Dec. 2 1, 1876] 



NA TURE 



155 



listener, with a fuller and clearer knowledge of the 

 Amazon and its tributaries, its basin, its products, its 

 people, its cities, and fragments of towns, its industries, 

 and its probable future, than he could get from reading 

 many other books. The second part especially, contain- 

 ing the results of the journey of 1873 systematically ar- 

 ranged, will be found extremely handy and valuable by 

 anyone who desires in brief space a general view of the 

 physical geography, natural history, ethnology, industrial 

 resources, commerce, prospects, and scenery of the vast 

 Amazonian region. Prof. Orton has evidently supple- 

 mented his personal knowledge of the region by an 

 extensive study of the contributions of others who have 

 written on the subject, so that while the classical works of 

 Bates and others, as well as the special papers of Prof. 

 Orton himself, will be resorted to by those who desire 

 to make a thorough study of the Amazonian basin, we 

 know of no single work containing a fuller, more bril- 

 liantly written, and at the same time more trustworthy 

 general account of the basin of the Amazon and its many 

 wonders. The following extract on the density of 

 population in the Amazonian valley will give our readers 

 some idea of the style of the work : — 



'•'• The valley of the Amazons is probably the most 

 thinly-peopled region on the globe, save the great deserts 

 and the polar zones. There are not 40,000 souls along 

 the banks of the rivers in the whole province of Ama- 

 zonas and the Lower Maraiion. Many cf the towns 

 marked on the maps do not exist, or are represented by 

 a solitary palm-hut. The visible population is almost 

 confined to the circumference of the valley ; as at Pard, 

 near the mouth of the river ; at Moyobamba and Tara- 

 poto, on the oriental side of the Andes ; and at Trinidad, 

 Santa Cruz, Cochabamba, and La Paz, on the head-waters 

 of the Madeira. The great basin is filled with a con- 

 tinuous, dark, primeval forest, rarely disturbed by the 

 hand of man, and into which daylight seldom enters. 

 Yet imagination peoples this pathless wilderness with un- 

 counted swarms of savages. There are, it is true, nume- 

 rous clans (we can hardly call them tribes) of Indians, 

 distinct in language, and often hostile toward each other. 

 But many of these so-called tribes, though dignified with 

 separate names, are insignificant in numbers, barely 

 mustering a hundred ; while the Mundurucii, the largest 

 known tribe in the valley, does not exceed 8,000— men, 

 women, and children. Nor are there any remains of 

 ancient walls to indicate a bygone civilisation, or even 

 shell-heaps in memory of a more primitive race. 



" Until the close of the Tertiary age the waters pre- 

 vailed over this heart of the continent ; and since then 

 vegetation has had the mastery, leaving little chance for 

 animal life. And until there is a decided change in the 

 physical geography of the valley, a large part of it must 

 remain unfit for permanent settlement, on account of the 

 annual floods ; for a rise of 40 feet in the river drives the 

 inhabitants from their summer resorts on the margin of 



■the streams to the higher terra Jirma within the forest. 

 In this way nomadic habits are engendered or perpetuated, 

 and poverty is almost inevitable, for half the year (flood- 

 time) it is hard work to get a living. Furthermore, this 

 regular inundation of the country and the lack of grassy 



Kampos (except on the Lower Amazons and the Btni 

 sgion) prevent the raising of domesticated animals, 

 which, if it does not lie at the foundation of agriculture, 

 certainly does aid in the transition from the savage to a 

 semi-civihsed state. In this respect the natives of Cen- 

 tral Asia and Africa, as well as the maize-eating tribes of 

 the Andes, have an advantage over the mandioca-eating 

 Indians on the Amazons." 



While minute criticism might find many statements 



and hypotheses in Prof. Orton's work to challenge ; while 

 some of his chapters may be considered by the lover of 

 severity of style as intolerably florid ; while in short any- 

 one who has a mind to might find something to object 

 to, we are sure that all into whose hands the work may 

 fall will agiee that few more attractive and at the same 

 time more instructive works of travel have been written. 

 Pror. Orton seems to anticipate that ere long the Amazon 

 will become a highway for tourists, as it well might — even 

 now it has a considerable service of steamers— and there- 

 fore gives many hints, directions, and statements of 

 expense that render his work valuable as a guide-book. 

 Not the least attractive feature are the many well- 

 executed illustrations of places, people, scenery, and 

 animal and plant life that enrich the volume. Two large 

 maps, one of the Maraiion and its tributaries and the 

 other of Equatorial America, add to the value of the 

 work, which will doubtless be brought within reach of 

 the English reading public by some enterprising pub- 

 lisher. 



OUR BOOK SHELF 



The Secret of the Circle, its Area Ascertained. By Alick 

 Carrick. Second Edition. (H. Sotheran and Co., 

 1876.) 



The Impossible Problem. By James Alexander Smith. 

 Printed for the Author's Use. (Shaw and Sons, 1876.) 



The only difference we have been able to detect between 

 this edition and its predecessor are that the last lines of 

 pp. 34 to 38 of the first edition are the first lines of pp. 

 35 to 39 of the second edition, with the corresponding 

 changes of the other lines of the several pages, that a 

 date has been omitted on p. 39, and fig. 2 on p. 41 shghtly 

 modified. With our copy we were favoured with a 

 number of J he Welshman (Sept. 29, 1876) containing 

 a very long notice of it, supplied to the editor of the 

 paper by an enthusiastic admirer of the work. An extract 

 or two will sufficiently illustrate the article. " Don't let 

 the reader run away with the idea that this is a prelude 

 to any long, complicated calculations, understandable only 

 by the initiated. As simple as truth itself, when ascer- 

 tained, the solution of this problem is as easy and capable 

 of absolute proof as any ordinary sum in addition and 

 subtraction." "This beautiful problem and mystery that 

 has tempted, attracted, and defeated the skill of thou- 

 sands of the most subtle and far-seeing minds for thou- 

 sands of years is found, when looked at in the right way, 

 to be as easy and as simple as the alphabet." " It will 

 not suffice for mathematicians to endeavour to show by 

 any fallible and inadequate system of computation now in 

 vogue that this result cannot be. The reader can judge 

 for himself." 



We in our former notice pointed out what we considered 

 defective in Mr. Carrick's proof. The work is a posthumous 

 one, hence it is that the second edition has experienced no 

 revision at the author's hands. 



Mr. Smith, in his pamphlet (8 pp.), arrives at the same 

 result as Mr. Carrick, viz., that rr = 3^, or the area of the 

 circle equals | of the square of the diameter -\- ^ oi that 

 square. The roads pursued are different. 



Though we cannot agree with Mr. Smith, we have read 

 his work with some interest, for there are some neat little 

 pieces of simple construction in it. His equations on 

 p. 5 may be put into the more general form : — 



to = {?,+P)x,y = (I +p)x,z = (I + 2P) X. 



We have not been able to see if other values would 

 satisfy his equations besides the one he has selected, 

 which leads him to draw the conclusion he does. 



