242 



NATURE 



{July II, 1889 



Werner's narrative presents a new geographical feature, 

 the warrant for which has probably by this tinrie been 

 confirmed or disallowed. But the chief interest attaching 

 to the book arises from the description of living persons^ 

 European or native, who take, or have taken, part in the 

 story of the Congo Free State. The narrative may not 

 always be as gratifying as truthful ; nor is the record of that 

 kind of warfare which tells us of the shooting of natives as 

 though they were but large game, quite pleasant reading ; 

 but allowance must be made for unrecorded provocations 

 and exigencies, and let us hope that conciliation will 

 have a wider field for exercise when the harder obstacles 

 to peaceful settlement shall have been removed. No civil- 

 ized being could wish for the renewal of days such as those 

 in which Mr. Werner " saw more than one poor wretch 

 put up his shield, only just in time to receive a ball right 

 through it and himself as well, and come rolling down the 

 clay bank into the river, dead as a door-nail." The 

 author has dwelt, moreover, upon a passage in his own 

 particular career which cannot but leave a painful impres- 

 sion on the mind of his reader. He had been told that 

 Tippoo Tip had threatened mischief to Major Barttelot 

 if certain conditions were unfulfilled, and he had been 

 restrained by circumstances from communicating intel- 

 ligence of the threat to that gallant and lamented officer. 

 It is easy to understand how this non-revelation of fore- 

 shadowed ill haunted his brain, and how mental distress 

 became aggravated by the sad news of Major Barttelot's 

 death ; but he may well derive consolation from the 

 conviction that the reported threat was the outcome of a 

 state of things which must have been fairly appreciated 

 by all Europeans in those days encamped in the neigh- 

 bourhood of Stanley Falls. 



Mr. Werner is no doubt right in assuming that 

 " facility of transport to the coast by means of railways 

 and steamers will do more, by making slave- caravans 

 unprofitable, to put down the curse of Africa," than the 

 extinction of elephants — an hypothesis much favoured by 

 recent writers. Were steam once made available for 

 traffic along the main thoroughfares of the Dark 

 Continent, the necessity for the employment of slaves in 

 the conveyance of ivory would naturally cease, and one 

 source of evil would thus be stopped by the mere force of 

 circumstances— means quite as efficacious as, and more 

 satisfactory than, armed intervention. In the final chap- 

 ter the author considers with much intelligence and 

 practical sagacity the different lines of communication 

 now being opened out between the coast and the interior 

 of Africa. These are notably, on the east, a land and 

 water route from Uganda to the sea-mouth of the Tana 

 River, passing through or skirting the possessions of the 

 British East African Company : to the westward, the 

 proposed railway to facilitate traffic between Banana and 

 Stanley Falls; and, on the south, communications develop- 

 ing under the far from insignificant agency of the African 

 Lakes Company. Truly, European enterprise is astir in 

 the land ; and England, the party most interested in the 

 movement, if she remain content to be the most re- 

 sponsible speculator in its risks, should further seek to 

 become the most important participator in its benefits. 



The attraction of this volume is enhanced by photo- 

 graphs and illustrations. Stanley's likeness is excellent, 

 and the sketch of Mata Bwyki highly characteristic. 



THE MATHEMATICAL METHOD IN 

 POLITICAL ECONOMY. 



Uiitersuchiingen iiber die Theorie des Prcises. Von 

 Rudolf Auspitz und Richard Lieben. (Liepzig : Verlag 

 von Duncker und Humblot, 1889.) 



THE usefulness of mathematical reasoning applied to- 

 political economy, the value of the methods origi- 

 nated by Cournot and developed by Jevons, may be 

 said to be still sub judice. The consideration of Messrs. 

 Auspitz and Lieben's diagrams and symbols tends to 

 confirm the opinion that mathematical analysis is a 

 potent, if not an indispensable, means of obtaining clear 

 general ideas in economics. The metaphysician who 

 twists and turns the terms force and energy without 

 grasping their mathematical signification is not more 

 likely to become entangled in his talk than the practical 

 man who reasons about supply and demand, and cost and 

 value, without having once for all considered the ideas in 

 their clearest and most abstract form. For the purpose 

 of this contemplation Messrs Auspitz and Lieben employ 

 a construction differing from most of their predecessors ; 

 namely, a figure in which the abscissa represents the 

 quantity of a certain commodity, the ordinate the amount 

 of some other article— in particular, money — which is ex- 

 changed for that which the abscissa represents. We 

 cannot, however, quite admit the state.nent : " Unsere 

 Kurven unterscheiden sich schon durch die zu Grunde 

 gelegten Koordinaten von Jenen unserer Vorganger.'- The 

 same construction is used in the papers of an eminent 

 English Professor, which, though unpublished, have been 

 widely circulated in the learned world. It has also 

 appeared in at least one English publication, ]\lr. Edge- 

 worth's " Mathematical Psychics," with due acknowledg- 

 ment to the distinguished originator. 



However, our authors have made the construction their 

 own by many important developments. They employ, 

 in addition to demand and supply curves, a less familiar 

 locus, which may be thus described. In the accompany- 

 ing diagram let any abscissa, O Q, represent a quantity of a 



certain commodity ; and let Q R represent the amount of 

 money which a consumer would be just willing to give in 

 exchange for the commodity OQ: in such wise that it 

 would be indiff'erent to him whether he procured O Q on 

 such terms, or did not consume the article at all. The 

 locus of this point O N is called the utility curve. Corre- 

 lated with this primary curve is the demand curve o n'. 



