4II2, 



NATUKE. 



[September 3, 1903 



there is no adequate ground for assuming that a limit 

 such as that of the series of rationals whose squares 

 are less than 2 does really exist. Instead of this 

 Mr. Russell defines a segment as a class of rationals 

 less than a variable term of itself, and shows that 

 segments possess all the usual properties of real 

 numbers. This theory agrees very closely with 

 Cantor's, the point of divergence being where Cantor 

 appears to regard the rational number a as identical 

 with the real number defined by the series (a, a, a, . . .) 

 whereas Mr. Russell will not admit this. On the one 

 hand it is obvious that the two concepts are as distinct 

 as "man" and " featherless biped," and therefore 

 cannot be identical ; but, on the other hand, it seems 

 unnecessary to insist too much on the distinction, 

 because no confusion need arise from using the ex- 

 pression "a" in two different senses. Thus, if b is 

 the irrational number defined as the series (. . . <2„. 

 a„ + 1, . . .) we may write d-a = {. . . f/„ - a, <?„ + j - rt, . . .) 

 and in this equation a is a series or so-called real 

 number on the le.'t and a rational number on the 

 right. The conclusion is that the series of rational 

 numbers cannot be completed exactly as it stands, but 

 the rationals must first be replaced by series, or, if 

 preferred, by segments, and then by means of other 

 series the continuum of real numbers can be con- 

 structed. 



Limitations of space forbid detailed comment on 

 part vi., in which, incidentally, Euclid gets some 

 rather hard knocks ; and in the matter and motion of 

 part vii. Newton's laws are condemned as confused, 

 worthless, and wholly lacking in self-evidence, while 

 we are told that force is a mathematical fiction, and 

 velocity and acceleration must not be regarded as 

 physical facts. 



On the whole the book is very interesting, although 

 somewhat too long. The presentation is admirably 

 clear, and the seriousness of the style is relieved here 

 and there by neatly turned bits of humour. It does 

 not pretend to say the last word on any subject, and, 

 indeed, bristles with unsolved difficulties, towards the 

 correct solution of which a great step is undoubtedly 

 made by its publication. R. W. H. T. H. 



ELECTROCHEMICAL ANALYSIS. 

 Quantitative Chemical Analysis by Electrolysis. By 

 Prof. Classen. Translated by Bertram B. Bolt- 

 wood. Pp. vii + 315. (New York: John Wiley and 

 Sons; London: Chapman and Hall, Ltd., 1903.) 

 Price 12s. 6d. net. 



ELECTROCHEMICAL methods of analysis are 

 now coming into such general use on the 

 Continent and in America, and to a smaller extent in 

 this country, that chemists will be prepared to welcome 

 the latest translation of Pro^ Classen's " Quantitative 

 Analyse durch Elektrolyse. " 



The translation is made from the fourth German 

 edition published in 1897, but, as the translator has 

 been allowed wide latitude by the author, he has 

 brought the book well up to date, and we find several 

 features in this book which are not in the German 

 original. 



NO. 1766, VOL. 6S] 



In chapters xiii. and xiv., for example, which deal 

 respectively with " measurements of current strength " 

 and " sources of current," there are quite a number of 

 new blocks, as, for example, Bredig's amperemano- 

 meter and the Weston ammeters and voltmeters. We 

 also find several new diagrams in chapter xvi., which 

 deals with the accessory apparatus employed in 

 analysis. As a matter of fact, we think, considering 

 that the book is devoted to electro-analysis, some of 

 the apparatus described is rather superfluous. A 

 quadrant electrometer is not usually to be found in a 

 laboratory devoted to electro- or any other analysis, 

 the description of such apparatus appertaining more 

 to works on physics or perhaps on general electro- 

 chemistry. In chapter xviii. the author gives details 

 as to "arrangements for analysis." The details 

 which are given refer mainly to the very thorough 

 installations at Aachen, and two photo-plates of the 

 laboratories, as they are at present, also one showing 

 the former equipment of the private laboratory, are 

 given. One cannot learn very much from these photo- 

 graphs, but they improve the appearance of the book, 

 and incidentally give an idea of the large number of 

 platinum basins which Prof. Classen possesses. 



On p. 153 we come to the analytical portion of the 

 book, the first metal dealt with being iron. For the 

 analysis of iron there is no doubt that Classen's 

 oxalate method is extremely satisfactory, and the 

 analytical results obtained are generally very accurate. 

 At the same time, as Kohn and others have shown, 

 this is really due to a balancing of errors. The iron 

 deposited always contains traces of carbon, but, on 

 the other hand, there is usually a trace of iron left 

 in the solution, and these two errors balance. Classen 

 states that iron, when deposited from solutions con- 

 taining citrates and tartrates, always contains carbon, 

 but leaves it to be inferred that when oxalates are em- 

 ployed, the metal is deposited free from carbon. Prof. 

 Classen employs the oxalate method not only for iron, 

 but he uses it for almost every metal, very often, too, 

 when other ways are vastly superior, and he seems 

 very much afraid that someone else will take, credit 

 for the method, because in almost every case we find 

 a bracket in which it is stated that this is the " method 

 of the author." As a matter of fact, there are only 

 a few cases in which the employment of oxalates has 

 any real advantage, as e.g. with iron and zinc. There 

 is certainly nothing to be gained by using it when 

 depositing copper, nickel, or mercury, where there 

 are many much more satisfactory methods. Cobalt, 

 according to the author, when deposited, shows its 

 characteristic metallic properties. Generally speak- 

 ing, when electrically deposited, cobalt is brownish or 

 smoky in appearance — are these its characteristic 

 metallic properties? 



Section ii. of the analytical portion deals with the 

 analysis of nitrates, and section iii. with the determin- 

 ation of the halogens. 



Section iv., on the separation of the metals, is 

 perhaps one of the best parts of the book. It may be 

 very easy, and generally is, provided one employs the 

 correct conditions, to analyse from pure salts of the 

 metals, but the electrolytic separation of metals is 



