#2 reads as if the book is sitting a bench. #2 should be re-written: Sitting on a bench, he is reading a book. #1 is fine.
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Anonymous 1.He is reading a book while sitting on the bench.
2.He is reading a book sitting on a bench. The game here is that the meaning of #2 changes, depending on whether you place a comma after "book."
As A/S says, without the comma, the book is on the bench.
With the comma, the reader is on the bench.
In your f