Using the word "in" means that the action takes place at the same time as something. However "by" is used to denote the manner or reason something was done. So "in doing so" actually means "while doing so", but "by doing so" means "because I did so".

Which is correct in so doing or in doing so?

Senior Member. They are both perfectly acceptable, but "in so doing" may be slightly old-fashioned.

What does it mean by in so doing?

To answer your question a. - "in so doing". It can be taken in context to mean, "by doing so" - "so", being the action they are taking or will take.