Jeff writes about John Marshall referring to Bayard's book:
Chief Justice Marshall added,
"With this exception, I do not recollect a single statement in your book which is not, in my judgment, entirely just."
We can therefore add Chief Justice John Marshall to the long, long list of genuine Justices and other legal authorities who refute the birther BS that it takes birth on US soil plus citizen parents for a person to be a natural born citizen.
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But on the other hand, According to Jeff, the opinion of John Marshall DURING A TRIAL is irrelevant.
Jeff writes:
I accept that Marshall quoted Vattel quite a bit.
I accept that he quoted the passage you like - but it wasn't in a case on citizenship, it was a case on international law.
...
Therefore, his quote in that case has no bearing on the meaning of (sic) [Natural born citizen.]
The quote to which Jeff is referring is this quote. 
John Marshall, Chief Justice of the Supreme Court: The Venus - 12 U.S. 253 (1814)
"The whole system of decisions applicable to this subject rests on the law of nations as its base. It is therefore of some importance to inquire how far the writers on that law consider the subjects of one power residing within the territory of another, as retaining their original character or partaking of the character of the nation in which they reside.Vattel, who, though not very full to this point, is more explicit and more satisfactory on it than any other whose work has fallen into my hands, says
"The citizens are the members of the civil society; bound to this society by certain duties, and subject to its authority, they equally participate in its advantages. The natives or indigenes are those born in the country of parents who are citizens. Society not being able to subsist and to perpetuate itself but by the children of the citizens, those children naturally follow the condition of their fathers, and succeed to all their rights."...
A domicile, then, in the sense in which this term is used by Vattel, requires not only actual residence in a foreign country, but "an intention of always staying there." Actual residence without this intention amounts to no more than "simple habitation."
So once more to recap, a comment about a book is of MAJOR IMPORTANCE, (Even though the book doesn't support Jeff's position) but a very explicit quote of Vattel DURING A TRIAL, is irrelevant.
Does that about cover it Jeff?