56 ILLINOIS ACADEMY OF SCIENCE 
form the nucleus of the resulting spiral. Spiral nebule with 
small nuclei are occasionally seen in the heavens. Of course 
they should be relatively rare, for a passage through the Roche 
limit cannot often take plave, though it is a half dozen times as 
likely to happen as a collision. 
While the picture of the fusiform bolt is fresh in mind, it 
may be observed that grazing approaches and glancing col- 
lisions are not instances of the touch or the overlap of spheres 
pursuing straight paths, as illustrations too often imply, but 
of the touch or the overlap of two elongated slightly curved 
fusiform bolts swinging violently about their common center 
of gravity on sharp conic curves. 
Collisions must in the nature of the case be rare compared 
with dispersive approaches of the different types. They 
need only be mentioned here to fill out the series. A glanc- 
ing collision is the next step beyond a grazing approach and 
must quite surely give a spiraloidal dispersion. A center-to- 
center collision must give a radial or irregular dispersion of 
extreme violence. 
The spiralizing whirl given to an assemblage of matter 
in swinging about another assemblage is probably not con- 
fined to continuous bodies like the stars, but applies also to 
clusters or galaxies of stars when these closely approach and 
swing about one another. It probably applies even more ef- 
fectively when the clusters pass through one another on curved 
paths. And so, if the view that some of the greatest of the 
spiral nebulz are only extremely distant assemblages of stars, 
a view not without serious objections, should yet prove true, 
it would perhaps only be a higher expression of the workings 
of the principle of disturbing and distorting approach. It is 
to be borne in mind that assemblages about common centers 
of gravity, whether continuously or disjunctively organized, do 
not pass one another on straight lines and at even pace, but 
bend their courses into elliptic, parabolic, or hyperbolic paths 
and greatly hasten their speeds, while differential attractions 
arise and increase with approach and inevitably impress their 
own peculiar qualities on the conjoint action. 
In assigning most spiral nebulz to the incidental effects 
of the close approach of stars, our hypothesis tallies well with 
