KECENT COSMOGONIES 211 



ward, or away, or parallel, with reference to each other. 

 We will, however, prescribe such a movement on the part 

 of both that shall make it possible for them to collide. 

 Imagine, then, a straight line joining the two, and exactly 

 at the middle thereof, and at right angles therewith, a 

 circular diaphragm having a diameter exactly equal to 

 said line of joinder. We will now stipulate, to begin with, 

 that both Alpha and the sun shall possess proper motions 

 which will cause them to impinge simultaneously on the 

 diaphragm, but we will leave to chance just where each 

 shall pierce it. 



By thus conditioning the sun to strike within the area 

 of the diaphragm, we have arbitrarily restricted him to a 

 little less than one-seventh of his original liberty of 

 movement, and so, too, with the star. By restricting 

 both, however, at the same time we enhance the chances 

 of collision, not by the sum, but by the product of these 

 amounts whence the probability against our premiss is, 

 say, fifty to one. 



We will now suppose both the star and sun to possess 

 diameters of a million miles (to make computation easy), 

 whence it would follow that (excluding the factor of 

 gravitation) they would be able to pass each other with- 

 out touching through a square or circular opening of 

 4,000,000,000,000 square-miles. Obviously, the chance of 

 either sun or star striking a particular spot on our dia- 

 phragm would be in the like ratio as the area of 

 the spot bears to that of the diaphragm or as 2,000, 

 OOO 2 is to 26,000,000,000,000 2 , i. e. as 1 to 169,000, 

 000,000,000. But not only this the sun and star must 

 both strike the same spot and they must do so at the same 

 instant of time, consequently we are obliged to square 

 the terms of our ratio a second time, the arithmetical re- 

 sult of which, for the sake of emphasis, I will write at 

 length, at the same time multiplying it by 50 for the rea- 

 sons before given. The chances, then, of the sun and 

 this particular star, by far the nearest of all, meeting and 

 colliding is only 1 in 1,428,050,000,000,000,000,000,000, 

 000,000, and even this is an underestimate. 



