October 1, 1886.] 



SCIEmjM. 



311 



suits, the methods of arriving at them, often in- 

 genious and depending on a refined analysis of 

 the subject-matter, seem to us of decided interest 

 to any who may be considering the part which 

 mathematical methods are capable of taking in 

 the development of economic science. We can- 

 not here enter upon a discussion of this general 

 question ; but we may be permitted to say that 

 we do not look forward to their giving important 

 direct aid in the investigation of the fundamental 

 questions of economics, though they may, when 

 the science has reached a more advanced stage, 

 be useful in the more minute discussion of special 

 problems. In a certain indirect and incidental 

 way, we think that mathematical inqtiiry may be 

 useful even to the fundamental theory ; for the 

 necessity under which the mathematician lies, of 

 clearly and exactly comprehending his premises, 

 will doubtless in some instances bring about a 

 more accurate view of economic phenomena. 

 Upon the mathematical economists themselves, 

 this necessity of accurate definition is apt to act 

 in a most harmful manner, as their writings abun- 

 dantly prove. When they have got hold of a 

 notion which lends itself to mathematical treat- 

 ment, the temptation is very great to unduly ex- 

 tend its province. Jevons's theory of utility in 

 relation to value is a conspicuous example of these 

 merits and defects. While the accurate analysis 

 of some features of the phenomena of value whijh 

 was a necessary preliminary to the mathematical 

 discussion has -been useful to economists in gen- 

 eral, the result^ reached by the mathematical 

 theory are open to the gravest objections ; and 

 this quite apart from any subsidiary defects, such 

 as those occurring in some of Launhardt's discus- 

 sions, as pointed out above. In the mathematical 

 development of the theory, its exponents overlook 

 two capital points, — first, that, under a regime of 

 separation of employments, the direct utility of a 

 product to its producer has little or no signifi- 

 cance ; secondly, that, when an addition to the 

 amount of a given commodity supplies with it a 

 new class of individuals who formerly could not 

 possess it, the utility thus arising is very different 

 — and, if measurable at all, its amount follows a 

 very different law — from that which arises from 

 an increase in the quantity possessed by those 

 who were already provided with the commodity. 

 We have not left ourselves space to speak of 

 other points, some of them very interesting, in the 

 section on exchange, nor to make more than a 

 passing mention of the other two sections, on pro- 

 duction and transportation respectively. On the 

 subject of money, the author takes, in our opinion, 

 a very erroneous view. In the section on trans- 

 portation, the mathematical premises come nearer 



than almost anywhere else to a representation of 

 the actual problem : a large part of the questions 

 there discussed are, in fact, such as are necessarily 

 considered in an essentially mathematical way, 

 though doubtless with little scientific method, by 

 railroad managers. A satisfactory idea of tlie 

 book can only be obtained by reading it. For the 

 benefit of those who may contemplate dohig so, 

 we may state that a knowledge of the first ele- 

 ments of the differential calculus will make the 

 little volume of two hundred pages sufficiently 

 easy reading. 



THE POPULATION OF MEDIAEVAL CITIES. 



Social science has certain problems of recon- 

 structing past conditions out of fragmentary re- 

 mains, which are analogous to that reconstruction 

 of terrestrial life and conditions which has been the 

 tx'iumph of modern natural science. History does 

 not now content itself with a mere narration of 

 events, but strives to portray the whole social con- 

 dition of the people, — to give a vivid picture of 

 society as it existed at the time. Modei-n histori- 

 cal writing has accomplished this to a greater or 

 less extent, and the rcoult is that our histories are 

 histories of the people rather than of dynasties. 



In one particular, however, this reproduction is 

 incomplete. The historians do not give us exact 

 statistical details of the relations of population, 

 industry, commerce, etc., without which any de- 

 scription of a modern community would be con- 

 sidered entirely incomi^lete. It is impossible for 

 them to do so, because such statistical investiga- 

 tions are entuely modern, most of them reaching 

 back only to the beginning of this century. In 

 former times there were no statistical bureaus, 

 no census of the people, no returns of trade and 

 commerce. There was no demand for such in- 

 formation, either for governmental or scientific 

 purposes. It is notorious that ancient and medi- 

 aeval writers had no sense for numbers. The 

 figures they give of the strength of armies or 

 the population of cities are mere estimates, and on 

 the face of them are often obvious exaggerations. 

 One of the most difficult problems the historian 

 has before him, i.3 to weigh the statements of dif- 

 ferent writers as to the number of people con- 

 cerned in any event, and very few purely literary 

 historians have the requisite scientific training for 

 such work. 



The pure historian must here appeal to the pro- 

 fessional statistician for help. The acute and 

 learned work of which we give the title is an ex- 

 ample of what German industry can accomplish 



Die volkszahl deutscher stadte zu ende der mittelalters 

 und zu beginn der neuzeit. Von J. Jastrow. Berlin, 

 Gaertner,lSSG. 8°. 



