BicKEETON. — On the Probability of Impact. 167 



my theory of " selective escape," that to be denser in the centre than at 

 the outside is an absokitely necessary condition of any body largely gase- 

 ous, and consisting of a mixture of molecules of varying weight. 



I shall now attempt to show that although the kind of impact Croll 

 suggests may well be considered improbable, yet the grazing impacts dis- 

 cussed in my papers are not only not improbable, but that evidence actually 

 demonstrates their occurrence. But it must not be supposed that my 

 theory suggests that even partial impacts between bodies of true stellar 

 mass of our own Universe are frequent events. The present evidence ap- 

 pears to show that, out of the tens of thousands of millions of stars that 

 stud our galaxy, only one or two graze each other sufficiently to produce a 

 temporary star in a hundred years. 



Proctor has, in my opinion, incontestably shown that the stars cluster 

 much more thickly in the Milky Way than in the other parts of the heavens. 

 Although these stars are mere points to us, yet we must not forget they 

 are suns ; and it is almost certain that hundreds among them have disks 

 many thousand times larger than our earth. 



These stars are all moving almost indiscriminately, with perhaps an 

 average velocity of twenty miles a second ; yet the space separating them is 

 so large, compared with their dimensions, that in a finite portion of time it 

 is improbable that any two approach each other in a straight line and come 

 into direct impact, for if two stars are not approaching each other directly 

 gravitation can never make them do so. It is quite otherwise with a graze ; 

 it is probable that gravitation increases a hundredfold the probability of 

 partial impact among bodies of very great mass compared with the chance 

 there would be from direct motion alone. 



Supposing the average velocity of stars to be twenty miles a second, and 

 a body with such independent energy to approach Sirius and graze its sur- 

 face, — the energy developed by its attraction will be many thousand times 

 its indedendent energy, unless the density of Sirius is incomparably less 

 than that of our sun ; and if this were the case its volume would be so great 

 that the chance of impact would be much increased. 



This furnishes a striking illustration of how enormously the deflection 

 due to gravitation will increase the probability of a grazing impact between 

 large cosmical bodies. It must be remembered that the probability of im- 

 pact is not simply proportional to the deflection but is directly as its square. 



It is impossible by the most careful watching to avoid collisions between 

 vessels on mid-ocean, but how much would the probability be increased if 

 all the ships that travel the Atlantic were steered by blind men, and if each 

 attracted another approaching near with such force that their own indepen- 

 dent motion was nothing to that developed by the pull ! 



