JANUARY 23, I902J 



NATURE 



273 



In geometry ; the second, third and fourth books of Euclid. 

 In algebra ; quadratic equations, or indeed any equation, surd or 

 rational, for one or two unknown quantities, except such as 

 ultimately demand the solution of a non-factorial cubic or 

 biquadratic ; the simplification of surd quantities and expres- 

 sions and problems in ratio and proportion. 



Trigonometry has to be taught from the beginning through 

 the equations of identity between functions of the ratios and the 

 values of the ratios of the simple angles to the logarithmic 

 solution of oblique triangles, with proofs of the requisite formulcv. 

 A sufficient knowledge of logarithms is demanded from the 

 student to prove the ordinary logarithmic laws — no reference is 

 made in the entire syllabus to the theory of indices— and to 

 prove the numerical laws of characteristic and mantissa belong- 

 ing to the decimal system of logarithms. He must also be able 

 to adapt and use — for any possible logarithmic computation — a 

 few seven-figure logarithms given at the end of his examination 

 paper, and obtain by means of proportional differences a result 

 corrected to six significant figures. 



All this work is to be taught between September and May to 

 pupils who, throughout the country, are generally accorded two 

 hours a week for the subject, and who, as evening students 

 otherwise employed through the day, are seldom able to give 

 much time to study. 



In some parts of the course — for instance, the equations set 

 for solution — a pedant's ingenuity is used to find novelty and — 

 for the beginner — difficulty. In other parts— as, for example, the 

 surds and logarithms — the monotony of treatment year by year 

 is one of the mainstays of the e.xamination-teacher. 



I have not exhausted the possible complaints against the 

 course. Its first four stages are almost equally bad throughout, 

 though the second is certainly the worst. But I have, I hope, 

 said enough to convince any experienced teacher of the subject 

 under other conditions of the urgent need we feel for changes. 



I wish to guard myself against one possible personal imputa- 

 tion. I am not complaining because I have failed ; I have 

 been, I believe, at least averagely successful in obtaining the 

 examination-product that South Kensington demands, and I 

 have, I hope, also taught some mathematics. But I protest 

 that my efforts towards the one end should be so severely handi- 

 capped by the necessity of attaining the other. 



Plymouth Technical School. C. J. Forth. 



Birds Capturing Butterflies in Flight. 



Mr. McKay's letter in Nature of January 16 (p. 247) is of 

 interest in pointing out that some butterflies are normally ex- 

 posed in flight to danger from certain birds. Nevertheless, I 

 believe this to be exceptional so far as this country is concerned. 

 At the present moment I have in my possession a specimen of 

 the day-flying moth Orgyia aiiliijtia, which my friend Mr. D. F. 

 Taylor saw seized when on the wing by a house-martin, which 

 relinquished its hold in consequence of a luckily aimed stick 

 from my informant. The left fore-wing shows plainly the mark 

 of the bird's beak, which, however, did not tear the wing, but 

 merely left a triangular area denuded of scales. So far as I am 

 aware, house-martins do not, as a rule, feed on Lepidoptera, and 

 this instance is probably to be regarded as a mistake on the part 

 of the bird. It is possible that other isolated examples of 

 similar mistakes may have been noticed, but their bearing on 

 the general question of the coloration and markings of butter- 

 flies must be very slight. Oswald H. Latter. 



Charterhouse, Godalming, January 17. 



An Unusual Rainbow. 



On June 16 last I was at Lucerne, and at about 4 p.m. 

 there was a remarkably brilliant rainbow over the lake. It was, 

 however, unlike any previous rainbow ever seen by me, inasmuch 

 as in addition to the ordinary bow of seven colours there was a 

 second band of orange colour and a second band of purple, 

 added to the other seven colours on the underside, but distinctly 

 part of the same unbroken and continuous band of colour ; in 

 other words, it was a bright broad rainbow composed of nine 

 instead of seven bands of colour. I have, since my return, met 

 with no person able to explain this phenomenon. I was quite 

 alone at the time. The rainbow lasted several minutes. It has 

 been suggested to me that possibly some scientific reader of your 

 paper could explain this very unusual appearance ; or, at any 

 rate, some other traveller at Lucerne on the day referred to may 



NO. 1682, VOL. 65] 



be able to confirm my description of what appeared to me so 

 very unusual that I should almost have hesitated to accept any 

 other person's description of it. Tho.mas Fuller. 



