August 23, 1900J 



NATURE 



3«9 



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.'\ 

 Snow-drifts on Ingleborough in July. 



On July 4 last I was on Ingleborough with a party of 

 geologists examining the swallow-holes which mark where 

 the water, running off the impervious drift and shale above 

 Newby Moss on the southern shoulder of the hill, first reaches 

 the Mountain Limestone. Some of these swallow-holes are 

 what we may call obsolete — that is to say, when new openings 

 have been formed and enlarged as time went on, some of the 

 chasms which obviously at one time carried off the flood-water 

 from a large gathering-ground, now receive only what oozes in 

 from the peat and drift immediately round it, or the rain which 

 falls directly on it : and rain seldom falls vertically up there. 

 Some of them seem to have been developed without any large 

 body of water having ever invaded them. They run to great 

 depths, the open shaft being from 30 to 360 feet deep, below 

 which the cavernous rock carries the water on through caves 

 and crevices and open joints far down to the valley below. 



In one of the vertical caves, which lies east of Long Kin and 

 luns down into the limestone rock to a depth of some 70 feet, 

 there were masses of snow to 4 feet in thickness. It was 

 speckled brown on the surface, from the particles of peat which 

 had been blown on to it, but was pure and white within. Obviously 

 the chasm had been filled by drifted snow during the winter, and 

 the summer's sun could not reach that depth to melt it, while 

 the earth temperature was lost on the moist pinnacled rock on 

 which it rested. No flood ever filled this particular chasm with 

 a swirling torrent, such as at times fills Weathercote Cave, 

 Hunt Pot, or even Gaping Ghyll up to the brim, and causes 

 them to overflow. 



Here, therefore, we had an accidental combination of con- 

 ditions favourable for the preservation of snow, long past mid- 

 summer, at a height of not more than 1500 feet above the sea, 

 on the flank of a Yorkshire mountain. 



This is an interesting fact to bear in mind when speculating 

 upon the causes of glacial conditions having so -recently pre- 

 vailed over the British Isles. We see here that half-way up 

 Ingleborough, in an exceptionally hot summer, the air tempera- 

 tiire alone could not remove last winter's snow. 



T. McKenny Hughes. 



The Total Eclipse of the Sun of May 17-18, 1901. 



In tht Nautical Almanac Circular (No. 18) local particulars 

 of this eclipse are given for four places in the eastern portion of 

 the shadow track, three of which, Padang, Pontianak and 

 Amboyna, are situated in Netherlands India. In the explana- 

 tions it is mentioned that, from inquiries which have been made, 

 it appears that the positions selected are the most accessible, 

 and that it would probably be impossible for observers to occupy 

 any neighbouring station for which the astronomical conditions 

 might be more favourable. 



Surely these inquiries have not been made on the spot, where 

 the information could best have been obtained. • Other localities 

 in the Government of Sumatra's west coast are as easily accessi- 

 ble as Padang, from which a railway leads to the interior ; and 

 other localities on the banks of the Kapuas as easily as Ponti- 

 anak. Moreover, many other places may give opportunity to 

 eclipse parties for observation, viz. on the islands of Lingga 

 and Singkep, on the banks oi the Barito and the eastern coast 

 of Borneo, in the Gulf of Tomini (Celebes) and in the Moluccas. 

 The conditions, however, will be most favourable in the western 

 part of the Archipelago, both on account of the longer duration 

 of totality and also for local resources. Through the Koninh- 

 lijhe Natuurkundige Veruniging at Batavia, data have been 

 gathered referring to the conditions of weather and cloudiness 

 at a numljer of stations most suitable for the observation of the 

 eclipse, and the data will be published in due time. The general 

 impression is, however, that the chance for fine weather is 

 nowhere very great. The Society will be pleased to procure 

 full information as to the choice of stations, and observers may 

 be sure to receive every available assistance from the local 

 authorities and officials in the Dutch colonies. 



J. J. A. MULLER. 



(President of the Kon. Natuurk. Ver., Batavia, July 17). 



