Do Research Papers have Public Domain Expiration Date?
From your question:
This is an article published more than 150 years ago. How long do I have to wait in order to download it and use it for free?
From a comment you posted:
Yes, I know I do still have to cite it, but I can't download it or use it for free. I have to pay even when it was published in the 19th century
As Buffy and anpami note, the original work probably isn't under copyright. But even if copyright has expired, there's no guarantee anyone will make it available for free. In particular, there is no obligation on the publisher to provide free (or indeed any) access to it.
In this case, there is a link to a PDF version from the Semantic Scholar page.
Well, regardless of the actual copyright situation, you can get it for free even now. Just use the DOI (10.1017/S0080456800032117) and use it at a, erm, (possibly not 100% legal) "Black Open Access" site called Sci-Hub. (The domain changes constantly, but it currently seems to be this one).
As regards a legal response, my guess is the following: Suppose that it is the UK's Copyright, Designs and Patents Act 1988 that is applicable in this case. Section 12 of that act tells us: "Copyright expires at the end of the period of 70 years from the end of the calendar year in which the author dies" when it comes to "literary works" (inter alia). If I remember correctly, there is a low threshold regarding what constitutes an original "literary work", so I would not worry about definitional disputes with reference to that research paper you linked to. As I am sure that the author has already left the earth more than 70 years ago, I would assume that the copyright has already expired. However, I am sure that Law Stackexchange has gathered more knowledge on the legal situation than I have.
In the US, at least, nothing published in the 19th century is likely to still be under copyright. See https://www.copyright.gov/help/faq/faq-duration.html.
For the UK it is similar but very slightly longer in a few cases. See: https://www.sheffield.ac.uk/library/copyright/duration.
Other places will differ, but probably not by a lot and most likely a shorter time under copyright.
But you still need to cite old works, even when they are out of copyright.
Maxwell's work is most likely to have lost copyright protection about 1950 since he died in 1879.
Any academic library should be able to provide a copy of such works, even if it has to borrow them from other libraries. Librarians are very good at finding such things and are generous about sharing them.