548 



NATURE 



[October 4. 1 900 



and blurred in outline. Indeed, we venture to think that 

 if a second edition be called for it would be a decided 

 improvement if the plates were photographed down to 

 octavo size, while at the same time the text might be 

 printed in larger type. 



As it is, however, the book is decidedly attractive, 



and ought to prove indispensable to all breeders of 



ornamental water-fowl. R. L. 



Catalogue of Eastern and Australian Lepidoptera 



Heterocera in the Collection of the Oxford tjniversity 



Museum. Part ii. Noctuina, Geometrina and 



Pyralidina. By Col. C. Swinhoe. Pterophoridas and 



Tineina. By the Right Hon. Lord Walsingham and 



John Hartley Durrant. Pp. vi + 630 ; with 8 plates. 



(Oxford : Clarendon Press, 1900.) 



The first volume of this important work was published as 



long ago as 1892 ; it included the Sphinges and Bom- 



byces ; and the second and concluding volume, which is 



nearly twice as thick as the first, has at length been 



issued. 



A great number of Lepidoptera Heterocera (moths) 

 were described by the late Francis Walker, not only from 

 the British Museum, but from various private collections, 

 chiefly from that of W. Wilson Saunders. After the 

 death of the latter, large portions of his collection found 

 their way into the Oxford Museum, and the types have 

 now been carefully identified, and a considerable number 

 figured. This is extremely important, as it will enable 

 lepidopterists at a distance to identify species with 

 more certainty than by descriptions alone ; and a figure 

 also helps to fix the identity of a species in case the 

 type should be lost or destroyed. 



About 2340 species of moths are enumerated in the 

 present volume, and we note that in addition to Walker's 

 types many described by Mr. F. Moore and other 

 entomologists are likewise contained in the Oxford 

 Museum ; nor must we omit to mention that several new 

 genera and species are described and figured by the 

 authors of the Catalogue for the first time. However, 

 the work is one which, notwithstanding its importance, 

 appeals so exclusively to specialists that a more lengthy 

 notice is hardly required in the columns of Nature. 



W. F. K. 

 Sir Stamford Raffles : England in the Far East. By 

 H. E. Egerton, M.A. Pp. xx + 290. (London : 

 Unwin, 1900.) 

 This volume, which is one of a series, entitled " Builders 

 of Greater Britain," and edited by Mr. H. F. Wilson, 

 does not call for much comment in a journal devoted to 

 science. The author of the biography naturally deals 

 mainly with Sir Stamford Raffles as an administrator in 

 the Straits Settlements and the Malay Archipelago, and 

 only incidentally, and that very briefly, refers to him as a 

 zoologist. Raffles was, as everybody knows, one of the 

 founders, and the first president, of the Zoological Society 

 of London ; and his bust adorns the lion house of that 

 society. Mr. Egerton, in narrating this fact, is chiefly 

 impressed by " how much innocent pleasure this distin- 

 guished child-lover has given to countless thousands of 

 children " by his successful eff'orts in this direction. He 

 mentions, however, the collections which he took care to 

 make, and which were largely reported upon by Dr. 

 Horsfield. In those days much that was brought back 

 from the East in the way of zoological specimens was 

 quite new to science, and the animals had to have names 

 given to them ; it is not such a great compliment as Mr. 

 Egerton seems to think to name a species Gymnura 

 rafflesii, after Sir Stamford. This compliment is usually 

 paid to the capturer of a new form, and it is ridiculous to 

 say that " Raffles' reputation in the scientific world is 

 attested by the fact that the great French naturalist, M. 

 Geofifroy St. Hilaire, described a new variety of animal 

 under the specific name ' Rafflesii.'" 



NO. 1614, VOL. 62] 



LETTERS 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 communications. ^ 



The Teaching of Mathematics. 



Prof. John Perry has asked me to write something in 

 criticism of the views he has lately expressed about the teach- 

 ing of mathematics. I am inclined to ask, What is the use ? 

 He knows my views pretty well, and others too ; and those 

 who don't can learn them if they want to by buying my books. 

 That is the best way, as it brings in one-and-threepences, and 

 so does some good. I think there is a great deal to be said on 

 both sides, and that if you are a born logic-chopper you will 

 think differently from Faraday. The subject is too large, and 

 I will only offer a few remarks about the teaching of geometry, 

 based upon my own experience and observations. Euclid is 

 the worst. It is shocking that young people should be addling 

 their brains over mere logical subtleties, trying to understand 

 the proof of one obvious fact in terms of something equally, or, 

 it may be, not quite so obvious, and conceiving a proiound dis- 

 like for mathematics, when they njght be learning geometry, a 

 most important fundamental subject, which can be made very 

 interesting and instructive. I hold the view that it is essentially 

 an experimental science, like any other, and should be taught 

 observationally, descriptively and experimentally in the first 

 place. The teaching should be a natural continuation of that 

 education in geometry which every child undergoes by contact 

 with his surroundings, only, of course, made definite and 

 purposeful. It should be a teaching of the broad facts of 

 geometry as they really exist, so as to impart an all-round 

 knowledge of the subject. It should be Solid as well as Plane ; 

 the sphere and cube, &c., as well as llie usual circle and square ; 

 models, sections, diagrams, compasses, rulers, &c. , every aid 

 that is useful and practical should be given. And it should be 

 quantitative as well. The value of -k should be measttred ; it 

 may be done to a high degree of accuracy. So with the area 

 of the circle, ellipse and all sorts of other things. The 

 famous 47lh. The boy who really measures and finds it 

 true will have grasped the fact far better than by a 

 logical demonstration without adequate experimental know- 

 ledge ; for it happens that boys, who are generally 

 very stupid in abstract ideas, learn a demonstration without 

 knowing what it is all about in an intelligent manner. It may 

 be said by logicians that you do no\. prove anything in this way. 

 I differ. It might equally well be said that you prove nothing 

 by any physical measurements. You have really proved the 

 most important part. What a so-called rigorous proof amounts 

 to is only this, that by limitation and substitution, arguing about 

 abstract perfect circles, &c., replacing the practical ones, you 

 can be as precise as you please. Now when a boy has learnt 

 geometry, and has become competent to reason about its con- 

 nections, he may pass on to the theory of the subject. Even 

 then it should not be in Euclidean style ; let the invaluable 

 assistance of arithmetic and algebra be invoked, and the most 

 useful idea of the vector be made prominent. I feel quite 

 certain that I am right in this question of the teaching of geo- 

 metry, having gone through it at school, where I made the 

 closest observations on the effect of Euclid upon the rest of 

 them. It was a sad farce, though conducted by a conscientious, 

 hard-working teacher. Two or three followed, and were made 

 temporarily into conceited logic-choppers, contradicting their 

 parents ; the effect upon most of the rest was disheartening and 

 demoralising. I also feel quite certain about the experiential 

 and experimental basis of space geometry, though that opinion 

 has been of slow growth. If I understand them rightly, it is 

 generally believed by mathematicians that geometry is pre- 

 existent in the human mind, and that all we do is to look at 

 nature and observe an approximate resemblance to the pro- 

 perties of the ideal space. You might assert the same pre- 

 existence of dynamics or chemistry. I think it is a complete 

 reversal of the natural order of ideas. It seems to me thai 

 geometry is only pre-existent in this limited sense ; that since we 

 are the children of many fathers and mothers, all of whom grew 

 up and developed their minds (so far as they went) in contact 

 with nature, of which they were a part, so our brains have grown 

 to suit. So the child takes in. the facts of space geometry 



