108 Transactions. — Miscellaneous. 



impact of approximately equal bodies has a far higher probability than com- 

 plete impact, and also that, cosmically, partial impact has a far higher 

 constructive capacity. 



I wish to state that I do not mean, that between unequal bodies partial 

 impact is more frequent than complete. It is certain that the impact of 

 particles of gas upon a body such as our Sun, must practically always be 

 complete. Mr. Beverly has made a calculation of probabilities on the 

 best assumption of the conditions of space attainable, and he finds that in 

 all bodies having a greater ratio of diameter than 6 to 1, complete impact 

 is more likely than partial. That when the equality of diameter is nearer 

 than 6 to 1, partial impact is more likely. Therefore, as an impact of any 

 bodies, whose diameters show a greater ratio than this, is an absolutely 

 insignificant cosmical event, unless one of the bodies had a stupendous 

 proper motion compared to its size, the matter may be thus considered to 

 be placed on a mathematical basis. In calculations relating to the energy 

 of bodies formed from diffused gas, it is impossible to talk of their total 

 energy, as such energy is indefinite if we only consider the body as becoming 

 infinitely small, and it is clearly impossible to say how small a body (such 

 as our Sun, for instance) may become. I have therefore found it much 

 more convenient to treat of the potential energy converted into other forms 

 of energy, which I call " changed potential energy," I believe it to be a 

 mistake to suppose that very highly-diffused gas, having a definite limit of 

 volume, is necessarily hot. It appears to me, that if the gas be so much 

 diffused that its surface-attraction is very small — that it must be cold, or 

 dissipating into space. There are four different lines of reasoning which 

 point to the conclusion, that as a nebula or gaseous sun gets smaller, it 

 gets hotter. I shall therefore assume that cold, infinitely diffused, disas- 

 sociated gas, possesses a maximum energy. 



Students of kinetics will readily be able to prove that were our Sun 

 twice its present mass and twice its diameter, the energy of attracting 

 a particle from infinity to its surface, without initial motion, would be 

 exactly the same as at present. It can also be shown that such a Sun has 

 lost exactly as much potential energy in forming itself from diffused gas 

 as two such Suns as our own Sun. Therefore, were two such Suns as ours 

 to come into impact, coalesce, and expand, until the whole of the heat of the 

 collision were used in expansion, then the new Sun would have twice the 

 mass, twice the diameter, one-fourth the density, and the same temperature 

 as that of either of the original bodies. Thus it may be seen that two 

 gaseous Suns attracting each other from infinity, without initial motion, 

 were they to produce one Sun at the same temperature, it would only be 

 twice the diameter. 



