54 ILLINOIS ACADEMY OF SCIENCE 
disturbing star, and hence the whole takes on a disk-like ar- 
rangement. When seen on edge the outline is narrowly 
elliptical. This discoidal form is well suited to give rise to a 
group of planets arranged also in discoidal form as is the case 
with our planetary system. 
The spiral feature, it is to be noted, relates to the streams 
of knots and haze, and not to the individual paths of each sep- 
arate constituent. These paths are held to be elliptical, in the 
main, and to be controlled by the center of mass of the spiral. 
The knots must inevitably be more or less rotatory, and when 
large they must control the immediate movements of the matter 
within their spheres of influence, and so there should be revo- 
lutions about sub-centers subordinate to the general revolution 
about the center of the nebula. 
The spiral form cannot last indefinitely. If the central 
mass is large and the dispersion only moderate, the inner 
parts must revolve much faster than the outer ones, and so 
the spiral streams must wrap up, growing more and more 
involute till they merge into a disk and thus take on one of 
the forms of planetary nebule. In some cases the spiral must 
merge into a disk in a short period. But if the dispersion be 
great and little matter left in the central part, the differ- 
ences in the rates of revolution of the several scattered parts 
may become small and the spiral wrap up at an exceedingly 
slow rate and hence its endurance be long. 
The mathematical tests of Dr. Moulton clearly implied that 
for the evolution of a spiral nebula suited to the formation 
of the present solar planets, the approach of the disturbing 
star must have been rather distant, for the explosive ejections 
amounted only to an extremely small part of the whole and 
the dispersion was relatively limited. Really close approaches 
of massive stars when one or both have highly explosive habits 
and when the velocity of approach is exceedingly high and the 
path at the critical stage is a sharp curve, must produce effects 
of a higher order, and give rise to spiral nebulze of a much 
larger and more dispersed type. Consider, for example, the 
case of a star of the smaller order passing through the Roche 
limit of a star of the more massive order. Let the stars have 
about the mean velocities of stars of the mature type before 
they appreciably affect one another. As the stars approach 
