The Kapteyn universe is an early (late 19th century/early 20th century) model of the universe developed by Jacobus Kapteyn, which consisted of what is now known as the Milky Way galaxy. It was a model developed before it was established that the spiral nebulae seen throughout the sky were, in fact, extremely distant structures similar to the Milky Way itself. When this was realized, such nebulae were eventually termed galaxies, borrowing a term originally that meant the Milky Way itself. The great debate took place before this realization was well-established.
Kapteyn's size-estimate of his universe was smaller than the disk of the Milky Way is now known to be, i.e., he estimated a diameter of about 17 kpc rather than the current estimate of 40 kpc. Kapteyn discounted any significant effect of reddening on his distance estimates based upon magnitudes, which his own analysis concluded to be a minor factor, thus many stars are actually nearer than he estimated. This would seem to give him a too-large galaxy-model rather than a too-small one, but his estimate of the entire galaxy was too small because much of the Milky Way is obscured, reddening being a major contributor.