Assuming it was your grandfather’s service arm in WWI, and that it is in original, unmodified condition, it would be worth quite a lot. If it is also the earlier first model, it’s worth even more. Collectors are always interested in original-condition service arms with provenance.
A year or so back, I saw one of the more common WWI .455 second model S&Ws in unmodified, excellent condition at Cabella’s for about $800. It was there a month or two then someone bought it. Of course, no one can say anything definite about price until they know the exact condition, what model it is, etc., but my guess is that yours would sell faster and for more money than the one I saw.