496 



NA TURE 



{Sept. 19, 1889 



this paper, the discovery of steam as a motive power has brought 

 the world into an extraordinary condition of contactiveness, and 

 quite recently several new companies have been formed in the 

 same spirit and on the same lines as those followed by the old 

 merchant adventurers. These later creations are being started 

 under more favourable conditions than their predece'^sors, for 

 they have all the advantages which modern science and modern 

 appliances can afford. The Englisli Government have wisely 

 encouraged and promoted the formation of these trading 

 corporations. In countries where climate and circumstances of 

 environment are not favourable to colonization by white men, 

 our colonial system of government progresses somewhat slowly. 

 It has not the elnsticity, nor the adaptability, to provide for the 

 many contingencies which must naturally arise when a few white 

 men maintain the position of rulers over large areas, peopled by 

 savage and uncivilized races. 



In the Island of Borneo there is the North Borneo Company 

 trading, governing, and civilizing a large portion of territory 

 with marked succc-s. 



On the west coast of Africa, the Royal Niger Company is 

 developing the great natural resouices of thai magnificent river, 

 and its tributary the Binue. 



On the east coast there is the Imperial British East African 

 Company, operating in what is known as the British sphere of 

 influence north of Zanzibar. Though not a twelvemonth has 

 passed since they commenced their work, their initiatory pro- 

 ceedings have been remarkably successful, and there is every 

 prospect of an early and rapid development of the territory 

 committed to their charge. In thi south-eastern portion of 

 Central Africa, the African Lakes Company have fairly estab- 

 lished themselves ; and a new company is now being formed to 

 open up and civilize a further portion of that section of the 

 African continent. 



The establishment of these great trading and governing centres 

 is likely to exercise most important influences. They are, as I 

 have before pointed out, from their organization and objects, 

 better adapted at the outset to compete with and overcome the 

 obstacles which present themselves to established forms of 

 bureaucratic government ; at the same time the Government of 

 this country can interfere in cases of necessity, by the grants that 

 have been made to them of Royal Charters, under which they 

 carry on their operations. 



A wise control and judicious administration combined with 

 the introduction of commerce and civilization will, at no distant 

 da.te, open these territories to the markets of the world, to the 

 missionary, and to the scientific explorer. The commercial 

 element of geography also enters very largely into their 

 promotion and prosperity because of the fields they open to our 

 home manufactures. It is important here to observe that, if 

 these territories had passed into the hands of other nationalities, 

 but a very limited quantity of British goods would ever have 

 entered into them, and their value, as a market for the industries 

 of the nation, would have been lost. 



The establishment of a Geographical Society in this city is of 

 real importance. Its objects should be the collection of infor- 

 mation, and the study of applied geography in all its varied 

 branches and aspects. It should aim to furnish complete infor- 

 mation concerning the geography of all parts of the globe. In 

 Chambers of Commerce our large trade centres have, no doubt, 

 means of guiding and controlling some of our most important 

 mercantile operations, but they afford no opportunities to the 

 student, they are not teaching bodies ; and there are instances 

 where considerable risks have been incurred and heavy losses 

 sustained in some of their ventures, simply from a want of 

 knowledge of geographical data. 



I should like to see a Geographical Society in every large city 

 of this Empire, conducted on the lines I have briefly suggested, 

 because the study of, and interest in, the commercial geography 

 of this great Empire and the world is too much neglected 

 amongst us. Past prosperity, and a tendency to run in the same 

 groove, narrow our commercial horizon. Slowly, but surely, 

 other nations, competing with us in many parts of the world, 

 are doing so successfully because of the study they make of 

 commercial geography. 



It is for this reason I have in my address dwelt strongly upon 

 the question and study of geography as an applied science, and 

 it is for a greater reason I urge its importance, viz. that we 

 may hand down to our children unimpaired the heritage be- 

 queathed us by our forefathers ; a heritage gained by courage, 



energy, perseverance, and patriotism— qualities which, unde^ 

 Gods blessmg, have made this nation the head of the commerce 

 of the world. 



SECTION F. 



ECONOMIC SCIENCE AND STATISTICS. 



Opening Address by Prof. F. Y. Edgeworth, M.A., 

 F.S.S., President of the Section, 



Points at which mathematical reasoning is applicable to 



political economy — 

 A. — Perfect competition — 



1. Simplest type of market. 



2. Complex system of markets ; simplified by certain 



abstractions. 



3. The rnore concrete problem of an exchange and 



distribution. 

 B. — Monopoly — 



1. Transactions between a single monopolist and a 



competing public. 



2. Transactions between two monopolists or combina- 



tions. 



The use of these applications of mathematics to political 

 economy illustrated by comparison with— 



1. Applied mathematics generally. 



2. The mathematical theory of statistics. 

 Conclusion. 



At the meeting of the British Association which was held at 

 Cambridge about a quarter of a century ago, Jevons submitted 

 to this Section a "general mathematical theory of political 

 economy," which, as he himself records, was "received without 

 a word of interest or belief." I propose to consider the justice 

 of the unfavourable verdict which our predecessors appear 

 to have passed on the mathematical method introduced by 

 Jevons. 



There is some difficulty in discussing so abstruse a subject in 

 this place. It is as if one should discourse on the advantages of 

 classical education on an occasion on which it might seem 

 pedantic to cite the learned languages. I shall evade this diffi- 

 culty by addressing to students some appended notes,^ which, 

 like the boy of proverb, are to be seen, not heard. 



The cardinal article of Jevons's theory is that the value in 

 exchange of a commodity measures, or corresponds to, the utility 

 of the least useful portion of that commodity. What a person 

 pays per month or year for a sack or ton of coal is not what he 

 would be willing to give for the same rather than be without 

 fuel altogether. Rather the price is proportioned to the 

 advantage which the consumer expects from the portion which 

 he could best dispense with— to the "final utility," in Jevons's 

 happy phrase. 



I shall not be expected here to dwell on a subject which has 

 been elucidated in treatises of world-wide reputation, such as 

 those of Profs. Marshall, Sidgwick, Walker, and I would add 

 Prof, Nicholson's article on "Value" in the " Encyclopaedia Bri- 

 tannica." Those writers seem to present what I may call the 

 economical kernel of Jevons's theory divested of the mathe- 

 matical shell in which it was originally inclosed ; whereas my 

 object is to consider the use of that shell — whether it is to be 

 regarded as a protection or an encumbrance. 



I may begin by removing an objection which the mere state- 

 ment of the question raises. The idea of reducing human 

 actions to mathematical rule may present itself to common-sense 

 as absurd. One is reminded of Swift's " Laputa," where the 

 beef was cut into rhomboids and the pudding into a cycloid, and 

 the tailor constructed a very ill-fitting suit of clothes by means 

 of rule and compasses. It should be understood, however, that 

 the new method of economical reasoning does not claim more 

 precision than what has long been conceded to another depart- 

 ment of science applied to human affairs — namely, statistics. It 

 is now a commonplace that actions such as suicide or marriage, 

 springing from the most capricious motives, and in respect of 

 which the conduct of individuals most defies prediction, may yet, 

 when taken in the aggregate, be regarded as constant and uni- 



» The appended notes are referred to by letters of the alphabet, thus : (a). 



