I 22 



NA TURE 



[June 7, 1894 



upon the results to be selected. No one who has not had 

 experience of this kind of work can appreciate the labour 

 involved ; it is comparatively easy when the abstractor 

 can confine himself to his own line of study, but when 

 he has to get up fresh subjerts for the purpose, the difti- 

 cultv is enormaasly increased. It would be manifestly 

 unfair to criticise a work of this kind on account of its 

 deficiencies, or even its errors. Any competent mathe- 

 matician who carries out such an undertaking is entitled 

 to the thanks of his fellows for whatever he puts before 

 them ; and when he does his work well, as Mr. Hagen 

 has done, he may be heartily congratulated upon a real 

 service rendered to mathematical science. 



The difficulty of dealing with the ever-increasing 

 volume of journal literature is one which is common to 

 all the sciences, but it is psrhips felt most acutely in 

 mathematics, where the lines of research are so 

 very numerous, and the workers in each are but few. 

 The want of treatises has to some extent been supplied 

 by the republication in a collected form of the scattered 

 papers of many eminent mathematicians. The value 

 of these complete editions cannot be exaggerated ; but 

 they necessarily aggravate the tendency to accumulate 

 all discoveries upon the greatest names, and throw still 

 further into the background the productions of the less 

 distinguished writers. The paramount merit of classified 

 indexes and books of an encyclopedic character is that i 

 they treat all papers with the same impartiality ; and 

 probably there are no works which do more for the 

 advance of science than those which, like the present, 

 have for their sole object to make available for general 

 use the stores of more or less inaccessible knowledge 

 which have been laboriously acquired and put on record. 

 Perhaps, too, when .Mr. Hagen has mapped out the whole 

 territory of mithematics, there may be found some who 

 will be willing to fill in certain regions on a larger scale 

 than so comprehensive a plan has permitted to him. 



A few words should be added with respect to the book 

 itself. It is beautifully printed, the pages are large and 

 handsome, and it is well indexed. The formulx are so 

 numerous, and the text is so conveniently divided into 

 short and clear paragraphs, that the language will pre- 

 sent no obstacle to anyone possessing the least acquaint- 

 ance with German. It is intended that the complete 

 work shall consist of four volumes, the second relating 

 to geometry. If carried out in its entirely with the same 

 care that has been bestowed upon the first volume, the 

 whole work will form a splendid contribution to tlie 

 history and progress of mathematics. 



J. W. L. Glaisher. 



MICRO- CHE.\TrS TR Y. 

 A Manual of Micro-chemical Analysis. By Prof H. 

 Behrens. With an introductory chapter by Prof John 

 \V. Judd. (London: Macmillan and Co., 1894) 

 T^IIE necessity of supplementing the microscopical 

 •*• examination of rocks and minerals by chemical 

 tests led Dr. Boricky in 1877 to devise his method of 

 micro-chemical analysis. He decomposed extremely 

 minute particles of the substance to be examined on a 

 glass slide, protected by a coating of Canada balsam, and 

 NO. (?84. VOL. 50] 



examined the fluosilicates formed by the aid of the 

 microscope. Since his time Prof Streng, Dr. Haushofer, 

 the author of the present manual, and others have devoted 

 themselves to improving and extending micro-chemical 

 methods. .Mthough originally introduced for the purpose 

 of enabling chemical tests to be applied to extremely 

 small particles, it has been found that these methods have 

 another and perhaps equally important claim to recogni- 

 tion. They often shorten the time required for a quali- 

 tative chemical examination. Thus Prof. Behrens tells 

 us that a solution containing calcium, magnesium, zinc, 

 manganese, cobalt, and nickel has been examined in 

 forty minutes ; and one containing silver, mercury, lead, 

 bismuth, tin, antimony, and arsenic in an hour. 



Up to the present time no general work on micro- 

 chemical .analysis has appeared in the English language, 

 so that the manual before us fills a definite gap in our 

 scientific literature. It is divided into three parts. The 

 first treats of the general method and of the reactions at 

 present employed in the identification of the ditierent 

 elements ; the second, of the application of the method to 

 the analytical examination of mixed compounds. 



The apparatus required is of the simplest character. A 

 microscope with magnifying powers of 50 and 200, a few 

 microscopic slides, some capillary tubes, one or two plati- 

 num spoons, some platinum wire and foil, a burner giving a 

 flame 5 mm. high, and a box of reagents, are almost all that 

 is absolutely necessary. An idea of the scale on which the 

 operations are conducted may be obtained from the fact 

 that, in establishing the limits of the applicability of the 

 several tests, the author worked with drops having a volume 

 of one cubic millimeter. The conditions which determine 

 thesuitabilityof any particular reaction for micro-chemical 

 work are obviously very different from those which 

 govern ordinary qualitative analysis. It is much more 

 important that the compounds formed should be easily 

 recognisable, than that complete precipitation should be 

 effected. The compounds by which elements are recog- 

 nised under the microscope are therefore, as a rule, those 

 which possess an appreciable though not very great 

 solubility; for such compounds most readily form well 

 characterised crystals. 



It is in the selection of suitable reactions that Prof. 

 Behrens has done so much to facilitate the application 

 of micro-chemical methods. In describing these re- 

 actions he gives in each case the limit of sensibility in 

 micro-milligrams, the precautions necessary to secure 

 the result, and the circumstances under which the par- 

 ticular reaction is applicable. The work is illustrated 

 with numerous figures representing the compounds re- 

 lied upon for diagnostic purposes ; but, as the author 

 points out, the only way of acquiring facility in the iden- 

 tification of these compounds, as well as confidence in 

 the method, is to go through the reactions and observe 

 the results under the microscope. 



The second part of the work treats of a systematic 

 scheme of examination, and of the micro-chemical 

 anal) sis of water, ores, rocks, alloys, and some combina- 

 tions of rare elements. It must be admitted that it is at 

 present quite impossible to formulate any general scheme 

 at all comparable with those in use in ordinary analysis ; 

 and the chemist, unaciiuainted with what has been done 

 by the aid of micro-chemical methods, would undoubtedly 



