When the Constitution refers to the “Law of Nations,” they are not referring to Vattel’s book. “The law of nations” was the 18th century term for what we today call “international law.” Vattel was one writer on that subject.
Chief Justice said..the source of “law of nations” written in the Constitution is from Vattel.
First I noticed you did capitalize ‘Law of Nations’ as to Vattel’s book (as done in the Constitution) and second you did not capitalize “law of nations’ when you noted a histoical term. I tend to think your spelling was correct usage.