Sept. 19, 1889J 



NA TURE 



501 



popularly suspected of complicity with crime, would do well to 

 lake every opportunity of clearing themselves from that imputa- 

 tion, so the mathematical economist is called on to disown em- 

 pliatically all sympathy with the ilagrant abuses to which the 

 injudicious use of abstract reasoning is undoubtedly liable. 



To ccnlinue the comparison which I was instituting between 

 the mathematical theory of economics and the calculus of prob- 

 abilities, they have one very unpleasant property in common — 

 a liability to slips. As De Morgan says,^ " Everybody makes 

 errors in probabilities at times, and big ones." He goes on to 

 mention a mistake committed by both Laplace and Poisson, the 

 ineptitude of which he can only parallel by the reasoning of a 

 little girl whom he had called a " daughter of Eve" ; to which 

 she retorted, " Then you must be a daughter of Adam." It is 

 not to be concealed that economic reasoning, even in its severest 

 form, is sometimes equally inconsequent. I should have hesitated 

 to assert that Cournot has made some serious mistakes in mathe- 

 matics applied to political economy, but that the authority of the 

 eminent mathematician Bertrand "■' may be cited in support of 

 that assertion. 



Again, the more abstract theories of value and of probabilities 

 seem to resemble each other in their distance from the beaten 

 curriculum. Each forms, as it were, a little isolated field on 

 the rarely crossed frontier and almost inaccessible 

 watershed between the moral and the physical 

 sciences. 



The same character of remoteness belongs per- 

 haps to another province, which is also comparable 

 with ours — the mathematical side of formal logic, 

 the symbolic laws of thought which Boole formu- 

 lated. There was a certain congruity between 

 Tevons's interest in his logical machine and in 

 what he called the "mechanics of industry." But 

 I venture to regard the latter pursuit as much more 

 liberal and useful than any species of syllogism- 

 grinding. 



If you accept these parallels, you will perhaps 

 come to the conclusion that the mathematical theory 

 of political economy is a study much more important 

 than many of the curious refinements which have 

 occupied the ingenuity of scientific men ; that as 

 compared with a great part of logic and metaphysics 

 it has an intimate relation to life and practice ; that, 

 as a means of discovering truth and an educational 

 discipline, it is on a level with the more theoretical 

 part of statistics ; while it falls far short of mixed 

 mathematics in general in respect of that sort of 

 pre-established harmony between the subject-matter 

 and the reasoning which makes mathematical physics 

 the most perfect type of applied science. 



But we must remember — and the mention of the 

 theory of probabilities may remind us— that any such 

 judgment is liable to considerable error. We cannot 

 hope to measure the utility of a study with pre- 

 cision, but rather to indicate the estimate on either 

 side of which competent judges would diverge — a 

 central point, which will be found, if I mistake not, 

 equally removed from the position of Gossen, who 

 compares the new science to astronomy, and the 

 attitude of Dr. Ingram towards the researches which 

 he regards as nothing more than "academic play- 

 things, and which involve the very real evil of restoring the meta- 

 physical entities previously discarded." ^ 



One more general caution is suggested by another of the 

 technical terms which we have employed. What we are con- 

 cerned to discover is not so much whether mathematical reason- 

 ing is useful, but what is its " final utility " as compared with 

 other means of research. It is likely that a certain amount of 

 mathematical discipline — say as much as Mr. Wicksteed imparts 

 in his excellent "Alphabet of Economic Science"— is a more 

 valuable acquisition to a mind already stored with facts than the 

 addition of a little more historical knowledge. 



But, in reverting to the subject of final utility, I am reminded 

 that Presidential addresses, like other things, are subject to this 

 law ; and that a discourse on method prolonged beyond the 



> Writing to Rowan Hamilton (" Life of Hamilton," by R. Graves, 

 vol. iii.). 



' Journal ties Savants, 18S3. I hope to show oA some future occasion 

 that M. Bertrand's censures of Cournot and Prof Walras .ire far too severe. 

 • u^^f '^"^ passage relating to Jevons in the article on '" Political Economy " 

 111 the " Eucycloptuiia Britannica," ninth edition. 



patience of the hearers is apt to become what Jevons called a 



discommodity. 



NOTES. 



{a) SiMi'LE Exchange. — The simplest case of exchange is 

 where there are two large groups of uncombincd individuals 

 dealing respectively in two commodities, e.i^. corn and money. 

 To represent the play of demand and supply, let any abscissa, 

 Ox in Fig. i, represent a certain price, and let the quantity of 

 commodity demanded at that price be xp. The locus of / may 

 be called the demand-curve. Similarly, X(j represents the 

 quantity offered at any price, O.v ; and the locus of q is called 

 the supply-curve. The price Oa, at which the demand is just 

 equalled by the supply, is determined by the intersection of these 

 ctirves. This is Cournol's construction. The converse construc- 

 tion, in which the abscissa stands for quantity of commodity, the 

 ordinate for price, is employed by Mr. Wicksteed in his excellent 

 " Alphabet of Economic Science." 



The diagrammatic representation which most closely cor- 

 responds to Jevons's formulae is that which the present writer, 

 after Prof. Mar.-hall, and Messrs. Auspitz and Lieben, inde- 

 pendently, has adopted. In this construction the two co- 

 ordinates respectively and symmetrically represent the quantities 



Fig. I. 



of the two commodities exchanged, the quid and the fro quo. 

 For instance. Fig. 2 may represent the state of supply and 

 demand in the international market between Germany and 

 England. The curve OE denotes that in exchange for any 

 amount of " linen," Oy, England is prepared to supply the 

 quafity of " cloth " yp ( = Ox) ; or, in other words, that in ex- 

 change for the quantity O^ of cloth England demands xp ( = O^') 

 of linen. The curve OG is similarly related to Germany's supply 

 and demand. The position of equilibrium is determined by the 

 intersection of these curves. 



{!)) Variations i.\ Supply. — Suppose, as Mill supposes 

 (" Pol. Econ.," book iii. ch. xviii. § 5), that there has occurred 

 an improvement in the art of producing Germany's export, 

 linen. The altered conditions of supply may be represented by 

 the displaced curve OG', Fig. 3, indicating that, whereas before 

 the improvement Germany in exchange for any (juautity, Ox, of 

 cloth offered only xq, she now offers xq'. The effect of the im- 

 proveirient on the rate of exchange will depend upon the form of 

 the curve OE beyond the point r. If the< intersection of the 



