52 ILLINOIS ACADEMY OF SCIENCE 
primary body so soon as it reached a point 2.44 times the radius 
of the primary, provided both were homogeneous bodies of 
the same density, and provided cohesion, elasticity and all 
expansive agencies are neglected. The principle holds in other 
cases of close approach than the special one studied by Roche. 
Now, if the Roche principle be extended to bodies affected 
by a strongly expansive and even explosive habit, as in the case 
of the sun, it is obvious that special effects must be predicated. 
The influence of the attraction of a passing star is of the 
differential kind made familiar by the tides. The differential 
pull of the passing star draws out the explosive body along 
the line joining it and the star, facilitating explosion along 
this line. At the same time it compresses the explosive body 
at right angles to this line, and so localizes and intensifies the 
explosive action. Thus the explosive body may be said to 
have become a Janus-faced piece of ordance belted and com- 
pressed about the middle, while it fires its projectiles toward 
and from the passing star. The projectiles shot toward the 
star are not only drawn toward it by its attraction during their 
flight, but are drawn forward by it in the direction of its own 
movement. The projectiles shot in the opposite direction 
suffer an opposite effect in pursuance of well known tidal 
laws. If the projectiles during their flight are sufficiently 
deviated by the passing star, they will assume elliptic, para- 
bolic, or hyperbolic orbits instead of returning to the sun as 
they do in the absence of the deviating effects of the star. 
If the forward pull of the passing star is relatively small, 
as is likely to be the case when the star is distant or small and 
the ejection from the sun is consequently short, the projectile 
will fall back to the sun, but it will carry back whatever mo- 
mentum it gained from the forward pull of the passing star, 
and this will accelerate or retard the rotation of the sun 
according to the relative direction of the sun’s rotation at the 
time. If the forward pull has a deviating effect greater than 
the radius of the sun, the projectile will fall into an elliptical 
orbit about the sun; the only exceptions being the cases in 
which the deviating effect is so great that it causes the pro- 
jectile to pass into a parabolic or hyperbolic orbit and be lost, 
or else into a reversed elliptical orbit about the passing star 
and thus become a secondary to it. All these cases are pos- 
sible, not only, but all these cases were actually encountered 
