582 



NA TURE 



[Oct. 21, i! 



tions in practical cremistrj- are generally conducted are 

 probably largely to blame for this unsatisfactoriness. Exa- 

 miners require aknowledge of the separation andidentifica- 

 tion of organic acids, in addition to the ordinary power of 

 analysing a mixture of inorganic substances ; one day is 

 probably considered sufticient time to devote to the exami- 

 nation. Candidates must make themselves acquainted 

 with a few of the tests for organic acids ; they find these 

 in all the text-books of analysis ; they repeat the tests, 

 and manage to stumble through the examination. The 

 truth is that the detection of organic compounds, even 

 when but a few of these arc present, is far too complex 

 and difficult a process for repetition in the hurry and 

 bustle of the examination-room. Were all organic 

 compounds omitted from the examinations in practical 

 chemistry at the leading schools of medicine and science, 

 we have no doubt that in a few years the processes for 

 detecting these compounds would be largely improved. 



We should strongly advise all students who wish to 

 acquire just that amount of knowledge of organic analysis 

 which may perhaps enable them to pass an examination 

 not to procure Dr. Barfoed's book, and as strongly advise 

 all who wish to study this branch of analysis in a thorough 

 and accurate manner to procure the book, or rather that 

 part of it which is now published, at once. The pub- 

 lishers of this work announce that the book will be 

 completed in three parts ; if the second and third are as 

 fully and accurately compiled as the first, the book will 

 undoubtedly be the standard work of reference in the 

 department of organic qualitative analysis. 



The first part, extending to 192 pp., contains the more 

 important acids, cellulose and starch. A full account is 

 given of the properties and reactions of each compound 

 so far as these are of value in qualitative analysis ; 

 methods of separation, varying according to the conditions 

 of complexity of mixtures, are also given. The book is 

 not arranged after the ordinary plan of the text-books of 

 inorganic analysis ; it is rather a full and accurate store 

 of information regarding the reactions of organic com- 

 pounds from which the student may 'select . materials 

 according to the special conditions of the problem pre- 

 sented to him. 



The work contains no preface or indication of the 

 ground to be covered by the completed book ; judging 

 however from the scope of the first part, the author would 

 seem to aim at presenting a complete account of the 

 reactions of all those commonly occurring organic com- 

 pounds which can, with a fair degree of certainty, be 

 identified by qualitative analysis. 



A Syjiopsis of Ekmciifajy Results in Pure and Applied 

 Mathematics ; containing Propositions, Formula:, and 

 Methods of Analysis, with Abridged Demonstrations. 

 By G. S. Carr, B.A. Vol. i. Pp. xxiv. 256. (London: 

 C. Hodgson and Son, 1S80.) 

 We shall not enter upon any discussion as to the utility 

 or inutility of such a work as the present, but simply 

 confine ourselves to an account of its contents. It is not 

 a work of yesterday, for the author tells us that it is 

 compiled from notes "made at various periods of the 

 last fourteen years, and chiefiy during the engagements 

 of teaching." Mr. Carr's chief aim has been so to arrange 

 his matter that the student may be assisted in the revision 

 of bookwork, hence he generally confines himself to indi- 

 cating the main features of a proof or to a mere reference 

 to the theorems by which the proposition is proved. To 

 aid in this end he has employed a system of cross-re- 

 ferences, each article being numbered progressively in 

 "large clarendon figures." A feature to which the author 

 rightly draws attention is the compression he has attained 

 without sacrificing clearness in his "last section, in which 

 in the space of twenty-four pages are contained more than 

 the number of propositions usually given in treatises on 

 geometricalconics," together with clear large figures, and 



in most cases the demonstrations. This, we think, he 

 has done well. This first part he divides into seven 

 sections. The first contains a large collection of mathe- 

 matical tables (Factor Tables, Values of the Gamma- 

 function, and many other useful and frequently-recurring 

 constants), in addition to an introduction on the C.G.S. 

 system of units. Algebra is treated of in articles 1-3S0; 

 Theory of Equations, 400-593 ; Plane Trigonometry, 6oo- 

 859; Spherical Trigonometry, S70-910; Elementary Geo- 

 metry, 920-1099; Geometrical Conies, 11 51-1267. It 

 will be seen from the above numbering that there are 

 breaks ; these have been " purposely made in order to 

 leave room for the insertion of additional matter, if it 

 should be required in a future edition, without disturbing 

 the original numbers and references." It is obvious to 

 object here that the new matter may not fit into the plan 

 adopted in this edition. 



Owing to causes which Mr. Carr names, the earlier part 

 of his work contains a rather long list of errata ; most of 

 these are pointed out, but not all. The utiUty of such 

 a work greatly depends upon its reliability for purposes of 

 reference, and our confidence is somewhat shaken when, 

 on opening the work casually, as we did at p. 6, we find 

 "logio'^ = i'497i499) log^'^ = 0-6679358," and this not 

 corrected elsewhere. 



Having carefully read the whole of the text, we can say 

 that Mr. Carr has embodied in his book all the most use- 

 ful propositions in the above subjects, and besides has 

 given many others which do not so frequently turn up in 

 the course of study. The work is printed in a good bold 

 type on good paper, and the figures are admirably drawn. 



E studio Microgrdfico ne Algunos Bos altos de Ctiidad- 



Real. Par Don Francisco Quiroga. (Madrid, 1880.) 

 In this memoir the author gives an account of the 

 microscopic characters exhibited by the basalts of the 

 volcanic district of the Campos de Calatrava, which 

 basalts he shows to have been erupted in Tertiary times. 

 These rocks appear to belong to Dr. Boiicky's classes of 

 the Nepheline-basalts and the Nephelinitoid-basalts, in 

 the former of which the nepheline is fully crystallised, 

 while in the latter it exists as a glassy base in which 

 crystals are beginning to make their appearance. The 

 primary minerals of these rocks are nepheline, augite, 

 magnetite, and olivine, which may be regarded as their 

 essential constituents, and apatite and hornblende, which 

 the author regards as accessory or accidental constituents. 

 The secondary or derivative minerals are kaholite, 

 hinsuite, and hematite, magnetite, serpentine, and ara- 

 gonite. The memoir is illustrated by a coloured plate of 

 rock-sections. 



// Binomio di Newton. Per Ignazio Cameletti. 7 pp. 

 (Genova, 1880.) 



By performing the successive multiplications and writing, 

 after the following fashion — 



(l + .r)'" = I 4- X (tn = I 

 X + x^ w = 2 



X -f .r^ 



.1^+ .1-3 



3, 



and so on, the author succeeds in an ingenious manner, 

 by summation of simple series, in getting the successive 

 coefficients of the general expansion, and so proves his 

 theorem, which is — 



{a -f b)'" = ci" -f s^ = -" w(;//- x)...{m-p^x) „« -/ ^/> 

 1.2..../ 



or the Binomial Theorem of Newton without having 

 recourse to the doctrine of combinations. 



