436 



NA TURE 



[September 6. 1900 



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 comviunications.'\ 



Railways and Moving Platforms. 



In reference to Prof. John Perry's letter in Nature of Aug. 30 

 on the subject of " Railways and Moving Platforms," will you 

 kindly allow me to state that I worked out a scheme for moving 

 platforms for railways in India in the year 1877, and that a 

 paper of mine on the subject was published in the professional 

 papers of the Thomason Civil Engineering College at Rurki in 

 India in 1877 o"" 1878? 



My plan was to have alongside of the main line a length of 

 about a mile of level line, with a steep incline at either end, for 

 the moving platform. 



The moving platform would acquire sufficient speed on these 

 inclines to run alongside of, and be made fast to, a train on the 

 main line running in the same direction at reduced speed. 



After the platform had been made fast, and passengers and 

 crates of luggage transferred to a similar platform on the train, 

 the train was to increase its speed, and finally release the plat- 

 form with sufficient way on to carry it up the incline at the other 

 end of its run, so as to be in readiness for the next train from the 

 opposite direction. 



This represented the case for moving platforms in its simplest 

 form to suit Indian traffic. Details, of course, can readily be 

 supplied. W. Sedgwick 



September 3. (Lt.-Col. late R.E.). 



The Migration of Swifts. 



Referring to the letter of Mr. O II. Latter in Nature of 

 August 30, there are swifts' nests in the roof of my house, and 

 the birds went to their nests as usual on the evening of August 

 II, but on the following evening, Sunday, August 12, they had 

 gone. In other houses close at hand swifts remained on the 

 13th and 14th, but by the evening of the 15th all had dis- 

 appeared. On one occasion some years ago a solitary swift 

 remained after his companions had departed, and consorted 

 with the neighbouring house martins until the last week in 

 September. 



A curious occurrence was observed by me on May 26 last, when 

 the swifts had already been for some time with me But on the 

 afternoon of that day I was on board the Transatlantique Com- 

 pany's steamer crossing the Mediterranean from Marseilles to 

 Algiers in order to observe the total eclipse of the sun. The 

 boat left Marseilles at one o'clock, and at 4h. 40m. , by which 

 time we were seventy miles from the land, a flock of birds was 

 seen following the ship in the distance. In a few minutes they 

 were flying round the ship, and turned out to be common swifts. 

 They were estimated to be about 200 in number. They 

 gradually forged ahead, leaving the ship behind, and in a few 

 minutes were lost in the distance. Several of the passengers 

 made a note of the occurrence. The course followed by the 

 swifts was one or two points to the right of the ship's course, or 

 about S.S.W., in the direction of the Balearic Islands. 



William Andrews. 



Steeple Croft, Coventry, September i. 



The Reform of Mathematical Teaching. 



The deeply interesting letter of Mr. David Mair on the above 

 subject in a recent number of Nature will no doubt be atten- 

 tively perused. Many, I imagine, could echo his experience 

 when he says, speaking of 100 boys at a " well-taught school," 

 " hardly one failed to write out the construction and proof, but 

 only one of the hundred carried out the practical construction. 

 Clearly our present Euclidian teaching has little to do with 

 geometry." 



Grave dissatisfaction in regard to the study of Euclidian 

 geometry has long been voiced in Great Britain and in France, 

 and the reason for the continued lamentable state of things in 

 that special scientific direction is not, I think, far to seek. 

 When Euclid, as a practical teacher, made use of his Propo- 



NO. 1 6 10, VOL. 62] 



sitions, theory and practice had doubtless that close associatior> 

 which Mr. Mair appears rightly to desire as a remedy for the 

 present extraordinary condition of Euclidian study. 



Now, if we assume that Euclid's own pupils were first of aU 

 drilled in a thorough knowledge of the sub-geometric properties 

 of the cube, we are led largely to modify the supposed indictment 

 against Euclid's method. 



Again, Euclid seems to me to have used constructions, not 

 only of a strict, but of a particular or edificial nature ; so that, 

 properly viewed, each succeeding proposition carried, not only 

 its specific teaching or lesson, but beautiful groups also oi 

 surrounding truths of an implicit character. 



If the foregoing remarks be valid, it is easy to see that only 

 two serious faults can be charged against Euclid's method — 

 namely, the use of false diagrams and indirect deipnonstrations. 

 The former, of course, being misleading, are not in harmony 

 with the modern Herbartian cumulative principles of " educa- 

 tive instruction." 



As to the second fault, the splendid argumentation of the 

 famous Simson in his " Notes" will not, I fear, greatly avail in 

 Euclid's favour. Mr. Mair rightly vindicates for the pupil the 

 power of " educational interest," another Herbartian doctrine, 

 by the by ; and I agree with him that "geometry is in worse 

 case than algebra," because with the latter, I opine, the notiork 

 of "izero" inevitably leads the mind towards the necessary 

 cubical standard. 



No one could reasonably wish the true Euclidian or edificial 

 geometry to be suppressed, but might without presumption 

 press for a reform in the way of presenting all geometrical 

 truths by a direct reference to those sub-geometric conditions 

 which have equal rank with the oldest of nature's immutable 

 laws. 



If for any school or pupil, instead of enlarging the mental 

 vision, and creating intellectual joys, the Euclidian tasks savour of 

 prolonged drudgery, mystery and confusion, as they assuredly 

 often do, such toil should perforce be abandoned to prevent, 

 at least, waste of time and energy, not to speak of the gair* 

 to human happiness. 



Possibly in the broad expanse of the educational economy the 

 universities of the world may eventually suggest practical 

 reforms of a vital kind in the teaching methods that affect 

 mathematical science. 



I am not competent to pursue the subject to any length, but 

 I might remind students that, although by a sort of repartee to 

 a kingly personage Euclid said there was ' ' no royal road to 

 geometry," he did not say there was no royal gate to it, and 

 that I trust I have, however faintly, herein indicated. 



August 25. Henry Woollen. 



The Trembling of the Aspen Leaf, 



It is well known that the vibratory motion of the leaf of the 

 aspen and other poplar trees is caused by a flattening of the 

 petiole at its junction with the lamina. The lower part of the 

 leaf-stalk is elongated and rigid, thus forming a basis upon 

 which the flattened portion of the stalk can, in virtue of its elas- 

 ticity, move to and fro as the wind acts upon the leaves of the 

 tree. It is stated by Kerner that this adaptation prevents the 

 leaves striking against each other and the branches of the tree, 

 whereby they might get bruised. In this connection it is a 

 noticeable fact that the poplars which exhibit this property of 

 leaf-vibration most strongly have sparsely distributed leaves, and 

 the foliage is scanty in comparison with other trees of the genus, 

 especially the abele, or white poplar. ■~. 



With reference to the abele, it may be noticed that the leaves 

 which possess the trembling motion in a slight degree are 

 covered with a white felting, which Kerner asserts is an adapta- 

 tion to protect the stomata from the excess of atmospheric 

 moisture which prevails in the damp situations and river-sides 

 where this tree commonly grows. Yet, it may he noted, the 

 aspen is found in precisely similar conditions, and must be 

 affected injuriously by any influence that would act unfavourably 

 upon the abele. Now, it has occurred to me that the real use 

 of the vibratory motion of the aspen leaf may be an adaptation 

 to throw off rapidly the excess of aqueous condensation liable 

 to take place upon the foliage of trees growing in marshy 

 situations. I should very much like to hear the opinions of 

 some of your readers on this point, which, if a true solution of 

 the matter, is interesting from the fact that the same end is 



