Galicia--Austrian Partition of Poland

The current definitive English history of Poland is a two volume work entitled "God's Playground" by author Norman Davies, published by Oxford University. I've been interested in understanding exactly where the borders were between the Austrian, Prussian, and Russian partitions of Poland. This can be important for identifying the correct villages of origin, and locating vital records.

Here is the map of the Austrian partition (also referred to as "Galicia") as well as accompanying text below. This all comes from pages 103-104 of "God's Playground", volume 2.

And here is my re-creation of the map above in Google Maps. I included Swierczow, which is where the Piorek's came from, as well as Walke/Walce (west of the Galician border) because it is my only lead on where the Gemza's came from right now.

"Walki", Poland---Possible Origin of the Gemza Family?

On his naturalization documents Peter Gemza (my great-great-grandmother's brother) noted that he was born in "Walki, Austria". Of course back then the historic Poland had been divided into Austrian, Russian, and Prussian partitions.

I was able to identify a city in SW Poland (modern day) called "Walce", which, according to Wikipedia, was called "Walchi" in some books in the early 1800's. This is my only lead for the identification of this city.

I need to dig into this more, because "Walce" appears to have fallen outside of the Austrian partition, but not by a lot.

English Wikipedia: https://en.wikipedia.org/wiki/Walce

Translated Polish Wikipedia (much more information): https://pl.wikipedia.org/wiki/Walce