Historians might one day tell us if the Queen did "purr", as David Cameron alleged, on hearing the result of Scotland's referendum.

The scholars could also explain if Alex Salmond's description of the monarch as a post-independence "Queen of Scots" was to her taste. We know enough: Scotland matters to the House of Windsor.

Last night the First Minister, Nicola Sturgeon, was received in audience at Buckingham Palace. You can guess, given every amiable precedent set by Mr Salmond, that the two women got on well. One oddity of British life is that for 62 years the monarch has dealt best with politicians who are not, in theory, allies of royalty. Business is business.

But is Ms Sturgeon a republican at heart? You would ask in vain. Where the monarchy is concerned, the Scottish National Party leadership has raised pragmatism to a fine art. Mr Salmond, part-socialist social democrat, made sure of that during the referendum argument. If surveys are right, republicanism's best showing in Scotland has touched the 40 per cent mark. That was never good enough for a man with a plan.

It's not a small figure, however. As Ms Sturgeon takes on her duties as a Privy Councillor and prepares for a private meeting with Mr Cameron, the SNP's direction under her leadership has yet to be revealed. Those tens of thousands of new members do not seem like instinctive royalists. Within the party's vaunted internal democracy they have real power. How might they choose? How might the First Minister assert control?

Traditionally, the party hierarchy would talk long and loud about bigger fish, and how they might be fried. The Westminster balance of power and the future of the Trident missile system count as huge prizes for Ms Sturgeon. Becoming bogged down in old arguments over the nature of independence under a British monarchy could be - will be - depicted as poor tactics.

There is a sense, nevertheless, that the SNP and the wider Yes movement has unfinished business where totemic Britishness is concerned. How much independence do you desire if your leader is charming a monarch who is, arguably, the entire point and purpose of the UK? "Queen of Scots" was Mr Salmond's too-glib compromise. His party, and many Yes voters, simply agreed to postpone an argument.

Such was the collective will, expressed in September's referendum. We send the First Minister of a devolved government to the Palace, not a head of state. We decided not to break each and every old British tie, least of all with the monarchy. We chose a strange political landscape in which Ms Sturgeon can speak more easily for a majority in her country than for - on this matter at least - her party.

There are tensions still to be revealed. Ms Sturgeon might not find affable compromises as easy to manage as Mr Salmond. Those legions of new SNP members might make full use of party democracy. The connection between the Privy Council and the nuclear deterrent in the event of a hung parliament next May could keep constitutional scholars busy. The council - the fact is too little understood - is Britain's court of last resort.