New and Cheaper Issue, with Portrait. 8vo. 6^. 
 
 TroUope. — a history of the commonwealth of 
 
 FLORENCE FROM THE EARLIEST INDEPENDPINCE 
 OF THE COMMUNE TO THE FALL OF THE REPUBLIC 
 IN 1831. By T. Adolphus Trollope. 4 Vols. Svo. Half 
 morocco. 2is. 
 
 Uppingham by the Sea, — a NARRATIVE OF THE 
 YEAR AT BORTH. ByJ. H. S. Crown Svo. z^. 6d. 
 
 Victor Emmanuel II., First King of Italy.— ms 
 LIFE. By G. S. Godkin. 2 vols., crown Svo. i6s. 
 "An extremely clear and interesting history of one of the most 
 
 ijnportant changes of later /iw^j."— Examiner. 
 
 Wallace.— THE MALAY ARCHIPELAGO: the Land of the 
 Orang Utan and the Bird of Paradise. By Alfred Russel 
 Wallace. A Narrative of Travel with Studies of Man and 
 Nature. With Maps and numerous Illustrations. Sixth Edition. 
 Crown Svo. 7j. dd. 
 * ' The result is a vivid picture of tropical life, -which may be read with 
 unflagging interest, atid a sufficient account of his scientific conclusions to 
 stimulate our appetite without wearying us by detail. In short, we mo- 
 safely say that we have never read a more agreeable book of its k<' 
 Saturday Review. 
 
 Ward.— A HISTORY OF ENGLISH DRAMATIC 1.ITERA. 
 
 TURE TO THE DEATH OF QUEEN ANNE. By A. W. 
 
 Ward, M.A., Professor of History and English Literature in 
 
 f^wens College, Manchester. Two Vols. Svo. 32^. 
 
 " As ftdl of interest as of information. To students of dramatic 
 
 literature invaluable, and may be equally recomtnended to readers for 
 
 mere pastime.^' — Pall Mall Gazette. 
 
 Ward (J.)— EXPERIENCES OF A DIPLOMATIST. Being 
 recollections of Germany founded on Diaries kept during the years 
 1840—1870. By JoHiN Ward, C.B., late H.M. Minister- 
 Resident to the Hanse Towns. Svo. loj-. 6d. 
 
 Waterton (C.)— wanderings in SOUTH AMERICA, 
 THE NORTH-WEST OF THE UNITED STATES, AND 
 THE ANTILLES IN 1812, 1816, 1820, and 1824. With 
 Original Instructions for the perfect Preservation of Birds, etc., 
 for Cabinets of Natural History. By Charles Waterton. 
 New Edition, edited with Biographical Introduction and Explana- 
 tory Index by the Kev. J. G. Wood, M.A. With roo Illustrations. 
 Svo. Cloth elegant. 21s.
 
 28 MACMILLAN'S CATALOGUE OF WORKS IN 
 
 Wedgwood.— JOHN WESLEY AND THE EVANGELICAL 
 
 REACTION of the Eighteenth Century, By JuLiA Wedgwood. 
 Crown 8vo. 8j. (>d. 
 
 Whewell.— WILLIAM WHEWELL, D.D., late Master of 
 Trinity College, Cambridge. An Account of his Writings, with 
 Selections from his Literary and Scientific Correspondence. By 
 I. ToDHUNTER, M.A., F.R.S. Two Vols. Svo. 25J. 
 
 White. — THE NATURAL HISTORY AND ANTIQUITIES 
 OF SELBORNE. By (iiLBERT White. Edited, with Memoir 
 and Notes, by Frank Buckland, A Chapter on Antiquities by 
 Lord Selborne, Map, &c., and numerous Illustrations by 
 P. H. Delamotte. Royal Svo. Cloth, extra gilt. Cheaper 
 Issue. 2\s. 
 
 Also a Large Paper Edition, containing, in addition to the above, 
 upwards of Thirty Woodbuiytype Illustrations from Drawings 
 by Prof. Delamotte. Two Vols. 4to. Half morocco, elegant. 
 
 4/. ifS. 
 
 "Mr. Delamotti s charming illustrations are a worthy decoration of so 
 dainty a book. They bring Selborne before us, and really help us to 
 understand why Whites love for his native place ncver grew cold" — 
 Times. 
 
 Wilson. — A MEMOIR OF GEORGE WILSON, M. D., 
 F. R. S.E., Regius Professor of Technology in the University of 
 Edinburgh. By his Sister. New Edition. Crown Svo. bs. 
 
