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
I don't understand what they want to say... Is this sentence correct or not?
"in them" = "in the Acts"
Ok, "in them" = "in the Acts" but I still not understand what means "of many other terms..." after it - I see no relationship at all... Or "of many ..." is a continuation of the first part: that's it should be understood as "the capitalization ... was ... of many terms"?
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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
I'll just rephrase this for you.

The capitalization of the term "United Kingdom" in the Acts was similar to way other terms in the Acts were capitalized. The term United Kingdom only started being used widely after the Act of Union was passed in 1800.

The original passage is ungrammatical; it looks like an amalgamation of several sentences.