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Interesting data about big differences in demographic developments of Jews in Russian vs. Austrian vs. Prussian parts of Poland in the 1800s:
Source is this book: http://www.wbc.poznan.pl/dlibra/publication?id=83913
Apart from differences in natural growth rates between Jews in those territories, also Jewish migrations contributed to those changes.
For example, most of Jews from Prussian Poland emigrated further west to various parts of Germany (including Berlin) during the 1800s.
Some Jews - namely those who were poor - were also forcibly expelled from Prussian Poland by German authorities, into the Russian Empire, between 1772 and 1806. There was also large-scale immigration of Litvaks (Jews from the Grand Duchy of Lithuania) to Congress Poland (which offered more job opportunities).
Meanwhile in Austrian-controlled Galicia, Jews emigrated to other parts of the Austro-Hungarian Empire.
This is why the % of Galician Jews among the total Jewish population of Austro-Hungary was declining.
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More about expulsions of Jews from Germany/Prussia (most of whom went into Russian-controlled areas after being expelled) can be found here:
"Polityka rządu pruskiego wobec Żydów polskich od r. 1793 do 1806", published in Poznan in 1923.
(English title*: "Policies of Prussian government towards Polish Jews since year 1793 until 1806")
*Translated title. I don't think this publication is available in English. In Polish PDF can be found online.
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