NO. 1608, VOL. 62] 



The Reform of Mathematical Teaching. 



Many schoolmasters tell us that boy-nature is so depraved 

 that his time must be fully occupied, and that a "regular hard 

 grind " is the only way to keep him out of mischief. They give 

 him things to grind that do not interest him ; it may be that he 

 does not understand them, or that they have no human interest. 

 And yet every boy has interests, and teaching directed towards 

 those interests would enthral him. The first aim should be to 

 attract the boy's attention, and a subject which no excellence of 

 teaching will make interesting to a particular boy is no fit subject 

 of study for him. 



The case of mathematics is bad. The reasoning is too abstract 

 for a boy's mind, but it has worse faults. Long strings of reason- 

 ing are employed to deduce fairly obvious conclusions from 

 premises no more obvious, e.g. in the theory of parallels. On 

 the other hand, incorrect proofs are given because the boy cannot 

 grasp correct proofs, e.g. for the binomial theorem. Geometry 

 is in worse case than algebra. Euclid's interest was logical 

 rather than geometrical ; he wished rather to put together a con- 

 sistent series of syllogisms than to give the best .solution of his 

 problems: witness his bisection of a straight line. In con- 

 sequence, the natural order of development is lost sight of. A 

 boy ought to be at home with rulei and compasses before he 

 reasons about the constructions possible with them, and yet most 

 schoolboys have never handled compasses. A few weeks ago I 

 asked some hundred boys in a well-taught school (as present 

 teaching goes) to give a certain construction of Euclid's, and also 

 to carry out the construction with ruler and compasses on a 

 given line. Hardly one failed to write out the construction and 

 proof, but only one of the hundred carried out the practical con- 

 struction. Clearly our present Euclidian teaching has little to do 

 with geometry. 



To lay before a boy a proof he does not understand is useless, 

 to prove the obvious is confusing, to give an incorrect proof is 

 immoral. Prof. Perry's plan to abolish proofs in the early stages 

 is a great step in advance of present teaching. For the boy of 

 mathematical ability it would perhaps be well to run theory 

 alongside, at the rate of five or six propositions for Euclid's 

 entire first book. This would, however, interfere with class 

 teaching, and the mathematical boy would lose little by going 

 through a good deal of the practical course before touching 

 theory ; if with a hint here and there he could be got to evolve 

 the theory for himself, he would gain much. 



Possibly a theoretical training leads one to look with too 

 favourable an eye on early theory. In any case, that in the 

 hands of a good teacher theory and practice could well go hand 

 in hand for boys even of average ability is shown by two able 

 papers by Mr. Branford, in the Journal of Education, on the 

 first teaching of geometry. We may finally reach this stage, but 

 till we have these good teachers practice should precede theory. 



David Mair. 



Functions of an Organ of the Larva of the Puss Moth. 



This season I am breeding, with the object of observing their 

 gradual growth and development, a number of the larvae of 

 Cerura (or Dicranura) vinula, the Puss Moth ; but I have 

 sought in vain for the function performed by the slender red 

 filaments, ejected, at the insect's will, from its twin tails. They 

 appear to shoot from their sheathes, just on the same principle 

 as do a cat's claws ; but to what purpose ? 



Surely such a beautiful, delicate organism could not have 

 been appointed to no purpose ! Is this merely an instance of 

 entomic mimicry, simulating, for its own protection, the sting of 

 some venomous insect ; or does this strange organ perform some 

 practical, active function ? 



I shall be very greatly obliged if you can tell me whether 

 this point has been already decided or not, and, in the latter 

 case, perhaps some of your correspondents will kindly com- 

 municate their views upon it. Arthur S. Thorn. 



4 Malcolm Road, Penge, August 10. 



Dark Images of Photographed Lightning Discharges. 



A VERY clear illustration of the reason why some of the light- 

 ning discharges in a photographed thunderstorm appear dark 

 was afforded me at Wednesfield, Staffordshire, about mid-day 

 on Thursday, July 19. There were a number of double flashes, 

 that is, two discharges occurring rapidly in the same apparent 