 Wilson (Daniel, LL.D.) — Works by Daniel Wilson, 
 LL.D., Professor of History and English Literature in University 
 College, Toronto : — 
 PREHISTORIC ANNALS OF SCOTLAND. New Edition, 
 with numerous Illustrations. Two Vols, demy Svo. 36^. 
 
 " One of the most interesting, leat-ned, and elegant works we have 
 seen for a long time." — Westminster Review^. 
 
 PREHISTORIC MAN : Researches into the Origin of Civilization 
 
 in the Old and New World. New Edition, revised and enlarged 
 
 throughout, with numerous Illustrations and two Coloured Plates. 
 
 Two Vols. Svo. 36^-. 
 
 "/i valuable work pleasantly written and well worthy of atttntion 
 
 both by students and general readers." — Academy. 
 
 CHATTERTON : A Biographical Study. By Daniel Wilson, 
 LL. D., Professor of History and English Literature in University 
 College, Toronto. Crown Svo. 6j. (id.
 
 HISTORY., BIOGRAPHY, TRAVELS, ETC, 29 
 
 Wyatt (Sir M. Digby).— fine ART : a Sketch of its 
 History, Theory, Practice, and application to Industry. A Course 
 of Lectures delivered before the University of Cambridge. By 
 Sir M. Digby Wyatt, M.A. Slade Professor of Fine Art. 
 Cheaper Issue. 8vo. 5J. 
 
 " ^« excellent handbook for the student of art. ^^ — GRAPHIC. " The 
 book abounds in valuable matter, and will therefore be read with 
 pleasure and profit by lovers of art." — Daily News. 
 
 Yonge (Charlotte M.)— Works by Charlotte M. Yonge, 
 Author of "The Heir of Redclyffe," &c., &c. :— 
 A PARALLEL HISTORY OF FRANCE AND ENGLAND : 
 consisting of Outlines and Dates. Oblong 4to. 31. ()d. 
 
 CAMEOS FROM ENGLISH HISTORY. From Rollo to Edward 
 II. Extra fcap. 8vo. Third Edition. 5^. 
 
 Second Series, THE WARS IN FRANCE. Extra fcap. 
 8vo. Third Edition. 5^. 
 
 Third Series, THE WARS OF THE ROSES. Extra 
 fcap. Svo. 5^. 
 
 '^^ Instead of dry details," says the NONCONFORMIST, " we have living 
 pictures, faithful, vivid, and striking." 
 
 Fourth Series. \Nearly ready. 
 
 HISTORY OF FRANCE. Maps* i8mo. 3^. dd. 
 
 \_Historical Course for Schools,
 
 30 MACMTLLAN'S CATALOGUE OF 
 
 POLITICS, POLITICAL AND SOCIAL 
 ECONOMY, LAW, AND KINDRED 
 SUBJECTS. 
 
 Anglo-Saxon Law. — ESSAYS IN. Contents: Law Courts 
 — Land and Family Laws and Legal Procedure generally. With 
 Select cases. Medium 8vo. iZs. 
 
 Arnold. — THE ROMAN SYSTEM OF PROVINCIAL ADMIN- 
 ISTRATION TO THE ACCESSION OF CONSTANTINE 
 THE GREAT. Being the Arnold Prize Essay for 1879. Ey 
 W. T, Arnold, B. A. Crown 8vo. 6s. 
 
 Ball. — THE STUDENT'S GUIDE TO THE BAR. By 
 Walter W. Ball, M.A., of the Inner Temple, Barrister-at- 
 Law. Crown 8vo. zs. 6d. 
 " The student will here find a clear statement of the several steps by 
 
 which the degree of barrister is obtained, and also usejul advice about 
 
 the advantages of a prolonged course of ' reading in Chambers. ' " — 
 
 Academy. 
 
 Bernard.— FOUR LECTURES ON SUBJECTS CONNECTED 
 WITH DIPLOMACY. By Montague Bernard, M.A., 
 Chichele Professor of International Law and Diplomacy, Oxford. 
 8vo. 9^. 
 " Singularly interesting lectures, so able, clear, and attractive." — Spec- 
 tator. 
 
 Bright (John, M.P.) — Works by the Right Hon. John Bright, 
 
 M.P. 
 
 SPEECHES ON QUESTIONS OF PUBLIC POLICY. 
 Edited by Professor Thorold Rogers. Author's Popular Edition. 
 Globe 8vo. 3^. td. 
 
