April 20, 1893] 



NA TURE 



581 



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 Nat URE. 

 iVo notice is taken of anonymous communications.^ 



Locusts at Great Elevations. 



The following account of the occurrence of swarms of locu-^ts 

 at great elevations in the Himalaya, and these stripping birch 

 trees, is from a privately printed record of an expedition to the 

 north-east of Kinchinjunga, in 1891, by Mr. White, the British 

 resident in Sikkim. That flights of locusts are carried from 

 the plains of India up to great heights in the Himalaya is a 

 well-known fact ; but not, I think, in the numbers nor with the 

 results to birch or other forest trees here recorded. 



The Camp, April. J. D. Hooker. 



"On July 19, 1891, I crossed the Lunglala Pass, 17,400 feet 

 .... On the Pass I saw the locusts that ha-1 infested 

 Darjeeling, for the first time, though subsequently I saw them 

 as high as 18,000 feet, where they were dying in the snow. It 

 will be remembered that this was the year of the great plague 

 of locusts in Malic. I heard that they had penetrated even into 

 Tibet. On the 21st I came down as far as Tangu, 12,750 feet, 

 where the locusts were in swnrm~ and dying in thousands. The 

 only plants they seemed to care about we'e the birches, and 

 these they stripped bare." 



The Sandgate Landslip. 



As I have just returned from Folkestone, and hive had oppor- 

 tunities for observing the recent " landslip" at Sandgate, perhaps 

 a note on it may be of some interest to readers of Nature, as I 

 do not think the explanation suggested by Mr. Blake in Natijre 

 (vol. xlvii. p. 467) is altogether applicable to the present 

 instance. 



So far as I could see from a careful examination of the ex- 

 posures, there is no trace of any movement of the solid rocks 

 of the cliff, as these are nowhere exposed in the fissures that 

 have been formed by the earth-movements ; and my impression 

 from all that I saw is that the "slip" has been entirely confined 

 to the debris which has accumulated in past ages against the 

 flank of the escarpment. On referring to the four types of 

 Bergstiirze or landslips described by Prof. A. Heim, of Ziirich, 

 some years ago in a monograph, which was summarised (with 

 additions) by myself in the Geological Magazine (Decade II., 

 vol. X. p. 160 et seq), it is not difficult to identify the Sanitate 

 incident with ihe first class of such phenomena, to which Prof 

 Heim gives the name " Schutlruischnng " ; that is to say, a 

 slide ox push o{ an accumulation of debris (Schutt). Such ac- 

 cumulations often in mountain rrgions occur as lateral moraines 

 or as talus ; and in my paper on the ori^jin of valley lakes 

 (Quar. Jour. ('.eol. Soc, vol. xxxix. , February, 1883) I have 

 attempted to show how such masses play an important part in 

 the formation of some lakes. The Snnilgate phenomenon I 

 take to be no more than a magnified instarce of what 

 occurs in many a clayey railway-cutiing. as railway-engineers 

 know loo well. There seems to be no occasion for importing 

 the noiion of "faulting" of the rocks themselves into the 

 question. Still less rational is the notion that vibraiioi s due 

 to the blowing-up of one or two ships lately had anything to do 

 with the catastrophe. Th» most elementary principles of 

 mechanics explain it completely. 



A mass of rock-fmgments and clayey material, such as may 

 constitute a "scree," .-icq'iires in time a certain amount of co- 

 herency from the oxidation of the irony constituents, or fmm the 

 solution anfl redeposition of carbonate of lime (where the 

 materials are calcareous) by carbonated atmospheric waters per- 

 colating the mass, or from both of these causes. If the mass is 

 fairly drained internally it may retain its stable condition for 

 any length of time, and be mistaken for a part of the solid 

 geotectony of the district, though in cases where the materials 

 are largely composed of decomposable silicates, it is evident that 

 there is a tendency for the proportion of the fine slippery clay- 

 material in the mass to increase. The consequence may be (and 

 often is) that there is a tendency in the whole mass to settle down 

 under the force of gravitation, and so a slow preliminary differen- 

 tial movement often goes on for years, before some new factor is 

 introduced to precipitate the disaster. There can scarcely be 



NO. 1225, VOL. 47] 



