162 Transactions. — Miscellaneous, 



bodies as to be incapable of an accurate solution. This ratio is certainly 

 not far from the truth. 



Some cosmical bodies, such as 1830 Groombridge, could not form binaries 

 by impact, for were two such bodies to come into about complete collision, 

 the parts not colliding would possess so much energy that they must escape 

 the total attraction, and could by no means become an associated pair. 

 Such a collision might, of course, form a pair of variables travelling away 

 from each other, and there are many examples of such to be found in the 

 heavens. It is even probable that, were they to completely collide, the heat 

 would be so great that every molecule would escape the attraction of the 

 mass and diffuse itself into space, thus producing a brilliant temporary star. 



On the other hand, a colliding pair of stars, without original proper 

 motion, must become associated no matter how small a part might be struck off 

 each. If the amount cut off be so great that the non-colliding parts cannot 

 escape the general mass, an annular nebula may be formed ; or, if the 

 impact be nearly complete, the two may form a star with a diameter only a 

 small multiple of the original stars. Calculation has shown that it must be 

 at least the sum of the original diameters. 



Without proper motion it would appear that the chance of a binary 

 being formed to that of coalescence is about four to one ; but, as this is 

 influenced by the amount of distortion before and during impact, and also 

 by the density, it is impossible to calculate it accurately. With proper 

 motion, and all stars appear to have more or less of this, the ratio becomes 

 larger, so that, taking all impacts not cosmically insignificant into conside- 

 ration, it is probable that something like a fourth are attended by escape of 

 the non-colliding parts, about a sixth coalesce entirely, and the remainder 

 form binary or multiple stars, associated by gravitation. The history of 

 such a pair appears to be roughly represented by the following illustra- 

 tion : — 



Suppose two equal stars with normal proper motion to come into partial 

 impact and strike off a fourth of each ; these two parts v/ill coalesce and 

 form a nebula. This coalesced part will exercise a large additional attrac- 

 tive power upon the retreating parts, and would associate the pair. For in 

 order that the parts shall escape, the stars would have required approxi- 

 mately a proper motion equal in energy to three-quarters of the energy 

 that a similar body would require to escape the independent attraction of 

 the central body. And this is certainly enormously above a normal proper 

 motion. Immediately after impact the associated pair will tend to move in 

 highly eccentric elliptical orbits. 



The extremely high temperature of the central body will make a tempo- 

 rary star of it, and although a nucleus consisting of the heavier atoms may 



