What assumptions did William Herschel make when estimating the structure of the Milky Way?

To estimate the structure of the Milky Way, William Herschel employed a method involving "star gages," which were counts of stars within the field of view of his telescopes. In his efforts to map the galaxy, he relied on several key, albeit vulnerable, assumptions:12

• Uniform Stellar Brightness: Herschel assumed that all stars possess the same intrinsic brightness. Based on this, he concluded that any variation in their apparent brightness was solely an index of their distance from Earth.2
• Statistical Distance: Following a concept adopted by Christiaan Huygens, Herschel assumed that the faintness of stars served as a reliable statistical measure of their distance.3
• Penetration Power: He assumed that his telescopes were sufficiently powerful to penetrate to the very edge of the Milky Way. By counting the number of stars in a given direction, he believed he could determine the distance from the Sun to the galactic edge in that specific line of sight.1

While these assumptions allowed Herschel to produce the first quantitative chart of the Milky Way's disk-like form, he eventually realized his telescopes were not powerful enough to reach the galaxy's true edge and abandoned the drawing.1