any doubt that the new factor in this case was the excessive rain- 

 fall of last February, and the want of sufficient under-draining 

 to carry away the water, which entered the mass of partly-com- 

 pacted debris from above. A small lateral valley parallel with 

 the general line of the escarpment had no doubt served as a 

 catchment agent for much of this water. This supposition is 

 borne out by the facts (i) that further to the east, where a land- 

 drain was laid some years ago, the mass below it remained stable ; 

 (2) that above the western end of the "slip" the military hos- 

 pital suffered no damage, the stability of its base being doubtless 

 due to the complete under-draining of the site, which, as my 

 kind friend and host Colonel Cranmer Byn;^ informed me, was 

 carried out before the hospital was built. It is probable, how- 

 ever, that at the point of maximum movement the springs from 

 the beds which form the plateau above had much to do with 

 the water-loggiiig and consequent diminution of the internal 

 friction of the debris which moved, and that the action of those 

 springs was exceptional or excessive in the early part of this year, 

 owing to the rise of the water-line in the ground at the back of 

 the escarpment. 



I have talked the matter over with Mr. Topley, who is an 

 expert on all matters of Wealden stratigraphy, and he agrees 

 generally with me as to the real nature of the phenomenon. 

 There is one obvious and only preventive against its recurrence. 



Wellington College, Berks, April 15. A. Irving. 



" Roche's Limit." 



I MUST thank your correspondent G. R. for correcting my 

 carelesness in giving Roche's limit round the sun as about a 

 tenth of the earth's distance, instead of about a ninetieth as it 

 really Ls. 



If R is the radius and D the density of a spherical planet, and 

 d the density of the tidally disturbed and infinitesimal satellite, 

 moving in a circular orbit so as always to present the same face 

 to the planet, then the distance at which the satellite is on the 

 point of being broken up by the tidal forces is 2*44 R x (D/r/jJ.i 

 This is Roche's limit, and the formula is correctly stated by 

 G. R. 



The mean density of Jupiter is about one third greater than 

 that of water, and it does not seem unreasonable to suppose that 

 the density of the fifth satellite may be as low as 2. This w»)uld 

 bring the limit to 2-13 R. 



Any plausible hypothesis as to the density of the stones f.>rm- 

 ing Saturn's rings will no doubt bring the limit somewhat inside 

 the outer edge of the rings. 



I must plead guilty to not having made these numerical 

 estimates whilst writing my review of Mr. See's paper. How- 

 ever, it still seems to me that the coincidences which I there 

 noted are very remarkable. 



The simple illustration by which G. R. obtains a fair approxi- 

 mation to Roche's limit is very interesting. 



The satellite is replaced by two small spheres of density d and 

 radius r, touching one another, in line with the large sphere of 

 density D and radius R. Suppose that when the point ol contact 

 is distant c from the centre of the large sphere, the small spheres 

 are on the point of being pulled apart ; then c is the approxima- 

 tion to Roche's limit. G. R.'s condition is that the excess of the 

 attraction of the large s|ihere on the nearer small one above the 

 attraction on the further one is equal to the attraction between 

 the small ones. In algebraical language this becomes 



^jrDRS.JWr 

 Whei ce 



\c-rY 



,-\ =(^Wr3)2 



d 



Treating ;■ as very small we have f = 2*52 R x (D/d)K 

 If the spheres r are not very small, i{D=d, and if R be taken 

 as unit of length, the equation for c becomes 



c*- 2<V- i6<r-f ;■•» == o. 



This quartic determines the approximate limit when the 

 satellite is not infinitely small. 



I shall now use this equation to find what size we must atlri- 



1 •• La figure d'une masse fluide soumise .^ I'attractipn d'un point i\o- 

 gxni." E. Roche. Acad. desSci. de Montpelier, vol. i. (184750). P- 243. 



