There are two books below Washington’s hand. One is open..the Bible..the one below the Bible is the Law of Nations.
Actually if you look at the picture close-up then it's evident that what's below the Bible is a cushion of some kind. Note the tassels on the corners.
You've always shown remarkable persistence and energy in ferreting out historical sources but I think you've let your enthusiasm carry you away on this one. The painting is from 1889 - a hundred years after the event - and can't be treated as a contemporary source. Why on earth would you think the Law of Nations was shown in it?