The Size of the Milky Way

early 1900s: Jacobus Kapteyn uses quantitative star counts to measure the size of the Galaxy. Kapteyn's Galaxy
~1920: Harlow Shapley uses RR Lyrae variable stars to get distances to globular clusters: Globular clusters have a roughly spherical distribution. Sun is ~ 15 kpc away from the center of the GC distribution. most distant GC is > 50 kpc away from the sun. Globular cluster distribution (modern day: note the different distance scale)

So we have two competing models for the Galaxy:

Kapteyn		Shapley
~ 10 kpc	Size	~ 100 kpc
near center	Sun's position	~ 15 kpc away from center

Who's right? Actually, both were wrong. Their observations were compromised by the effects of interstellar dust, the presence of which was unknown at the time.

Kapteyn's problem: because dust make stars fainter, Kapteyn couldn't see the already faint stars at large distances, so he thought the Galaxy was "running out of stars" at about 10 kpc away.
Shapley's problem: since he was observing clusters of stars (instead of individual stars) he could see them further away. But since dust made them fainter, he thought they were even further away than they actually were.

Of the two, Shapley was much closer to the truth. When the effects of dust were realized and corrected for, studies of galactic structure entered the modern era.