  Data on perihelion fragmentation of the Great September Comet of 1882 (C/1882
R1), a prominent member of the Kreutz sungrazer system, are employed to
estimate the size of the nucleus along the radius vector at the time of
splitting. The prolate-spheroidal nucleus is assumed to fragment tidally at
perihelion along planes normal to this direction. The relative velocities,
derived by Sekanina & Chodas (2007) from revised positional-separation data on
six fragments collected originally by Kreutz (1888) are interpreted as measures
of the Sun's differential gravitational acceleration on the centers of mass of
adjacent fragments at the time of breakup and therefore a function of
heliocentric distance. Their total of 7.8 m/s is equivalent to nearly 38 km in
the sum of distances of the centers of mass along the radius vector and to the
nuclear size of about 60 km. The observed sheath of diffuse material, the
remains of the crumbling part of the nucleus that ended up enveloping the train
of the six fragments, included a population of less massive fragments. They are
expected to feed, over centuries in a distant future, an influx of dwarf
sungrazers reminiscent of the current stream of SOHO Kreutz comets. It is
speculated that the parent comet of C/1882 R1 experienced similar fragmentation
in the early 12th century and one of its major fragments -- a bright sungrazer
-- may return in the mid-21st century.
