Consider the two following extracts:
[...], which precedes the main verb in the present participle form, working.
–The Teacher's Grammar of English with Answers: A Course Book and Reference Guide
If you use the verb dye in present participle form, the e must be retained to avoid confusion: dyeing.
–Write in Style: A guide to good English
Both sources appear to be about good English. One is for teachers; the other is for good writing. One of them uses "the present participle form" (with the), whereas the other uses "present participle form" (without the).
Does the really matter at all in the extracts above? Is one of them more correct (or considered good usage) than the other? Or is it the case that both of them are correct but hint at different things?