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When reading a book, he heard a strange sound coming from outside.
By reading a book, he heard a strange sound coming from outside.
I would like to ask whether these two sentences are grammatically OK and have the same meaning. In the case of the first one I am not sure whether the conjunction can be used together with the gerund.
"By" + gerund is never temporal, always instrumental.
By reading a book I discovered how economics works.
"By reading a book, he heard a strange noise coming from outside" means that reading a book was the method he used to hear the noise.
"When" + gerund is temporal, so it fits here; but it tends to treat the event as an indivisible unit. If you are talking about something which happened during the event, "while" is more common:
While reading a book, he heard a strange noise coming from outside">
i. When reading a book, he heard a strange sound coming from the outside.
ii. By reading a book, he heard a strange sound coming from the outside.
i is unusual and ii might be ungrammatical.
i rather implies the implausible
i'. Whenever he read a book, he always heard a strange sound.
The following would be more plausible and more "grammatical":
iii. While reading a book, he heard a strange sound.
iii'. Whilst reading a book, he heard a strange sound.
Both iii and iii' (British usage) imply a one-time event.
With reference to ii, by marks an instrumental, agentive, or locative semantic relation:
iv. He opened the bottle by hitting it with a hammer. (instrumental, causative, manner)
v. He put the bottle by the window. (location)
vi. The sound was caused by the book. (agentive, a "passive sentence")
vi seems closest in possible meaning to ii, but it is hard to imagine how the book could cause his hearing so, I'm afraid we can only regard ii as ungrammatical.
