If I wanted to write a novel using three characters from a book published in 1910 - is this ok?
I want to write the back story (my own invention) - in the vein of Wide Sargasso Sea.
Any advice would be appreciated.
Copyright is a whomping complicated issue. The most likely answer to your question is "yes" as nearly all written works prior to 1923 are in the public domain. You should read this and this as starting points to understanding copyright law — and remember they are only the beginning, not the end, of understanding copyright law.
Now, you asked about a book published in 1910, but you mentioned Wide Sargasso Sea. I can easily find a Wide Sargasso Sea published in 1966. Off hand I can't find one published in 1910. What book are you talking about?
Note that you can kindof use characters from a copyright-protected book for the purposes of parody (in that it's protected free speech) and a lot of leeway is given to not-for-profit fan-fiction, but you generally cannot use characters for any other purpose. If it is in the public domain, then these rules are relaxed... However...
Please bear in mind that building on somebody else's story is generally taboo. The original author (assuming he/she is living) and the author's descendants won't be appreciative. Nor may many of the fans of the original work.
You are in a very awkward position. As well as being a book, Howard's End is a film, and said film is copyrighted
You would be entering a minefield.
This might work. You could base your characters on the ones from HE and re-name them. In your acknowledgements you could acknowledge EMF and state your characters were inspired by his. To be safe you would also have to change place names that appear in HE. It is a method I have used in one of my novels. Your inspired characters must remain "inspired by" and not copied.
I'm not a lawyer. The correct answer is you should pay for and talk to a lawyer experienced in intellectual property law (copyrights, patents, trademarks) before you attempt to publish. Pay for it, don't just have a casual conversation, the pay makes you an official client: Whether ultimately proven right or wrong, the fact that you sought and bought legal advice would go toward mitigating any damages found against you later.
The book Howard's End was published in 1910, so is in the public domain.
The Movie, however, is from 1992, so well within copyright.
In general, profit from the creation of fictional characters and settings belongs to either the copyright holder or others they give permissions to; for whatever reason.
Elements taken from the original book should be fair game; but you would need to ensure any original elements from the movie, including dialogue, realized scenes or realized characters (realized = made real), are NOT used. So I would not base your descriptions upon anything you saw in the movie; if they are not in the BOOK then don't use them, because the rights to use the creative products OF the movie fictional elements belongs to Merchant Ivory Productions.
You could proceed with writing to see if you have a story; but I would keep a 1910 version of the book beside you and footnote any reference you make to the characters back to the book. It is my understanding that since it is in the public domain you can copy directly from the book; whole chapters, the entire book.
But if you are interspersing book elements with your own original work, be sure to have a footnote for where you found it in the 1910 book. You can always delete the footnotes in a version you send for publication (but keep them in your own master copy).
Don't slack, be diligent. If it were me, I get immersed in the writing and might think I surely saw some thing in the book, and leave off the footnote, only to discover in the lawsuit that --- Golly, I can't find that in the book anywhere but it is clear as day in the damn movie. If you reference the fictional world of the book, find and keep the proof that it came from the book, and was therefore public domain.
This may be far more proof than you need, but it would be better to be over-prepared than under-prepared.