;40 



NA TURE 



[August ii, 1898 



degrees of virulence— growing side by side in difterent pto- 

 portions and at different periods of the disease, it is very 

 difficult to determine. At the same time it must be 

 acknowledged that Dr. Hewlett and Miss Knight bring 

 forward considerable evidence in support of their thesis. 



Other papers of equal importance, but of less general 

 interest, are those by Messrs. W. St. C. Symmers and Alex. 

 G. R. Foulerton. Drs. Macfadyen and Hewlett describe 

 a method for the sterilisation of milk by a coil-heating 

 apparatus, by means of which successful Pasteurisation 

 may be carried out (at a temperature of from 68'' to 72° 

 C), such temperature having little, if any, injurious 

 effect on the milk, but increasing its keeping quality 

 enormously. They also show that the diphtheria bacillus, 

 the typhoid bacillus, the tubercle bacillus and strepto. 

 coccus pyogenes are rendered incapable of doing any 

 harm by being treated in this apparatus, along with milk. 

 Mr. Lunt contributes an interesting article on the 

 sterilisation of water by filtration through the Berke- 

 feld filter. The methods he uses are exceedingly in- 

 genious, and the results obtained apparently very 

 trustworthy. He comes to the conclusion that the 

 Berkefeld filter keeps back all organisms for at least 

 twenty-four to forty-eight hours, and that only water 

 bacteria can pass through this filter at any time, except 

 in those cases where there is a rapid oscillation in 

 the pressure under which the water is passed through 

 the filter. Under these circumstances organisms of all 

 kinds appear to be " percussed " through the fine pores 

 of the filtering candle. 



A paper " On the bacillus of bubonic plague — Pesstis," 

 by Dr. R T. Hewlett, gives some interesting inform- 

 ation concerning this organism. In " Bacteria and dust 

 in air," Dr. Macfadyen and Mr. Lunt give the results of 

 a repetition of some of Dr. Aiken's experiments on dust 

 particles in the air ; they give in addition, however, an 

 enumeration of the number of micro-organisms that 

 were present in duplicate samples of air ; they find that 

 the number of dust particles is enormously greater 

 than the number of bacteria. In one case in the open 

 air there was just one organism to every 38,300,000 

 dust particles present ; whilst in the air in a room^ 

 amongst 18,000,000 particles of dust only one organism 

 could be detected. Mr. Lunt furnishes the final paper 

 in the volume : on a convenient method of preserving 

 living pure cultivations of water bacteria, and on their 

 multiplication in sterilised water. Mr. Lunt falls in with 

 the theory that has been put so strongly forward during 

 the last year or two, that although water organisms grow 

 well in water, those organisms which do not belong to 

 this group gradually die out. He obtains results of 

 considerable interest as regards the classification of cer- 

 tain species of bacteria in a group called water bacteria, 

 having the following characters: {a) to be found in 

 natural water ; {b) capable of living for very long periods 

 in sterilised water ; {c) capable of very rapid multiplication 

 in sterilised water ; {d) showing no signs of degeneration 

 when kept for long periods in sterilised water. This 

 article is of considerable practical value, and forms a fitting 

 conclusion to a series of papers which will have a far more 

 than ephemeral interest. We congratulate the British 

 Institute of Preventive Medicine on the manifestation of 

 useful activity afforded by the present volume. 

 NO. 1502, VOL. 58] 



A NEW TEXT-BOOK ON ELEMENTARY 

 ALGEBRA. 

 Introduction to Algebra, for the Use oj Secondary Schools 

 and Technical Colleges. By G. Chrystal, M.A., LL.D. 

 Pp. xviii -f- 412 -f- xxvi. (London : Adam and Charles 

 Black, 1898.) 



' I ""HE appearance of this book marks another stage in 

 -»- the improvement which is at last being effected in 

 English treatises on elementary algebra. How different 

 it is from the old-fashioned text-book will be partly 

 realised by observing that the first sixty-two pages are 

 assigned to the discussion of the fundamental laws of 

 algebra ; that upwards of fifty pages are devoted to 

 elementary curve-tracing ; and that the elementary 

 tneory of rational functions is presented in a correct and 

 fairly methodical shape. The notions of degree, homo- 

 geneity, and symmetry are introduced, as they ought to 

 be, at an early opportunity, and their importance duly 

 emphasised, and illustrated ; in this and other ways the 

 student's attention is directed to the all-important subject 

 of algebraic form. The chapter on the resolution of 

 integral functions into factors is both clear and scientific ; 

 this fact alone distinguishes Prof. Chrystal's work from 

 the great majority of its predecessors. The binomial 

 theorem, for a positive integral exponent, instead of 

 having a special chapter devoted to it, and being treated 

 as a sort of mathematical Rubicon, is deduced, in pass- 

 ing, as a particular case of distributing a product. 

 Finally we may remark (a propos of a recent correspon- 

 dence in this journal) that the solution of a quadratic 

 equation is made to depend on the factorising of its 

 characteristic, and the ordinary method by " completing 

 the square" is ignored, except, oddly enough, in one 

 example, where, it is quite unnecessary, and the factoris- 

 ation is otherwise obvious. 



In the matter of notation, also, and in methods of 

 work, the author has shown himself independent of 

 tradition : thus the method of detached coefficients is 

 employed whenever it is convenient, and the symbols 

 2 and II are freely used from the outset. With this we 

 entirely agree ; on the other hand, the use of the solidus 

 appears to us excessive ; for instance, we find the worked 

 examples in Chapter xv. difficult to follow. But, of course, 

 a person in the habit of constantly using this notation 

 might be of a different opinion. 



All competent and honest teachers who wish to make 

 their pupils think, and not merely to acquire that shallow 

 unreasoning dexterity which scores in examinations, but 

 is otherwise of little use and even, by itself, pernicious, 

 will welcome this work as the best intermediate class- 

 book that has yet appeared. In some respects it com- 

 pares favourably with the author's larger treatise : less 

 encyclopaedic, it has the advantage of greater unity ; 

 and, what is more important, it is written after a wider 

 experience of teaching and examining. The effect of 

 this appears in various ways ; in remarks on common 

 errors of beginners, in leading up to general laws by 

 particular examples, in occasional anticipation of 

 theorems to be presently proved, and in the statement 

 of results not within the scope of the treatise, but 

 intelligible and stimulating to the student, who thus gets 

 some glimpses of the regions he may some day hope to 

 explore. 



