486 



NA TURE 



[March 27, 1902 



who does not think of Euclid merely as a lower school subject ? 

 At the British Association discussion a great mathematician was 

 astonished that I should ever have had to study the fifth book of 

 Euclid. He said he was more fortunate, because he was never 

 taught it. Well, I was never compelled to study it, but I took to 

 it through mere affection such as my critic deems it his good 

 fortune never to have experienced. What I regret is that any 

 kind of demonstrative geometry was given me when a boy, but 

 since it was given me I am glad to think that I had Euclid's 

 philosophy undefiled. I even dipped into those books now 

 never published — the seventh, eighth, ninth, tenth, and also the 

 thirteenth, fourteenth, and the books added by some Greek 

 author wliose name I forget, the fifteenth and sixteenth. At 

 the same time, I feel that if demonstrative geometry is to remain 

 a school subject for the average boy, it is absolutely necessary 

 to replace the second and fifth books by algebra. The view to 

 which I hold most firmly of all my views about the teaching of 

 mathematics is that demonstrative geometry ought never to be 

 taught to boys at all ; it ought never to be taught in schools. 

 It is a higher university subject. Euclid's treatment of propor- 

 tion and of incommensurables is one of the most beautiful parts 

 of that exact philosophy which the conventional schoolmasters 

 are constantly seeking to degrade. The old philosophers 

 thought that only a very few men of the most acute race that 

 ever lived on this earth were fit to begin the study of geometry, 

 and we use it as " an instrument for the cultivation of the 

 mind " of the average young barbarian. Even my sense of the 

 parlous state of the country cannot prevent me from grinning at 

 the Rabelaisian humour of the position. Boys are not swine, 

 but if you will force pearls upon them for food (poor boys, they 

 do not know that the pearls are only cheap imitations) you 

 must expect but small results either physically or spiritually. 

 It must always be a pleasant memory to them, however, that 

 they once did have pearls to trample under foot or to give 

 them indigestion, and one may say that they are fairly safe from 

 pearl hunger all the rest of their lives. Will any of my oppo- 

 nents deny that they ceased to study Euclid when they left 

 school, except in the way of their trade as teachers ? How 

 many of them know anything of — I need not say Euclid's real 

 philosophy — but even of modern geometry and the beautiful 

 system of transversals developed by the Irish geometers? I 

 recollect a lovely year of my life in which I was introduced to 

 three new things — Tennyson's " Idyls " and McDowell's 

 "Geometry" and Homer's "Odyssey" (Bohn's translation), 

 and I hardly know even now which of the three gave me most 

 pleasure. But I had had the good fortune not to have pearls 

 forced upon me as a boy. Yes, Caesar wrote a book for the 

 third form ; what man who ever passed through the third form 

 would now read Casar ? Euclid wrote a book for the lower 

 school ; a lower school book let it remain. 



And (a-fii)- = a--*-2iii-(-i- is equivalent to II. 4. And if 

 nia + nb _ nic+nd 

 b d' par£qb pc + qd 



mortal philosophy of the fifth book. "Great God, I'd rather be 

 a pagan cradled in a creed outworn I " I would rather be utterly 

 ignorant of all the wonderful literature and science of the la.st 

 twenty-four centuries, even of the wonderful achievements of 

 the last fifty years, than not to have the sense that our whole 

 system of so-called education is as degrading to literature and 

 philosophy as it is to English boys and men. 



We are not the heirs of all the ages, and we shall not for 

 very long remain in the foremost files of our time if we depend 

 upon the schoolmasters. I place my faith in the common sense 

 of the common people. In one way or another I find that they 

 are learning to compute, to gain a knowledge of natural science. 

 I know of many hundreds of night-school boys who were poor 

 who are now successful engineers, and already youths are being 

 NO. 1 69 1, VOL. 65] 



warned from trying to become engineers because their public 

 school education would actually prevent their having a chance 

 of success. They cannot understand the most elementary 

 lectures in applied science. I know of a large employer who 

 has already told the headmaster of a great public school that 

 he will no longer employ public school boys unless a more 

 rational method of teaching mathematics is adopted. And he 

 is a public school boy himself ! I am constantly being asked 

 to recommend men to teach mathematics in technical schools 

 and colleges, and warned that I must not recommend a 

 Cambridge man. There is nobody who has a higher respect for 

 Cambridge mathematics, for the achievementsof past and present 

 Cambridge men, than I have ; but if Cambridge men will 

 put themselves altogether out of sympathy with the needs of 

 young engineers ; if they will make no attempt whatsoever to 

 Icok at things from the new point of view to which we have 

 been forced ; if without any attempt at examination they will 

 in an off-hand way settle it that what we ask for is an illogical 

 and soul-debasing non-educational preparation of an olla podrida 

 of mere formulje, then in sorrow -and not without some anger we 

 must try to get on without them. They do not know what a 

 lovely bit of fighting they are leaving us to do all by ourselves, 

 but I sincerely hope that they will not hamper us. Indeed, they 

 must sooner or later help us against the common enemy, even if 

 they are only to be armed as were the children of the mist. 

 Because Isaac Newton was such a superb bowman and the 

 English yew was ever the finest of materials, they will insist on 

 the use of the antiquated weapon only. I sincerely hope that 

 the English yew, which is very much of a graveyard tree, may 

 not yet flourish over the grave of British industry. 



But enough of these notions. I see a great fight ahead of our 

 people, and bows and arrows are better than no weapons, as a 

 twentieth of a loaf is better than no bread at all, and I welcome 

 any instalment of reform, however small, in the teaching of mathe- 

 matics in the public schools of England. And so long as my 

 help is not rejected on the ground that I openly ask for a much 

 greater reform and may be dangerous to my friends on that 

 account, so long am I anxious to give my help and proud that 

 it should be accepted. John Perry. 



Birds attacking Butterflies and Moths. 



With reference to my previous letter in Xatukio (January 

 16), I would say that the butterfly referred to was the Terias 

 silhetana or Terias lacta, probably both. 



Another bird that frequently catches these butterflies on the 

 wing is the Indian Bee Eater (Meropi vinWis). 



During a Christmas camp this season I came across a field 

 where some twenty or thirty King Crows were busily engaged in 

 catching butterflies ; the day I first saw them, butterflies were 

 numerous in this field, and it was easy to get undamaged speci- 

 mens of Terias silhelana, Terias laela, Juiumia lemonias, 

 Tarucus theoplirastus^ Laniptdes etpis, Catopsilia pyranthe^ 

 and some others which were not being caught in flight. Some 

 three or four days later few King Crows were to be seen, 

 the butterflies were much diminished in number, and nearly 

 all those caught were damaged specimens. The birds perched 

 on the tall dryjowari stalks and made short flights on all sides, 

 catching their prey sometimes on the wing, sometimes on the 

 ground. 



I could not say with certainty wh.at buitertlios were caught 

 on the wing. 



The King Crow and the Bee Eater are two of the commonest 

 birds in this part of the country, and must cause a good deal of 

 destruction in the course of a year. Annie E. McKav. 



India, February 21. 



"Nature-Study" Exhibition. 

 Wii.i. you kindly permit me, while thanking y:u for the 

 attention which you have already directed towards the above 

 txhibition, to state that it has now been arranged to hold it at 



