Trumpler and Shapley

Hershcel and later Kapteyn counted stars in various directions to determine the shape of the Milky Way and our position in the Milky Way but came up with the wrong answer. Why?

Are we near the center of the Milky Way galaxy?

We are not at the center of the Milky Way galaxy. Herschel and Kapteyn were unaware of the existence of dust in the interstellar medium (ISM).

Dust particles are agglomerations of billions of atoms. They are thought to be either silicate material or graphite material sometimes with a coating or water ice. Because they are composed of the trace elements of the Universe, they are exceedingly rare compared to hydrogen and helium in the interstellar medium. There is roughly 1 hydrogen atom per sugar cube (per cubic centimeter) in the ISM while there is roughly 1 dust particle (grain) per cubic footbal field in the ISM. They are the principal absorbers and scatterers of radiation, however. Hydrogen atoms can only absorb very specific energies of radiation. They are transparent to the bulk of the radiation produced by stars and so they do not dim distant stars very much. Dust absorbs radiation over large wavelength regions very efficiently.
Dust only lets us see out to a few kiloparsecs (less than 5 - 10,000 light years into the Milky Way galaxy in optical light -- 1 parsec = 3.3 light years). This means that

Dust makes distant stars appear fainter than simply their distances would imply ===> we overestimate the distances to stars and we cannot see extremely distant stars.
The existence of dust in the ISM was inferred by Trumpler in the 1930's through studies of the star clusters known as Galactic Clusters. Without accounting for dust, Trumpler found that the sizes (in kilometers) of clusters increased with their distance from us. That is, the farther away a cluster was, the larger Trumpler inferred its true size to be! One would like to believe that clusters are more or less the same and the clusters closer to us are systematically smaller than those farther away.
How can the existence of dust resolve this problem?

What is our Location in the Milky Way Galaxy?

This issue was resolved by Shapley through observations of the ancient star clusters known as globular clusters. The globular clusters are believed to have formed very early in the history of the Milky Way and reflect the initial shape of the cloud which formed the Galaxy (and, as such, are distributed in a spherical distribution about the center of the Galaxy). Using variable stars known as RR Lyrae stars (as distance indicators--more on this important topic later), Shapley deduced the distribution of globular clusters in the Milky Way. He demonstrated that the Sun was in the disk of our Galaxy.