10 Prof. G. H. Darwin. On the Mechanical [Nov. 15, 



and what is called the radius of " the sphere of action " is simply the 

 distance between the centres of a pair when they graze, and is there- 

 fore the sum of the radii of a pair, or, if of uniform size, the diameter 

 of one of them. 



The 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 3g- grams. From these, the values for other 

 masses are easily derivable. 



It is known that meteorites are actually of irregular and angular 

 shapes, but certainly no material error can be 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 dispersion 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^ kilometers per second, being v/f 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 independent of 

 the size of the meteorites. The mean free path between collisions 

 ranges from 42,000 kilometers at the centre, to 1,300,000 kilometers 

 at radius 16, and to infinity at radius 44J. The mean interval 

 between collisions ranges from a tenth of a day at the centre, to three 

 days at radius 16, and to infinity at radius 44^. The criterion of appli- 

 cability of hydrodynamics ranges from -Q^^Q-Q at the distance of the 

 asteriods to -g-gVo a * radius 16, and to infinity at radius 44^. 



All these quantities are ten times as great for meteorites of 

 3J kilos., and a hundred times as great for meteorites of 3J tonnes. 



From a consideration of the tables in the paper it appears that, 



