I might also suggest:
"B. Harrison, grandson of W. Harrison, [did something worth expending words to describe, etc.]"
or,
"W. Harrison's grandson, B. Harrison, [did something worth expending words to describe, etc.]"
Not only do words take their meaning from the context of the sentence in which they occur, but sentences acquire additional meaning, in turn, from the utterances that precede and/or follow them. An isolated predication, like The air [copula-inflection] hot, at best only provokes the question, "Well, what about the air and hot?", as the British pragmatist philosopher F. C. S. Schiller put the case in Formal Logic: a Scientific and Social Problem (1912).
In the particular example that began this thread, the "sentence" basically names the subject twice: once as the proper noun "B. Harrison," and again as the possessive noun phrase "the grandson of W. Harrison," without saying anything of significance about the subject. This multiple-naming of the subject reduces the copula-inflection, in effect, to a pair of commas that separate appositives (either words or phrases) from each other and from the rest of the sentence that should hopefully follow.
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"If it was so, it might be; and if it were so, it would be; but as it isn't, it ain't. That's logic." -- Tweedledee
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