Nov, 29, 1888] 



NATURE 



105 



agh autumn and winter, if it be mikl. With regard to 

 folium subterraneum, as it was about thirty years ago when 

 •rved it, I cannot now be certain that it was actually cleisto- 

 aous ; but it grew with just the same habit as the above, and 



most probably self-fertile as they are. 



George Henslow. 



[ose-Blackening as Preventive of Snow-Blindness. 



BEG to send you an extract from a letter just received from 

 son, of the Indian Geological Survey Department, and who 

 present engaged by the Maharajah of Kashmir in exploring 

 reporting on his sapphire mines. Since it refers to former 

 imunications in Nature (vol. xxxviii. pp. 7 and loi), upon 

 xbject of interest to travellers, it may be of use. 

 may here mention that my son speaks of having found the 

 cene Nummulitic limestone in Zanskar at a height of 18,500 

 above the sea. Sir J. D. Hooker tells me that he has 

 riously observed the Nummu!ites-in Tibet, at a height of 

 COO feet. J. D. La Touche. 



tokesaj', Craven Arms, November 20. 



Some time ago there was a letter in Nature describing a 

 thod of protecting the eyes from sun-glare, when crossing 

 jw, by blackening the nose and cheeks under the eyes. I 

 the dodge the other day, when 1 was crossing the snow- 

 is and glaciers from Zanskar, and found it very successfid. 

 shikari and some of the other natives were much amused 

 ien I produced a piece of charcoal, and proceeded to bhcken 

 face ; but they also tried it, and said that it relieved them 

 much. I do not know how the effect is produced, but it 

 much the same as when one went off the snow on to a patch 

 moraine or rocks clear of snow. The blackening seemed to 

 the reflected rays in some way. The natives expressed the 

 ling by saying that it cooled their face-;. I found it quite 

 jible to walk over the snow for many miles without glasses, 

 "which are a nuisance, especially on rough ground ; but without 

 the blackening I had to put them on. The sun at these high 

 altitudes has much greater effect than in England when the 

 ground is covered with snow." 



Amber. 



In Nature (vol. xxxvi. p. 63), I find the following note-: — 

 "The largest piece of amber ever discovered was recently dug 

 up near the Nobi's Gate, at Altona. It weighed 850 grammes." 

 I begto state that a piece of amber, weighing 5 '6 kilogrammes, 

 is in the possession of Messrs. Stantien and Becker, in Konigs- 

 berg, and that pieces weighing 65 and 9*5 kilogrammes can be 

 seen in the Berlin Mineralogical Museum, both discovered off 

 the sea coast of North Germany. Even as far inland as Silesia, 

 a piece of Baltic amber, weighing 3 kilogrammes, has been 

 found in the bed of the River Oder, near Breslau. Baltic amber 

 occurs in Sile- ia also as high as 1400 feet above the level of the 

 sea. A. B. Meyer. 



Royal Museum, Dresden, November 19. 



ON THE MECHANICAL CONDITIONS OF A 

 SWARM OF METEORITES} 



II. 



'T*HE next point to consider is the mass and size which 

 ■*■ must be attributed to the meteorites. 

 The few samples which have been found on the earth 

 prove that no great error can be committed if the average 

 density of a meteorite be taken as a little less than that 

 of iron, and I accordingly suppose their density to be six 

 times that of water. 



Undoubtedly in a meteor-swarm all sizes co-exist (a 

 supposition considered hereafter) ; for even if originally 

 of uniform size they would, by subsequent fracture, be 

 rendered diverse. But in the first consideration of the 

 problem they have been treated as of uniform size ; and, 

 as actual sizes are nearly unknown, results are given for 

 meteorites weighing 3^ grammes. From these, the values 



' .\bstract of a Paper read before the Royal Society on November 15 by 

 Prot G. H. Darwin, F.R.S. Continued from p. 83. 



for other masses are easily derivable. It is known that 

 meteorites are actually of irregular and angular shapes, 

 but certainly no material error can ht incurred when we 

 treat them as being spheres. 



The object of all these investigations is to apply the 

 formulae to a concrete example. The mass of the system 

 is therefore taken as equal to that of the sun, and the 

 limit of the swarm at any arbitrary distance from the 

 present sun's centre. The theory is of course more 

 severely tested the wider the dipersion of the swarm, 

 and accordingly in a numerical example the outside limit 

 of the solar swarm is taken at 44^ times the earth's distance 

 from the sun, or further beyond the planet Neptune than 

 Saturn is from the sun. This assumption makes the limit 

 of the isothermal sphere at a distance 16, about half-way 

 between Saturn and Uranus. 



In this case the mean velocity of the meteorites in 

 the isothermal sphere is 5.^ kilometres per second, being 

 ,^|.; of the linear velocity of a planet revolving about a 

 central body with a mass equal to 46 per cent, of that 

 of the sun, at distance 16. In the adiabatic layer it 

 diminishes to zero at distance 44^. This velocity is in- 

 dependent of the size of the meteorites. The mean free 

 path between collisions ranges from 42,000 kilometres at 

 the centre, to 1,300,000 kilometres at radius 16, and to 

 infinity at radius 44^. The mean interval between col- 

 lisions ranges from a tenth of a day at the centre, to 

 three days a: radius 16, and to infinity at radius 44i. The 

 criterion of applicability of hydrodynamics ranges from 

 ff^ioo at the distance of the asteroids, to ^iixia at radius 

 16, and to infinity at radius 44^. 



All these quantities are ten times as great for meteorites 

 of ih kilogrammes, and a hundred times as great for 

 meteorites of 3^ tonnes. 



From a consideration of the tables in the paper it appears 

 that, with meteorites of 3^ kilogrammes, the collisions 

 are sufficiently frequent even beyond the orbit of Neptune 

 to allow the kinetic theory to be applicable in the sense 

 explained. But if the meteorites weigh 3^ tonnes, the 

 criterion ceases to be very sinall at about distance 24 ; 

 and if they weigh 3125 tonnes, it ceases to be very 

 small at about the orbit of Jupiter. It may be concluded 

 then that, as far as frequency of collision is concerned, 

 the hydrodynamical treatment of a swarm of meteorites 

 is justifiable. 



Although the nun^kerical results are necessarily affected 

 by the conjectural values of the mass and density of the 

 meteorites, yet it was impossible to arrive at any con- 

 clusion whatever as to the validity of the theory without 

 numerical values, and such a discussion as the above 

 was therefore necessary. 



I now pass on to consider some results of this view of 

 a swarm of meteorites, and to consider the justifiability 

 of the assumption of an isothermal-adiabatic arrangement 

 of density. 



With regard to the uniformity of distribution of kinetic 

 energy in the isothermal sphere, it is important to ask 

 whether or not sufficient time can have elapsed in the 

 history of the system to allow of the equalization by 

 diffusion. 



It is shown therefore in the paper that in the case of 

 the numerical example primitive inequalities of kinetic 

 energy would, in a few thousand years, be sensibly equal- 

 ized over a distance some ten times as great as our 

 distance from, the sun. This result, then, goes to show 

 that we are justified in assuming an isothermal sphere as 

 the centre of the swarm. As, however, the swarm 

 contracts, the rate of diffusion diminishes as the inverse 

 :| power of its linear dimensions, whilst the rate of gener- 

 ation of inequalities of distribution of kinetic energy, 

 through the imperfect elasticity of the meteorites, in- 

 creases. Hence, in a late stage of the swarm, inequaU- 

 ties of kinetic energy would be set up, there would be a 

 tendency to the production of convective currents, and 



