Horn/Technique/Right Hand

Origins and reasoning
The original horn had no valves. The technique for playing notes between the open partials of the harmonic series was opening and closing the throat of the bell with the hand. When valves were added to the instrument, horn players opted to keep the hand in the bell. They had three primary reasons for doing so:
 * 1) The tone is darkened significantly, recreating the timbre of the Natural Horn.
 * 2) Pitches are more easily controlled. The deeper the hand goes into the bell, the lower the pitch.
 * 3) The hand is in place to perform extended techniques like stopped and echo horn.

The American method

 * 1) Assemble right hand as though it is going to be shaking another hand.
 * 2) Bring the thumb in so it points in the same direction as the other fingers.
 * 3) Place the hand inside the bell with the metal touching the back of the hand.

Some of the weight of the horn should be held up by the thumb and possibly the index-finger.

The French method

 * 1) Hold right hand out flat with palm down and drop thumb to create a 90-degree angle with fingers.
 * 2) Place the hand inside the bell until the thumb hits the bottom wall of the bell.

Some of the weight of the horn should be held up by the first knuckles and the back of the hand.

If you experiment with both of these positions, you will quickly learn how much the placement of the hand in the bell affects the overall timbre and volume of the instrument.

Miscellaneous Information
The hand should certainly "disrupt" the sound coming out of the bell. Otherwise, there would be no point to having the hand it the bell. However, the hand should not be disturbing the sound enough to cause it to sound stuffy.

Visually depicted, one should imagine as though sound is emerging as a stream of water and the palm is carefully guiding the stream along the back of the forearm.