Sept. 29, 1887] 



NATURE 



507 



authorities on European lands is especially noticeable. 

 We are aware that this is intentional on the part of the 

 author, but we hardly think that he has been well advised. 

 It is among the multitude of modern books of travel, for 

 the most part indifferent or bad, that guidance would be 

 most valuable. H. J. Mackinder. 



OUR BOOK SHELF. 



Chemistry and Heat. By R. G. Durrant, M.A., F.C.S. 

 (London: Rivingtons, 1887.) 



This little book is a collection of laws and definitions 

 connected with chemistry and heat, intended more espe- 

 cially for the use of students preparing for examination 

 in these subjects. It is to be regarded chiefly as a com- 

 panion to more extensive treatises, and as a substitute for 

 the extracts and notes which the average student would 

 make for himself. 



The various laws are stated very clearly, and the 

 examples illustrating them have been happily chosen. 

 The subject of heat is only considered in so far as it 

 enters into chemical work. The laws relating to atomic 

 weights are particularly well arranged, and zinc being 

 taken as a typical element, a whole chapter is devoted to 

 the method of estimating its atomic weight. A chapter 

 is also devoted to the determination of vapour densities 

 by the well-known methods of Dumas, Hofmann, and 

 Victor Meyer, each being illustrated by a numerical 

 example. In all cases the details of the calculations are 

 gone through with great care. 



At the end of the book is a table showing the charac- 

 teristic tests for the more important metals and acids. 

 This is not nearly up to the same standard as the earlier 

 part of the book, but still it will be of service where expe- 

 dition is of maximum importance. We are afraid, hew- 

 ever, that the results obtained by analyses without 

 separations would not always be perfectly trustworthy. We 

 should have expected the author to be aware that separa- 

 tions are indispensable for most examinations in practical 

 chemistry. Several specimens of analyses are given in 

 detail. 



We have no doubt that the book will prove a useful 

 addition to the already large family of hand-books pre- 

 pared for the use of the fortunate student of chemistry. 



• A. F. 



On Overwork and Premature Mental Decay. By C 

 H. F. Routh, M.D., M.R.C.P. Fourth Edition. 

 (London : Bailli^re, Tindall, and Cox.) 



Dr. Routh takes a very gloomy view of some of the 

 characteristics of the present age. He holds that in- 

 sanity and premature mental decay are decidedly on the 

 increase, and this fact he attributes chiefly to overwork. 

 Whether or not he is correct in his interpretation of the 

 statistics relating to insanity, there can be no doubt that 

 overwork is far too common in these days of excessive 

 competition, and Dr. Routh has done good service by 

 showing clearly in this little book the inevitable conse- 

 quences of any severe and continuous strain upon the 

 powers either of the mind or the body. As to remedies 

 for the evil consequences of overwork, he offers many 

 wise suggestions, and prudent readers will probably be 

 all the more inclined to pay attention to his counsels 

 when they find that he lays stress mainly upon the neces- 

 sity for periods of rest, for the cultivation of a variety of 

 intellectual interests, and for rigid self-control. Dr. Routh 

 has added to the value of his work by discussing in the 

 I present edition the efiects of overwork upon women and 

 young persons. 



LETTERS TO THE EDITOR. 



[The Editor Joes not hold himself responsible for opinions 

 expressed by his correspondents. Neither can he under- 

 take to return, or to correspond with the writers of, 

 rejected manuscripts. No notice is taken of anonymous 

 com m unications. 



[The Editor urgently requests correspondents to keep their 

 letters as short as possible. The pressure on his space 

 is so great that it is impossible otherwise to insure the 

 appearance roen of com?nuni(cUions containing interesting 

 and novel facts. "[ 



Hall and Knight's " Higher Algebra." 



In your issue of September i (p. 409), there appeared a review of 

 our " Higher Algebra," bearing the signature " R. B. H." The 

 work under consideration is a sequel to an elementary text-book, 

 as the title-page asserts ; it does not profess to be anything more, 

 and we should have thought that any reader would have recog- 

 nized that "Higher" and "Elementary" are merely used as 

 relative terms. This point has been practically ignored by your 

 reviewer, and in consequence his remarks contain certain 

 inaccuracies and misconceptions likely to leave a false im- 

 pression on the mind of the reader. 



In the first place, " R. B. H." complains that we postpone 

 to our thirty fourth chapter the discussion of the fundamental 

 laws of algebra, the "remainder theorem," symmetrical expres- 

 sions, and identities. As a matter of fact, these things do not 

 appear here "for the first time;" propositions scattered over 

 the "Elementary Algebra" are here summarized, and in some 

 cases rediscussed ; and, with regard to the "remainder theorem," 

 its proof and easy applications are to be found in the twenty-ninth 

 chapter of the elementary work — a chapter which also contains a 

 section on identities and transformations, especially those which 

 can be treated cyclically. Hence, in criticising the miscellaneous 

 chapter of the more advanced work, it should be remembered 

 that for the most part it merely extends and develops what has 

 elsewhere already been treated far more comprehensively than is 

 usual in an Elementary Algebra. 



In the chapter on " Miscellaneous Equations," we are told 

 that " there is no hint or caution given that the root obtained 

 may not satisfy the original equation unless the sign of one or 

 iDore of the radicals involved in it is changed," and our attention 

 is called to an example on p. 99. Surely " R. B. H." must 

 have read this page somewhat carelessly, for at the head of it 

 there stands a remark containing the required hint, while 

 reference is made to a note in the " Elementary Algebra," in 

 which the point is fully discussed. 



The remarks on our chapter on permutations and combinations 

 are somewhat vague and indefinite, and we do not gather which 

 proofs are held to be " very difficult to understand." We have 

 used the methods of this chapter very successfully with boys 

 of ordinary intelligence for twelve years or more, and we have 

 always found the proofs contained in Arts. 141, 152, 153, 

 and 156 far more intelligible than those given in other text-books. 

 The illustration given by " R. B. H." may be useful enough for 

 blackboard work, and it is hardly conceivable that any teacher 

 of experience would attempt to handle this part of algebra with- 

 out a frequent and ready use of such exemplification ; but we 

 fail to see how a proof oi the general formula for the number of 

 permutations of n things & together could be framed on these lines 

 in a form suitable for a text-book. 



To the other points raised by your reviewer we do not reply 

 because they are mostly matters of opinion, and whether we 

 have been judicious in our arrangement and subdivision of the 

 subject is a question which can only be decided by the ex- 

 perience of teachers using our books. But we may perhaps 

 remark that the obvious necessities of a school text-book should 

 not be overlooked. In its present form our "Elementary 

 Algebra " contains upwards of 360 pages, and if we had included 

 all the sections now suggested by " R. B. H." the book would 

 have been increased by 150 pages or more, and would have been 

 practically useless, for it would have been published at a price 

 quite prohibitive for school use. 



Our two books have been designed to form one complete 

 treatise, and we venture to think that anyone who will fairly 

 criticise the work as a whole will not find the glaring omissions 

 and " defect of plan" suggested by your reviewer. 



-H. S. Hall. 

 S. R. Knight. 