 '^ Mr. Bri^hi's speeches will ahvays deserve to be studied, as an 
 apprenticeship to popular and parliamentarv oratory ; they will foi-nt 
 materials for the history of our time, and many brilliant passages, 
 verhaps some entire speeches, will really become a part of the living litera- 
 ture of England." — DAILY News. 
 
 LIBRARY EDITION. Two Vols. 8vo. With Portrait. 2$^. 
 PUBLIC ADDRESSES. Edited by J. Thorold Rogers. Svo. 
 
 14J. 
 
 Bucknill, — HABITUAL DRUNKENNESS AND INSANE 
 DRUNKARDS. By J. C. Bucknill, M.D., F.R.S., late 
 Lord Chancellor's Visitor of Lunatics, Crown Svo. 2s. 6d,
 
 WORKS IN POLITICS, ETC. 
 
 Cairnes. — Works by J. E. Cairnes, M.A., Emeritus Professor of 
 Political Economy in University College, London. 
 
 ESSAYS IN POLITICAL ECONOMY, THEORETICAL 
 and APPLIED. By J. E. Cairnes, M.A., Professor of Political 
 Economy in University College, London. 8vo. loj'. 6d. 
 
 POLITICAL ESSAYS. 8vo. los. 6d. 
 
 SOME LEADING PRINCIPLES OF POLITICAL ECONOMY 
 NEWLY EXPOUNDED. 8vo. 14^-. 
 
 Contents : — Part I. Value. Part II. Labour and Capital. Part 
 III. International Trade. 
 
 "A work which is perhaps the most valuable contribution to the science 
 made since the publication, a quarter of a century since, of Mr. Micls 
 ' Principles of Political Economy.^ " — Daily News. 
 
 THE CHARACTER AND LOGICAL METHOD OF POLL 
 TICAL ECONOMY. New Edition, enlarged. 8vo. 7s. 6d 
 
 " These lectures are admirably fitted to correct the slipshod generaliza- 
 tions ivhich pass current as the science of Political Economy." — Times. 
 
 Clarke.— EARLY ROMAN LAW. THE REGAL PERIOD. 
 By E. C. Clarke, M.A., of Lincoln's Inn, Barrister-at-Law, 
 Lecturer in Law and Regius Professor of Civil Law at Cam- 
 bridge. Crown 8vo. 5^. 
 
 Cobden (Richard). — SPEECHES ON QUESTIONS OF 
 PUBLIC POLICY. By Richard Cobden. Edited by the 
 Right Hon. John Bright, M.P., and J. E. Thorold Rogers. 
 Popular Edition. 8vo. 3^-. 6d. 
 
 Fawcett. — Works by Henry Fawcett, M.A., M.P., Fellow of 
 Trinity Hall, and Professor of Political Economy in the University 
 of Cambridge : — 
 
 THE ECONOMIC POSITION OF THE BRITISH 
 
 LABOURER. Extra fcap. 8vo. 5-f. 
 MANUAL OF POLITICAL ECONOMY. Fifth Edition, with 
 
 New Chapters on the Depreciation of Silver, etc. Crown 8vo. 
 
 12S. 
 
 The Daily News says: ^^ It forms one of the best introductions to the 
 principles of the science, and to its practical applications in the problems 
 of modern, and especially of English, government and society." 
 
 PAUPERISM : ITS CAUSES AND REMEDIES. Crown 8vo. 
 5^. td. 
 
 The AtheN/^um calls the work "a repertory of interesting and well 
 digested information ." 
 
 SPEECHES ON SOME CURRENT POLITICAL QUES- 
 TIONS. 8vo. los. ed. 
 " They will help to educate, not perhaps, parties, but the educators of 
 parties. ' ' — Dai L Y N ews.
 
 32 MACMILLAN'S CATALOGUE OF 
 
 Fa W C e 1 1 . — continued. 
 ESSAYS ON POLITICAL AND SOCIAL SUBJECTS. By 
 Professor Fawcett, M.P., and Millicent Garreti 
 Fawcett. 8vo. \os. 6d. 
 " They will all repay the perusal of the thinking reader ^ — DAILY 
 News. 
 
 FREE TRADE AND PROTECTION : an Inquiry into the 
 Causes which have retarded the general adoption of Free Trade 
 since its introduction into England. Third Edition. 8vo. ^s. 6d. 
 ' ' No greater service can be rendered to the cause of Free Trade than a 
 clear explanation of the principles on which Free Trade rests. Pro- 
 fessor Fawcett has dotie this in the volume before us with all his habitual 
 clearness of thought and expression." — Economist. 
 
