Caption: William Herschel's (1738--1822) map of the Milky Way (1785) as deduced from his star gage method. The star gages were what we would call star counts.

Herschel was attempting to map the shape of the Milky Way in relative distances.

Features:

1. The essential assumptions of Herschel's star gage method were as follows:
   1. The Milky Way has a uniform distribution of stars of each type out to a sharp boundary beyond which there is nothing until you reach other galaxies if they exist.

      Herschel was aware of the theory that at least some of the nebulae (historical usage), but yours truly can find NO statement about what he thought of it (No-407). Maybe he just thought that the theory was possible. He did know that some nebulae (historical usage) were NOT other galaxies since he discovered what we call a planetary nebula which was fairly clearly gas surrounding a star (No-407,436)

   2. His large 20-foot telescope (reflector, primary diameter 18.5 inches ≅ 47 cm) he could see all stars out to the Milky Way boundary.

2. With Herschel's assumptions, the star gage (i.e., star count) in a given direction is approximately a relative distance measurement to the boundary of the Milky Way.

   Herschel could NOT determine absolute distances.

3. Now Herschel was aware that his assumptions were NOT exactly right. But his hope was that they were right enough on average to obtain reasonably accurate results.

4. From his star gages, Herschel did produce a crude map (which is the shown in the image) of the Milky Way which was the main goal of his survey of stars.

5. The crude map is believed by yours truly to have been intended to show the Milky Way in cross section (Timberlake 2011).

   With this interpretation, the map is remarkably suggestive. It shows something like a very oblate spheroid structure with complicated small features and with the Solar System near the center.

   Yours truly would understand the map better if yours truly actually read Herschel's 1785 article describing it (William Herschel, 1785, On the Construction of the Heavens), but the article is 55 pages long, and so is left to be read sine die.

6. Of course, the idea that the Milky Way had a flattened structure of some kind preceded Herschel and follows from qualitative observations.

   The cosmological theorizers Thomas Wright (1711--1786) and Immanuel Kant (1724--1804) and the mathematician Heinrich Lambert (1728--1777) had all thought in terms of a flattened structure (see Astronomer file: immanuel_kant.html).

7. What was new about Herschel's work was the quantitative relative distances and the quantitative location of the Solar System.

   Sadly, what was new was wrong.

   Herschel himself discovered that his second assumption was probably wrong. When he starting using his 40-foot telescope (reflector, primary diameter 1.22 m ≅ 48 inches, operational 1787--1815), he saw stars he could NOT see before and he recognized that telescopes of even greater light-gathering power than the 40-foot telescope might see stars farther away than he was seeing with the 40-foot telescope and this is, in fact, true. In any case, Herschel realized he could NOT guarantee that he was seeing stars all the way to the boundary of the Milky Way (No-408; Timberlake 2011).

   The situation for his star gage method was worse than Herschel knew. Interstellar dust (of which he was unaware) prevented Herschel from seeing all the way to the boundary of Milky Way in directions inside the Milky Way disk in which the Solar System is embedded.

   This is still true for visible band (fiducial range 0.4--0.7 μm =400--700 nm = 4000--7000 Å). We can only see ⪅3 kpc in most directions in the Milky Way disk (FK-563). To see through the Milky Way disk, we use radio astronomy (starting in the 1940s: Wikipedia: Radio astronomy: History), particularly for the hydrogen 21-centimeter line (21.1061140542 cm, 1420.4057 5176 67(9) MHz ≅ 1420 MHz). It is using the hydrogen 21-centimeter line that the Milky Way disk and Milky Way spiral arms have been mapped.

8. Herschel could see bright stars to or, at least, globular clusters beyond the Milky Way disk when looking out of the Milky Way disk since distances to the surface of the Milky Way disk are shorter there than through its bulk and there is much less obscuring interstellar dust.

9. Herschel's project to map the Milky Way was a brilliant pioneering effort in cosmology and statistics as applied to astronomy despite being doomed to failure in its main aim given the limited astronomical techniques and astrophysical knowledge of his time.

10. Later astronomers, most famously Jacobus Kapteyn (1851--1922), who used and advanced on Herschel's star gage method also failed to get the true shape of the Milky Way and our location in it. The essential reason was still obscuring interstellar dust.