558 



NA TURE 



[April 17, 1902, 



LETTERS TO THE EDITOR. 



[ The Editor does 7iot hold himself responsible for opinions ex- 

 pressed by his correspondents. Neither ean he undertake 

 io return,, or to tot respond with the writers of rejcuei 

 manuscripts intended for this or any other part of NatUKE. 

 No notice is taJcen of anonvmous communications.'\ 



The Permeability of Iron Alloys. 



In a paper in the last number of the Proceedings of the 

 Royal Society, Prof. Barrett refers to the increased permeability 

 conferred on iron by alloying it with aluminium, and suggests 

 an explanation on the supposition that the aluminium would 

 remove traces of oxygen from the iron. 



Some seven years ago, in the course of a series of measure- 

 ments on the magnetic properties of iron alloys, I found that 

 aluminium, phosphorus and arsenic decreased the coercive 

 force and hysteresis loss very considerably, whilst aluminium 

 very largely increased the permeability — the others less so. 

 Silicon produced little effect, but probably slightly improved 

 the iron. On mentioning this to my colleague, Prof Arnold, 

 he at once pointed out that these elements are just those which 

 increase the size of the crystals in iron. Annealing, which also 

 improves permeability and lessens hysteresis, also increases the 

 scale of the crystals. It is probable, therefore, that the increase 

 of permeability due to these substances is a secondary effect due 

 to the increased size of the iron crystals. A foreign substance 

 might be expected to act deleteriously in two ways: (i) by 

 occupying space better filled by iron, (2) by combining with iron 

 and forming a less magnetic chemical compound. Phosphorus 

 and silicon would act in both ways, aluminium in the first 

 only, which might account for a larger difference between its 

 indirect favourable action on the iron crystals and its direct 

 deleterious action. It would be interesting if investigators in 

 this direction would try to correlate their permeability measure- 

 ments with the results of microscopical analysis as well as 

 chemical. W. M. HiCKS. 



University College, Sheffield, April 10. 



Reform in Mathematical Teaching. 

 Some of Prof Perry's followers seem to me to miss a point 

 which he realises clearly — viz. that the key to the whole position 

 is in the examination system. 



(1) The strength of the present system is very great. An 

 impending examination converts the teacher from an enemy of 

 the idle and refractory pupil into an ally — to the comfort of all 

 parlies. The success of his pupils at examinations gives a 

 teacher some return for his labour ; otherwise he would have to 

 comfort himself by hoping that Kipling's great lines, "There- 

 fore praise we famous men," might some day in some degree 

 apply to him. The realised hope would be worth ten thousand 

 times the immediate return, but hope deferred is discounted at 

 very heavy rates. 



(2) The present system might be very much better. Examin- 

 ing work is often badly paid; in the main and in the long run, bad 

 pay means bad work. Thring said that you might have one 

 generation of martyrs, but the second would be cheats. 



The band of fossil examiners, each with his fossil syllabus, does 

 much more harm than Procrustes. A is clever, but he must not 

 go beyond the syllabus ; B is slow, but he must be bustled 

 along and pot through the course somehow. 



The fate of anything new or fresh is pretty sure. There is a 

 Cambridge yarn about some one who set his favourite question, 

 "Define a differential coefficient," but instead of getting the 

 expected three or foiir lines of cram, he got the substance of 

 five or six pages of Harnack's new German book on the calculus. 

 He rose to the occasion and promptly marked it o. 



(3) But written examinations have inherent and inevitable 

 defects, clearly indicated by Dr. Lathom " Examinations 

 considered as a means of selection." The old style of question, 

 which was rather reproduced than parodied by the famous 

 " Very small elephant whose weight may be neglected, and 

 whose coefficient of friction was ,^'7 - \'3." "i^y l>c replaced by 

 "The relation between the weight and length of tusk of an 

 elephant being represented by the equation W = A/'-f B/+C," 

 and so on . . . but a system of written examinations based on 

 the new model would in the end be like unto the first. 



The following axioms are put forward in the hope that they 

 may be condemned as truisms : — 



NO. 1694, VOL 65] 



(1) Examinations are not to be multiplied beyond necessity. 