 Fawcett (Mrs.) — Works by Millicent Garrett Fawcett. 
 
 POLITICAL ECONOMY FOR BEGINNERS. WITH QUES- 
 TIONS. New Edition. i8mo. 2s. 6d. 
 
 The Daily News calls it ^^clear, compact, and comprehensive;" and 
 the Spectator says, ^^Mrs. Fawcett' s treatise is perfectly suited to its 
 purpose." 
 
 TALES IN POLITICAL ECONOMY. Crown 8vo. 3^. 
 
 * ' The idea is a good one, and it is quite wonderful what a mass oj 
 economic teaching the author manages to compress into a small space.. .The 
 true doctrines of International Trade, Currency, and the ratio between 
 Production and Population, are set before us and illust7-ated in a masterly 
 manner'' — Athen^^um . 
 
 Freeman (E. A.), M.A., D.C.L,.— comparative 
 
 POLITICS. Lectures at the Royal Institution, to which is 
 
 added " The Unity of History," being the Rede Lecture delivered 
 
 at Cambridge in 1872. 8vo. 14^. 
 
 " We find in Mr. Freeman's new volume the same sound, careful, 
 
 comprehensive qualities which have long ago raised hitn to so high a place 
 
 amongst historical writers. For historical discipline, then, as well as 
 
 historical information, Mr. Freeman's book is full of value." — Pall 
 
 Mall Gazette. 
 
 Goschen. — REPORTS AND SPEECHES ON LOCAL TAXA- 
 TION. By George J. Goschen, M. P. Royal 8vo. Sj. 
 " The volume contains a vast massof information of the highest value." 
 
 — ATHEN/CUM. 
 
 Guide to the Unprotected, in Every Day Matters Re- 
 lating to Property and Income. By a Banker's Daughter. 
 Fourth Edition, Revised. Extra fcap. 8vo. 3^. 6d. 
 '■'■Many an unprotected female will bless the head which planned and 
 the hand which compiled this admirable little manual. ... 1 his book 
 was very much wanted, and it could not have been better done." — 
 Morning Star.
 
 WORKS IN POLITICS, ETC. 33 
 
 Hamilton. — money and value: an Inquiry into the 
 Means and Ends of Economic Production, with an Appendix 
 on the Depreciation of Silver and Indian Currency. By Rowland 
 Hamilton. 8vo. 12s. 
 
 " The subject is here dealt with in a luminous style, and by presenting 
 it from a new point of vietu in connection with the nature and functions 
 ef money, a genuine service has been rendered to commercial science.''' — 
 British Quarterly Review. 
 
 HarwOOd. — disestablishment : a Defence of the Principle 
 of a National Church. By George Harwood, M.A. 8vo. \2s. 
 
 Hill. — Works by OCTAVIA Hill :— 
 
 HOMES OF THE LONDON POOR. Extra fcap. 8vo. y. 6d. 
 *^ S/ie is clear, practical, and definite." — Globe. 
 
 OUR COMMON LAND ; and other Short Essays. Extra fcap, 
 8vo. 35. 6d. 
 
 Contents : — Our Common Land. District Visiting. A More 
 Excellent Way of Charity. A Word on Good Citizenship. Of en Spaces. 
 Effectual Charity. The Future of our Commons. 
 
 HistoricuS. — LETTERS ON SOME QUESTIONS OF 
 INTERNATIONAL LAW. Reprinted from the Times, with 
 considerable Additions. 8vo. "js.' 6d. Also, ADDITIONAL 
 LETTERS. 8vo. 2s. ed. 
 
 Holland,— THE treaty relations of RUSSIA AND 
 TURKEY FROM 1774 TO 1853. A Lecture delivered at Oxford, 
 April 1877. By T. E. Holland, D.C.L., Professor of Inter- 
 national Law and Diplomacy, Oxford. Crown 8vo. 2s. 
 
 Hughes (Thos.)— THE OLD church : WHAT SHALL 
 WE DO WITH IT? By Thomas Hughes, Q.C. Crown 
 8vo. 6s. 
 
 Jevons. — Works by W. Stanley Jevons, M.A., Professor of 
 Political Economy in University College, London. (For other 
 Works by the same Author, see Educational and Philo- 
 sophical Catalogues.) 
 
 THE COAL QUESTION : An Inquiry Concerning the Progres* 
 of the Nation, and the Probable Exhaustion of our Coal Mines. 
 Second Edition, revised. 8vo. 10s. 6d.
 
