I don't understand what they want to say... Is this sentence correct or not?
The capitalization of "United Kingdom" in the Acts was in line with the treatment in them of many other terms and that the name United Kingdom only came into general usage with the Act of Union 1800
"in them" = "in the Acts"
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I'll just rephrase this for you.
The capitalization of "United Kingdom" in the Acts was in line with the treatment in them of many other terms and that the name United Kingdom only came into general usage with the Act of Union 1800