266 SCIENCE AND METHOD. 



moment the attraction takes possession of it again and 

 brings it back towards the nucleus, and accordingl)^ 

 there will be centripetal currents. We must assume 

 that the centripetal currents are in the first rank and 

 the centrifugal currents in the second rank, if we take 

 as a comparison a company in battle executing a 

 turning movement. Indeed the centrifugal force must 

 be compensated by the attraction exercised by the 

 central layers of the swarm upon the exterior layers. 



Moreover, at the end of a certain length of time, 

 a permanent status is established. As the swarm 

 becomes curved, the attraction exercised by the 

 advancing wing upon the pivot tends to retard the 

 pivot, and that of the pivot upon the advancing wing 

 tends to accelerate the advance of this wing, whose 

 retrograde motion increases no further, so that finally 

 all the radii end by revolving at a uniform velocity. 

 We may nevertheless assume that the rotation of the 

 nucleus is more rapid than that of the radii. 



One question remains. Why do these centripetal 

 and centrifugal swarms tend to concentrate into radii 

 instead of being dispersed more or less throughout, 

 and why are these radii regularly distributed ? The 

 reason for the concentration of the swarms is the 

 attraction exercised by the swarms already existing 

 upon the stars that emerge from the nucleus in their 

 neighbourhood. As soon as an inequality is produced, 

 it tends to be accentuated by this cause. 



Why are the radii regularly distributed ? This is 

 a more delicate matter. Suppose there is no rotation, 

 and that all the stars are in two rectangular planes in 

 such a way that their distribution is symmetrical in 

 relation to the two planes. By symmetry, there would 



