Would gravity appear to get less as you neared the centre of the Earth?

Sir Isaac Newton actually discusses this topic in his "Principia". He was able to show mathematically that if a person is inside a hollow sphere where the walls of the sphere are made of matter of uniform density, then the net g-force is zero anywhere inside the hollow part, so you could float around from place to place inside such a sphere without ever feeling any g force. Therefore, as you descend into the Earth's interior, you are effectively through successive hollow spheres of matter of uniform density, so the only gravity that you would feel is the gravity of the sphere below you, and none of the rest. The Earth's radius is ~4,000miles, so if you descended 2,000miles downward, you would only feel the gravity equal to standing on the surface of a sphere that is only 2,000 miles in radius, (4,000-2,000=2,000). The deeper you go, the smaller is the sphere of matter that would exert its gravitational g force upon you, until you reach the center, where all of Earth's matter cancels out and you would experience zero g. (This would be the same as you just orbiting the Sun with no Earth around you.)