 34 MACMILLAN'S CATALOGUE OF 
 
 Jevons. — continued. 
 
 THE THEORY OF POLITICAL ECONOMY. Second Edition, 
 revised, with new Preface and Appendices. 8vo. 105. (yd. 
 
 ' ^Professor yevons has done invaluable service by courageously clahning 
 political economy to be strictly a branch of Applied Mathematics" 
 — Westminster Review. 
 
 PRIMER OF POLITICAL ECONOMY. iSmo. xs. 
 
 Laveleye. — primitive property. By emile de 
 
 Laveleye. Translated by G. R. L. Marriott, LL. B., with an 
 Introduction by T. E. Cliffe Leslie, LL.B. 8vo. i2j. 
 
 " It is almost impossible to over-estimate the value of the well-digested 
 knowledge which it contains ; it is one of the tnost learned books that 
 have been contributed to the historical department of the literature of 
 economic science." — Athen^um. 
 
 Leading Cases done into English. By an Apprentice 
 OF Lincoln's Inn. Third Edition. Crown 8vo. 2s. 6d. 
 
 " Here is a rare treat for the lovers of quaint conceits, who in reading 
 this charming little book will find enjoyment in the varied metre and 
 graphic language in zvhich the several tales are told, no less than in the 
 accurate afid pithy rendering of some of our most Jamiliar ' Leading 
 Cases.'' " — Saturday Review. 
 
 Lubbock, — ADDRESSES, POLITICAL AND EDUCA- 
 TIONAL. By Sir John Lubbock, Bart., M.P., &c., &c. 
 Svo, pp. 209. 8s. 6d. 
 The ten speeches given are (i) on the Imperial JPolicy of Great 
 Britain, (2) on the Bank Act of 1844, (3) on the Present System 
 of Public School Education, 1876, (4) on the Present System of 
 Elementary Education, (5) on the Income Tax, (6) on the National 
 Debt, (7) on the Declaration of Paris, (8) on Marine Insurances, 
 (9) on the Preservation of Ancient Monuments, and (10) on Egypt. 
 
 Macdonell.— TPIE LAND QUESTION, WITH SPECIAL 
 REFERENCE TO ENGLAND AND SCOTLAND. By 
 John Macdonell, Barrister-at-Law. Svo. loj. 6d. 
 
 Martin.— THE statesman's YEAR-BOOK: a Statistical 
 and Historical Annual of the States of the Civilized World, 
 for the year 1879. By Frederick Martin. Sixteenth Annual 
 Publication. Revised after Official Returns. Crown 8vo. los. 6d. 
 
 The Statesman^ s Year-Book is the only tvork in the English language 
 which furnishes a clear and concise account of the actual condition of all 
 the States of Europe, the civilized countries of America, Asia, and
 
 WORKS IN POLITICS, ETC, 35 
 
 Africa, and the British Colonies and Dependencies in all parts of the 
 world. The nrw issue of the work has been revised and corrected, on the 
 basis of official reports received direct from the heads of the leading Cover n- 
 metits of the world, in reply to letters sent to them by the Editor. Through 
 the valuable assistance thus given, it has been possible to coded an amount 
 ofinforination, political, statistical, and co>ni/iercial, of the latest date, and 
 of unimpeachable t7-iistzaorthihess, such as 710 publication of the same 
 kind has ever been able to furnish. ^'As indispensable as Bradshazv.'" — 
 Times. 
 
 Monahan.— THE method of LA.W: an Essay on the 
 Statement and Arrangement of the Legal Standard of Conduct. 
 By J. H. Monahan, Q.C. Crown 8vo. 6j. 
 " Will be found valuable by careful law students who have felt the 
 
 importance of gaining clear ideas regarding the relations betiueen the parts 
 
 of the complex organisrn they have to study." — BRITISH QUARTERLY 
 
 Review. 
 
 Paterson. — the liberty of the subject and the 
 
 LAWS OF ENGLAND RELATING TO THE SECURITY 
 OF THE PERSON. Commentaries on. By James Paterson, 
 M.A. , Barrister at Law, sometime Commissioner for Englisli and 
 Irish Fisheries, etc. Cheaper issue. Two Vols. Crown Svo. 21s. 
 ' ' Two or three hours'' dipping into these volumes, not' to say reading them 
 through, will give legislators and stump orators a knoiuledge of the liberty 
 of a citizen of their country, in its principles, its fulness, and its modi- 
 fication, such as they probably in nine rases out of ten nroer had before. " 
 — Scotsman. 
 
