ADDRESSES 55 
one another these velocities will rise to such a degree that 
when the smaller star is passing through the Roche limit of 
the larger star, its velocity may reach some few hundred kilo- 
meters per second—depending upon the masses of the stars— 
without making the case an unusual one. Neglecting dispersion 
for the moment, the smaller star must swing around the larger 
star in a sharp conic curve and all the while be subject to 
extreme differences of gravitative pull from the larger star. 
Under the Roche principle these differences would be sufficient 
to wrench the small star into fragments if it were merely 
a passive body held together by its own gravity; i.e. its self- 
gravity would be somewhat more than neutralized. It follows 
that in the process all the expansive potency of the star is 
set free for dispersional work. But this is not done promis- 
cuously nor instantaneously. The star, during its approach, 
has suffered tidal elongation, giving rise to tidal cones fore 
and aft and to compression about the middle portion. The 
cones have grown higher and sharper, and the middle has 
become more and more compressed as the approach grows 
closer, so that when the Roche limit is entered the star is 
rather a fusiform bolt than a sphere. It is moreover con- 
stantly undergoing torsion by the changing direction of the 
mutual pull of the two stars. The tidal cones also are con- 
stantly lagging because a gaseous body is viscous. While 
therefore we may say that the total explosive force of the small 
star has been set free by the time it has entered the Roche 
limit, the explosive action has all the while been directed fore 
and aft by the differential way in which the gravity of the 
large star has acted. Since the tidal cones—the two muzzles 
of our gigantic piece of ordnance—constantly lag, and since 
the curve about the larger star is sharp, the projectiles are 
never shot directly at or from the larger star, but at a point 
in its rear and at a point opposite this. The ordnance itself 
however, is on a rapid swing and the successive projectiles 
take changed paths. This may help the layman to see how 
the projectiles successively shot forth during the swing will 
be related to one another at any instant. Theoretically, under 
these conditions, about all the substance of the smaller star 
will be shot away in the form of projectiles. The ordnance 
is at once missile and ammunition. Only the necessary in- 
completeness of the theoretical action leaves matter behind to 
