Caption: William Herschel's (1738--1822) map of the Milky Way (1785) as deduced from star gages which 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---and I think Herschel thought so????.
   2. His large reflector telescopes could see all stars out to the Milky Way boundary.

2. With Herschel's assumptions, the count of stars (i.e., the star gage) 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 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, 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.????

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

8. Sadly, what was new was wrong.

   This was principally because insufficient light-gathering power and interstellar dust prevented Herschel from seeing all the stars in any direction in the Milky Way.

   Interstellar dust limits the distance we can see in the visible band (fiducial range 0.4--0.7 μm) in the Galactic disk to less than ∼ 3 kpc in most directions (FK-563).

9. So Herschel could NOT, in fact, see stars to the boundary of the Milky Way.

   However, he 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.

10. Herschel in later years recognized that lack of light-gathering power and other problems had defeated the main goal of his survey to map the Milky Way (Timberlake 2011). It's NOT clear if he considered interstellar dust and other interstellar medium (ISM) as obscuring his sight.

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

12. Later astronomers, most famously Jacobus Kapteyn (1851--1922), who advanced on Herschel method also failed to get the true shape of the Milky Way and our location in it. The essential was reason obscuring interstellar dust. Only with the advent of radio astronomy 1940s did the structure of the Milky Way become observable. Interstellar dust is transparent in the radio band (fiducial range 3 Hz -- 300 GHz = 0.3 THz, 0.1 cm -- 10**5 km) or at least part of it.