The Chicago Manual of Style is a much thicker tome than New Hart’s Rules, which I normally use instead as it refers to UK English. Its index is also far more comprehensive than the index in the UK book and it is relatively simple to use.
However, it is far easier to turn to the online version of Chicago to find specific answers to queries quickly, even if you cannot see the full answers unless you subscribe (which starts from $39 per year). Although it is handy to have a print copy of the book, when the next edition is published I will probably opt for online access.
Explanations in Chicago are far clearer, easier to find and laid out in a far more accessible manner than in the rather dense text of New Hart’s Rules. Chicago always leaves me feeling that I have understood what to do and when, while New Hart’s Rules is sometimes quite unclear and could definitely do with explaining everything in more detail.
I’m also impressed by section 5.220 Glossary of Problematic Words and Phrases, which is often useful.
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