Mead Gravity and Eggs

The more historically correct Newton story is that he was lolling under a tree, eating an apple and drinking a mead when an egg fell from a nest and did dirty him somewhat.
Like all things connected this brings me to the subject of Eggs, Gravity and Mead.
Of course you do not need a hydrometer when making mead, with a known weight of honey and a known volume of added water it is a trivail matter to calculate the starting gravity.
But what happens if you are making mead from cappings or have either an unknown weight or volume and you broke your hydrometer. Well the mead that Newton was drinking under the tree was not made with the aid of a hydrometer but most likely with an egg (though not the one that dirty him somewhat).
Now we all know that if you place a hen’s egg in a bowl of water, if it floats ..its rotten. So first get a fresh egg , it should, in that same bowl of water sink and sit pretty flat.
Place this egg in your honey water mix to establish the gravity, the higher the gravity the higher the egg will float.
At 1085 the top of the egg just touches the surface.
By 1095 it will be 18mm above, 1100 20mm, 1110 25mm and 1120 30mm.
Of course at the end of fermentation the egg is going to sink, unless it was the egg you started with…
This is where the apple comes in.