  The stability of a system of $N$ equal sized mutually gravitating spheres
resting on each other in a straight line and rotating in inertial space is
considered. This is a generalization of the "Euler Resting" configurations
previously analyzed in the finite density 3 and 4 body problems. Specific
questions for the general case are how rapidly the system must spin for the
configuration to stabilize, how rapidly it can spin before the components
separate from each other, and how these results change as a function of $N$.
This paper shows that the Euler Resting configuration can only be stable for up
to 5 bodies, and that for 6 or more bodies the configuration can never be
stable. This places an ideal limit of 5:1 on the aspect ratio of a rubble pile
body's shape.