(2) No examination is entitled to any confidence in which 

 teachers or persons in close touch with the teachers have no 

 part. 



(3) Viva voce examinations are essential if weight is to be 

 attached to the results of a single examination. 



It would be most interesting if Prof. Perry, who has influence 

 and persuasiveness, could arrange an experiment. 



Get answers to a paper from a dozen candidates, good and 

 b.id mixed, have facsimile copies made, and submit them to 

 twenty or so competent examiners. The discrepancies in the 

 marks would, I think, be surprising. 



If the examiners adopt the received plan of cutting each 

 question into several bits and giving marks for each little bit, 

 they will get results more concordant and more entirely out of 

 relation to common sense or real life. C. S. Jackson. 



Woolwich. 



Theki; are two places in Prof. Perry's letter appearing in 

 your issue of March 27 in which he mentions schoolmasters in 

 terms of, in the one case praise, in the other blame. The first 

 passage is where he congratulates the " reformers " " on having 

 with them the good wishes of every thoughtful teacher of the 

 whole country," but in the last passage he expresses the con- 

 viction that we shall " not very long remain in the foremost files 

 of our time if we depend upon the schoolmasters." I hope that 

 teachers are good for more than mere good wishes, and I think 

 Prof Perry will find that the reform he laments as scarcely 

 within sight has not only begun, but is actually bearing fruit in 

 the place in which, though the subject of controversy, the noise 

 of the conflict is heard least — the schoolroom. Schoolmasters, 

 like others, move with the times, and the " conventional school- 

 master " is a much rarer bird than the conventional examiner or 

 the conventional inspector. I suppose syllabuses and text- 

 books are a necessity still, but the competent teacher of mathe- 

 matics needs not to be bound by anything of the kind. Per- 

 sonally, I see no necessity for this ideal text-book one hears 

 about which is to replace Euclid, and those who caricature him ; 

 we are better without a text-book at all. Let a master be 

 engaged capable of making his own syllabus for his own pupils, 

 and give him a free hand to introduce modern geometry, 

 differential calculus, &c. , as he sees fit ; such a man will welcome 

 the appreciation of a competent inspector, himself a mathe- 

 matician and, beyond that, a successful teacher of mathematics. 

 As I have already hinted, reform in the schoolroom proceeds as 

 rapidly as examiners will allow, rather more so in fact, for I 

 know that many boys learn much that no examination they 

 have been in for, or are likely to take, tests. My own work 

 is in such a small way that I do not care much to bring it for- 

 ward, but I must confess to periods of guilty satisfaction when I 

 have robbed time from examination teaching and introduced 

 boys, much to their interest, and I feel sure profit, to such 

 things as coaxal circles, theory of inversion, cross ratios, and 

 fundamentals of the integral calculus. Let the mouse help the 

 lion I 



I feel sure Prof. Perry and his fellow reformers — if they will 

 find out what is being done on the spot by the teachers, or if the 

 latter have as yet shrunk from any sort of attempt at reform, 

 what their wishes and opinions are — will find conv'ention at 

 least as hateful to the teachers as to themselves. Of course, I 

 am not speaking, as I am not qualified to speak, on behalf of 

 those who form what I may term the "aristocracy" of the 

 teaching profession ; I myself and my teaching friends are 

 mostly engaged in the small .schools, large in number, situated 

 in industrial districts, where the endowed school fights for an 

 existence with the "technical" or even the higher-grade 

 Board School, where boys leave between fourteen and sixteen, 

 at the latter of which ages they are supposed to have the 

 groundwork on which a knowledge of engineering can be built 

 up. Vet to these Euclid must be taught. Of course, as a 

 matter of fact, Euclid is not t.aught to them ; they pass examina- 

 tions in a subject that goes by that name, the satisfaction I per- 

 sonally have felt being in the reports of examiners, who, intend- 

 ing to reprove, have written, "the constructions and principles 

 of proof were well known, but the wording of Euclid was not 

 adhered to, and some points in the proofs were omitted. The 

 riders were well done. ' In these schools, " practical plane and 

 solid geometry " is a subject taught throughout ; and there is 

 many a germ which only requires a little encouragement to 

 bear great fruit. I think that the power behind the reformers 



