We use the effective action of the E-n non-critical strings to study i
ts BPS spectrum for 0 less than or equal to n less than or equal to 8,
We show how to introduce mass parameters, or Wilson lines, into the e
ffective action, and then perform the appropriate asymptotic expansion
s that yield the BPS spectrum, The result is the E-n character expansi
on of the spectrum, and is equivalent to performing the mirror map on
a Calabi-Yau with up to nine Kahler moduli. This enables a much more d
etailed examination of the E-n structure of the theory, and provides e
xtensive checks on the effective action description of the non-critica
l string, We extract some universal (E-n-independent) information conc
erning the degeneracies of BPS excitations. (C) 1997 Published by Else
vier Science B.V.