Bristol, January 17. 



Change of Pitch of Sound with Distance. 



In Mr. West's letter in Nature of December 12, 1901, he 

 suggests that a lowering of pitch with distance may have been 

 noticed, although his experience has been the reverse. My 

 grandfather, the late Mr. Henry Knaiiff, who, during his life- 

 time, was an organist and organ builder in Philadelphia, men- 

 tioned having noticed this lowering of pitch on several occasions. 

 In long churches, with the organ over the front doorway, he 

 claimed that the voice of the celebrant at the altar sounded dis- 

 tinctly flat to a listener at the organ, but on adv.ancing to the 

 altar this flatness disappeared. I have never noticed this 

 myself, but I have not his ear for small differences of pitch. 



Paul R. Heyl. 



Boys' High School, Reading, Penna., U.S.A. 



TO THE MOUNTAINS OF THE MOOm 



MR. J. E. S. MOORE has undoubtedly written an 

 interesting and original book on the lake region 

 of Central Africa, a book which in many respects deserves 

 to rank with that remarkable pamphlet (it was little more 

 in volume) by the late Prof. Drummond on Nyasaland 

 (miscalled in this instance "Central" Africa). Prof. 

 Drummond's journeys up and down the Zambezi-Shire and 

 the length of Lake Nyasa, with a climb on to the Nyasa- 

 Tanganyika plateau superadded, were wholly unremark- 

 able as a work of exploration, but Drummond con- 

 trived to see and put into pithy sentences what a legion 

 of African explorers had seen but never expressed before. 

 Drummond's little book should long remain a classic, and 

 many of his expressions are quoted by the more modem 

 African travellers with force, but without acknowledg- 

 ment. Mr. Moore avows his indebtedness to Drummond 

 on more than one occasion, but his own work is quite as 

 original in its way, though perhaps dashed with a spite- 

 fulness which was absent from Drummond's writings. Mr. 

 Moore's book is a true account of what he has seen, but 

 a partial one, that is to say, he has told no untruth, but 

 he has left untold at least a third of the whole account. 

 In order to be original, in order to counteract the rather 

 wearisome optimismof most works of African travel written 

 during the last ten years, he has been careful to insist on 

 all the faults which a white man may legitimately find 

 with the climate, soil and insalubrity of Central .Africa. 

 He deliberately ignores much that might be permanently 

 attractive to the European settler, much that is profitable 

 to European commerce, and much of the good that has 

 been done by European pioneers, whether Government 

 officials, missionaries or traders. It is a pity in some 

 respects that Mr. Moore's work is not complete, that he 

 should have striven so much after originality as to refrain 

 from writing a perfectly balanced book conveying an 

 impartial verdict. It is, perhaps, best and fairest to 

 regard Mr. Moore's work as a "two-thirds" book, a 

 description giving two-thirds of the whole truth and 

 leaving the reader to supply the missing third from the 

 many other publications describing East-Central Africa 

 between the White Nile and the Zambezi which have 

 appeared since 1890. There is no doubt that Mr. Moore 

 is eminently readable ; he is so interesting that his 

 occasional descents into sheer flippancy and his careless- 

 ness in the spelling of names may easily be forgiven, 

 except, perhaps, by those whose names are incorrectly 

 spelt I By a curious fatality there is scarcely a single 

 European surname or a native place-name of any import- 

 ance in the whole book which is not incorrectly spelt. 



1 "To the Mountains of the Moon." By J. E. S. Moore. Pp. xvi-f35o 

 (London : Hurst and Blackett, Ltd., 1901.) 



