Place a large overlapping piece of foil over the bottom of the springform tin, and then insert the pan ring over it. Fold the foil up and around the sides of the tin and place the whole thing on a second piece of foil, also folding it and pressing it securely up around the tin so that you have a water-tight covering. Actually, I sometimes find some water dribbles out from this supposedly secure casing on unwrapping, but it doesn't seem - as long as you unwrap the outer layer straightaway - to cause any sogginess.
Process the biscuits until they are like crumbs, then add the butter and pulse again. Line the bottom of the springform tin, pressing the biscuits in with your hands or the back of the spoon. Put the tin in the fridge to set, and preheat the oven to 180°C/ gas mark 4.
Beat the cream cheese gently until it's smooth, and then add the sugar. Beat in the eggs and egg yolks, then finally the lime juice. Put a full kettle on.
Pour the cream cheese filling onto the chilled biscuit base, place the tin in a roasting tray and pour hot water from the recently boiled kettle around the foil-wrapped cheesecake to come about halfway up the sides of the springform; don't overfill as you'll only spill it on the way to the oven. Transfer it as steadily as you can to the oven and cook for 1 hour or so, checking after 50 minutes. It should feel set, but not rigidly so. You want to be able to detect, below the skin, the slightest, sexiest hint of a quiver within.
Take the roasting tin out of the oven, then gingerly remove the springform from its water-filled tin, stand it on a rack, peel off the outer layer of foil, tear away the side bits of the first layer of foil and leave it to cool. When the cheesecake has cooled down completely, place it in the fridge and leave it there till 20 minutes or so before you want to eat it.
Transfer to the plate you're going to serve it on (it will need to be one without a lip, or a cake stand) and unclip. The underneath bit of the first layer of foil, along with the base of the tin, are going to have to stay in place, unless you like living really dangerously. I don't mind a bit of risk in the kitchen, but fiddling about with something as desirably lacking in solidity as this dreamlike cheesecake is beyond even my clumsily impatient foolhardiness.
It makes life easier if, when you cut it, you heat the knife and cake slicer (and I find I need to use both, the one to cut, the other to lift up and ferry slice to waiting plate) under a very hot tap first.