54 SCIENCE PROGRESS 



would be expelled from them. On account of the perturbations 

 of their paths by the second body, these would not fall back 

 into the sun, but would go on revolving round it as a system 

 of secondary nuclei, with a large number of very fine particles 

 also revolving round the sun ; each particle, however small, 

 would revolve independently, so that the system would in this 

 respect resemble the heterogeneous nebula mentioned at the 

 close of the last paragraph. The mathematical investigation 

 of this hypothesis would be extremely difficult, but there seems 

 to be no obvious objection to it. It will be seen that the nuclei 

 would be initially liquid or gaseous, having been expelled from 

 the sun. Thus this hypothesis implies a formerly molten earth. 

 The smaller particles would soon become solid, but the gaseous 

 part initially expelled and not under the influence of a secondary 

 nucleus would remain gaseous, although its density would be 

 very small. The orbits would be highly eccentric. 



The second part of the hypothesis deals with the later 

 evolution of the secondary nuclei. Its authors believe that these 

 would steadily grow by picking up the smaller particles, which 

 are called planetesimals, and in the process they would have the 

 eccentricities of their orbits reduced. That this is qualitatively 

 correct can easily be proved mathematically. There is, 

 however, a serious objection to its quantitative adequacy. 

 Consider any arbitrary planetesimal. Its chance of colliding 

 with another planetesimal in a definite time is proportional to 

 the sum of the surfaces of the planetesimals, while its chance 

 of colliding with a nucleus is proportional to the sum of the sur- 

 faces of the nuclei . Further, if the eccentricities of the planetary 

 orbits are to be considerably affected by accretion, the mass 

 picked up by each planet must be at least as great as the original 

 mass of the planet. Now the more finely divided the matter is, 

 the more surface it exposes, and hence before accretion the 

 mass picked up must have presented a much larger surface than 

 the planet did. 



Hence collisions between planetesimals must have been 

 far commoner than collisions between planets and planetesimals. 

 Further, as the velocity of impact must have been comparable 

 with an orbital velocity on account of the high eccentricity of 

 the orbits, the colliding planetesimals must in nearly all cases 

 have turned to gas ; for it is known that meteors entering the 

 earth's atmosphere at such velocities are volatilised. Hence 



