Parallels in Hamlet - the King's body natural and body politic

In Hamlet 4.2.24-7, after Hamlet has slain Polonius, this exchange occurs:

Rosencratz:  My Lord, you must tell us where the body is and go with us to the King.
Hamlet:        The body is with the King, but the King is not with the body.

This cryptic utterance has caused endless puzzlement. At first blush it sounds like a mere nonsense  designed to strengthen the impression of Hamlet's madness. But there is far more to it than that, and we may discover what from a Bacon passage. In his speech in a law case in 1608 called "The case of the Post-Nati of Scotland,", which turned on the question whether, when England and Scotland were united, the natives of both kingdoms, born after James I's accession, would be naturalized in both lands. Bacon said of this: "The natural body of the King hath an operation and influence into his body politic, as well as his body politic hath upon his body natural....[Bacon then cited authorities for two propositions: (a) There is in the King not a body natural alone, but a body natural and politic together; (b) Though there be in the King two bodies, and that these two bodies are conjoined, yet they are no means confounded the one by the other].

Regarding Hamlet's line "The body is with the King, but the King is not with the body", the Arden editor (one of the few commentators, it seems, to have understood the line) points out correctly that Hamlet has two meanings. One is: "The body is in the King's Palace, but is it not the King himself who has been killed", But the secondary meaning (based on the Elizabethan political doctrine referred to above by Bacon) treats the body as that of the King, and is: "The body natural is necessarily with the King, but the body politic is not, because he is not the rightful King [having murdered the previous King, his brother]"

The distinction between "body natural" and "body politic" was not invented by Bacon. He learned it through law cases reported in Plowden's Reports. Then in 1603 Bacon suggested for the Crowns of England and Scotland be united in James I under the name of 'Great Britain' as an expression of the perfect union of bodies, politic as well as natural.

Thus the distinction between "body natural" and "body politic" was very much on Bacon's mind around the time when Hamlet Q2 was issued in 1604 (the line is not in Q1, 1603) since he was the King's principal advocate in Parliament of the proposed union of England and Scotland. It seems that the references in the scene Shake-Speare was writing to "body" and "king" made him think of the distinction between the King's body natural and his body politic; and that he then realized that he could use the distinction as the basis of a piece of seeming madness to put into Hamlet's mouth. If ever a legalism "slipped" from Shake-Speare this is it. And no one had more cause than Bacon to have it in the forefront of his mind in 1604. As to Will Shakspere, even if he knew of this fine, abstruse point of constitutional law, it would hardly have engrossed him when writing about  Polonius's murder.