Make an egg float in water

We all know that an egg sinks to the bottom if you drop it into a glass of ordinary water. This is actually a test for rotten eggs - they float. 

But, how do you make any egg float in water? The results are very interesting and can teach you some fun facts about Physics. 

What we need:

One Raw Egg

A Glass of Water

Lots of Salt

Method: 

1. Pour water into the glass until it is about half full.
2. Stir in lots of salt (about 6 tablespoons).
3. Carefully pour in plain water until the glass is nearly full (be careful to not disturb or mix the salty water with the plain water).
4. Gently lower the egg into the water and watch what happens.

Observation:

If we were careful when we added the tap water to the salt water we will see the egg to amazingly float in the middle of the glass. 

Why does this happen?