We have observed 22 galaxies at 100 mum with the Kuiper Airborne Observator
y in order to determine the angular size of their FIR-emitting regions. Thi
s one-dimensional array data constitutes the highest spatial resolution eve
r achieved on luminous galaxies in the far-infrared. Most of these galaxies
are very luminous far-infrared sources, with L-FIR > 10(11) L.. We clearly
resolved six of these galaxies at 100 mum and have some evidence for exten
sion in seven others. Those galaxies that we have resolved can have little
of their 100 pm flux directly emitted by a pointlike active galactic nucleu
s. Dust heated to similar to 40 K by recent bursts of nonnuclear star forma
tion provides the best explanation for their extreme FIR luminosity. In a f
ew cases, heating of an extended region by a compact central source is also
a plausible option.