 Phillimore. — private LAW AMONG THE ROMANS, 
 from, the Pandects. By John George Phillimore, Q.C. Svo. 
 \(>s. 
 
 Rogers.— COBDEN AND POLITICAL OPINION. By J. E. 
 Thorold Rogers. Svo. loj-. bd. 
 " Will be foundmost useful by politicians of every school, as it forms a 
 sort of handbook to Cobden^s teachittg.^' — Athen^UM. 
 
 Stephen (C. E.)— the service of the poor ; 
 
 Being an Inquiry into the Reasons for and against the EstabHsh- 
 ment of Rehgious Sisterhoods for Charitable Purposes. By 
 Caroline Emilia Stephen. Crown Svo. 6.f. 6d. 
 ** The ablest advocate of a better line of work in this direction that wt 
 have ever seen." — Examiner. 
 
 Stephen. — Works by Sir James F. Stephen, K.C.S.I., O.C. 
 
 A DIGEST OF THE LAW OF EVIDENCE. Third Edition 
 with New Preface. Crown Svo. (ys.
 
 36 MACMILLAN'S CATALOGUE OF 
 
 Stephen . — continued. 
 
 A DIGEST OF THE CRIMINAL LAW. (Crimes and 
 
 Punishments. ) 8vo. i 6j. 
 " We feel sure that any person of ordinary intelligence who had never 
 looked into a law-book in his life might, by a ferv days' careful study of 
 this volume, obtain a more accurate understanding of the criminal law, 
 a more peifect conception of its different bearings a more thorough 
 and intelligent insight into its snares and pitfalls, than an ordinary 
 practitioner can boast of after years of study of the ordinary text- 
 books and practical experiejtce of the Courts unassisted by any competent 
 guide." — Saturday Review. 
 
 A GENERAL VIEW OF THE CRIMINAL LAW OF ENG- 
 LAND. Two Vols. Crown 8vo. \New edition in the press. 
 Stubbs. — VILLAGE POLITICS. Addresses and Sermons on 
 the Labour Question. By C. W. Stubbs, M.A., Vicar of 
 Granborough, Bucks. Extra fcap. 8vo. 3^. dd. 
 
 Thornton. — Works by W. T. Thornton, C.B., Secretary for 
 
 Public Works in the India Office : — 
 ON LABOUR : Its Wrongful Claims and Rightful Dues ; Its 
 
 Actual Present and Possible Future. Second Edition, revised, 
 
 8vo. \dfS. 
 A PLEA FOR PEASANT PROPRIETORS : With the Outlines 
 
 of a Plan for their Establishment in Ireland. New Edition, 
 
 revised. Crown 8vo. 'js. 6d. 
 INDIAN PUBLIC WORKS AND COGNATE INDIAN 
 
 TOPICS. With Map of Indian Railways. Crown 8vo. Ss. 6d. 
 
 Walker. — Works by F. A. Walker, M.A., Ph.D., Professor of 
 Political Economy and History, Yale College : — • 
 THE WAGES QUESTION. A Treatise on Wages and the 
 
 Wages Class. 8vo. 14^. 
 MONEY. 8vo. 16s. 
 
 " It is painstaking, laborious, and states the question in a clear and 
 very intelligible form. . . . The volume possesses a great valtie as a sort 
 of cncyclopccdia of knowledge on the subject'' — Economist. 
 
 Work about the Five Dials. With an Introductory 
 Note by Thomas Carlylk. Crown 8vo. 6j. 
 "^ book 'which abounds with wise and practical suggestions." — PALI, 
 Mall Gazltte.
 
 WORKS ON LANGUAGE. 37 
 
 WORKSCONNECTED WITH THE SCIENCE 
 OR THE HISTORY OF LANGUAGE. 
 
 Abbott.— A SHAKESPERIAN GRAMMAR : An Attempt to 
 illustrate some of the Differences between Elizabethan and Modern 
 English. By the Rev. E. A. Abbott, D.D., Head Master of the 
 City of London School. New and Enlarged Edition. Extra 
 fcap. 8vo. 6s. 
 " Valuable not only as an aid to the critical study of Shakespeare, 
 
 but as tending to familiarize the reader with Elizabethan English ?« 
 
 general. " — Athen^um. 
 
 Besant.— STUDIES IN EARLY FRENCH POETRY. By 
 Walter Besant, M.A, Crown 8vo. 8j. 6d. 
 
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