466 



NATURE 



[September 13, 1900 



matter of fact, B. colt is a short rod, hardly longer than 

 broad, frequently showing only very feeble motility, and 

 usually having only i to 3 flagella, which stain with 

 difficulty ; whereas the typhoid bacillus occurs as long, 

 thin, slender rods and filaments, which (the rods) are 

 actively motile and move about in a fashion quite 

 different from the colon bacillus. Moreover, the flagella 

 average ten in number, and stain readily. The state- 

 ment that B. colt is frequently present in dirty water 

 must be accepted with reserve, unless it be assumed that 

 the word "dirty" is meant by the author to convey the 

 idea of fouling with matter of an excremental sort. Again, 

 the author, speaking of the staphylococci (s.p. aureus, 

 -citreus and albus), says that in nature these germs are 

 found everywhere. We venture to dispute the truth of 

 this remark, which is stated as if it were a fact ; yet in our 

 judgment it is merely a supposition, and an erroneous one. 



These few criticisms are made in no carping spirit ; 

 indeed, the book as a whole strikes us as being one of 

 the best that has been written on the subject, and in 

 many respects it is quite unique. The chapters dealing 

 with the circulation of nitrogen and carbon in nature are 

 altogether admirable. We can find no words sufficiently 

 strong to recommend this book to the perusal of all 

 students of bacteriology, and particularly to those 

 interested in biology from the technical point of view. 



Unstinted praise must be given to the translator ; in 

 -offering to English readers a translation of Prof. Alfred 

 Fischer's " Vorlesungen iiber Bakterien " he has placed 

 us under a deep debt of gratitude. A. C. Houston. 



OUR BOOK SHELF. 



A Walk Throii^h the Zoological Gardens. By F. 



G. 



Aflalo, F.R.G.S., F.Z.S. Pp. 232. (London : Sands 

 and Co., 1900.) 



It is not by any means abundantly clear that a guide to 

 ■ the Zoological Society's Gardens is needed, inasmuch as 

 there already exists the well-known and accurate guide 

 to the Society's collection by Mr. Sclater. Although it is 

 true that the author does not call his book a "guide" in 

 the title, he nevertheless observes in the preface that it is 

 his object "to conduct the reader from house to house 

 .and from paddock to paddock, pointing out the chief 

 features of interest " on the way. We must, therefore, 

 ■consider the book as intended to be a guide. As such it 

 -does not appear to us to be at all informing ; it would 

 have been well, too, to avoid positive error. The author 

 -calls a sea-lion a seal, which — seeing that true seals are 

 often exhibited — is confusing. The African Mudfish, 

 Protopterus, often on view in the Reptile house, is dubbed 

 Lepidosiren, which, we need scarcely explain, is a South 

 American Dipnoan. There are other errors of fact, and 

 -certain statements which are so loose and confused that 

 they are practically erroneous. It is naturally impossible 

 in a small book like the present to give an exhaustive 

 account of all the animals to be seen in the course of a 

 year or two in the Gardens. But the author leaves out 

 so many important beasts that he fails to convey a real 

 notion of the extent and variety of the collection. By 

 cutting out the tale of how he rescued a blue pencil from 

 a cormorant, which afterwards swallowed a lady's 

 parasol, and by forbearing to mention that porcupines 

 ■" pare their teeth on elephants' tusks " (!j, and generally by 

 avoiding gossip of a totally uninteresting and equally un- 

 instructive kind, Mr. Aflalo might have grappled more 

 •successfully with the immense amount of material at his 

 • disposal. 



NO. 161 I, VOL. 62] 



LETTER TO THE EDITOR. 



[The Editor does not hold himself responsible for opinions ex- 

 pressed by his correspondents. Neither can he undertake 

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

 manuscripts intended for this or any other part of Nature. 

 No notice is taken of anonymous comtnunications.'\ 



The Reform of Mathematical Teaching. 



To your issue of August 2 Prof. Perry contributes an indict- 

 ment of the present system of mathematical teaching in this 

 country. As he invites criticism, one need not apologise either 

 for defending existing methods or for criticising his suggested 

 improvements. His main attack seems to be directed against 

 mathematics as an educational subject, and in particular the 

 teaching of Euclid falls under his ban. The elements of abstract 

 reasoning are, he says, quite unnecessary to a boy's mental de- 

 velopment. Why does he not add that common-sense is of no 

 value also ? 



Do we always first learn by actual trial, as is stated in his 

 article ? Do we throw ourselves into deep water and learn to 

 swim forthwith? Do we set about jumping, cycling, billiards 

 or cards without any previous explanation ? Surely, as a rule, 

 in these matters we are taught, not only what to do at the start, 

 but also, if we can grasp them, the guiding principles. In a 

 game of whist, who does not dread the unreasoning partner who 

 has learnt the rule " Third player plays highest," and blindly 

 acts upon it ? " 



Euclid, though it might advantageously be shortened by the 

 assumption of a few more axioms and postulates, is not, I venture 

 to say, at all a "soul-destroying, weary, worrying study for the 

 schoolboy." Of course it may be made so, but to every boy, 

 with care, it may become interesting, and, in the experience of 

 many teachers, it proves a more engrossing subject to their 

 classes than either arithmetic or algebra. 



Prof. Perry very properly points out some of the weak spots 

 in present-day arithmetic. He instances "our abominable 

 system of weights and measures." One may suggest that that 

 system is hardly the fault of our system of mathematics ; it is 

 entirely its misfortune. Will he not, instead of girding at the 

 unfortunate teachers of mathematics, agitate for a conference of 

 delegates from all bodies interested in this most important 

 question ? 



Later on in his article it is stated that practice, interest, dis- 

 count, tare and tret, alligation, position, &c. , are at this day 

 taught exactly as during the last century. This statement is 

 absurd. 



It is true that discount, percentages, stocks, areas, &c., are 

 all dependent on the rule of proportion ; but for purposes of 

 explanation and of interest it is certainly as well not to lump 

 these together in one heterogeneous muddle under the head of 

 "Proportion." If such a method were in vogue, or if the 

 whole of arithmetic were, by means of formulas, reduced to 

 multiplication and division, one would certainly see " the film 

 of dulness covering a boy's face as he entered the class-room." 



As regards the syllabus quoted by Prof. Perry, it is easy to 

 agree with him thus far — that it is admirably adapted for a 

 technical training. In practical mathematics, where mental 

 training is of minor importance, exigencies of time will compel 

 the teacher to omit explanations, or only to give them roughly, 

 for his chief object is to enable his pupils to apply mathematical 

 results, as distinct from reasoning, to problems in engineering, 

 science, or kindred subjects. 



On the other hand, the average boy's mathematical education 

 up to the age of fifteen or sixteen is an absolutely different 

 matter ; to put it crudely — the teacher's main effort is to enable 

 his pupil to ask and to answer reasonably the question 

 "Why?" 



At present there is really no orthodox system, but, in my 

 opinion, the methods enunciated in the principal text-books of 

 the day do, with slight exceptions, tend to develop a boy's 

 mental powers. 



When the boy has decided on his profession, then by all 

 means continue his education on the lines suggested by Prof. 

 Perry. 



Finally (if one may misquote his opening words), " it is very 

 important to try to get a view of our system of teaching mathe- 

 matics, which is not too much tinted with pleasant (or possibly 

 unpleasant) memories of science and engineering." 



W. F. Beard. 



