Pitcher Drops Ball While on Rubber

 
1. With no runners on base, the pitcher is in wind-up position, and the batter has a 3-1 count. While the pitcher is taking his signs from the catcher, he drops the ball and it rolls down the mound and it stops when it hits the grass. What action should be taken by the umpire?
 
Call
When the pitcher is on the pitching rubber, if he drops the ball and it crosses either foul line, then the pitch is declared a "ball". If dropped when no runners are on base and the ball does not cross either foul line, then it is called "no pitch" (a rare "do-over"). If there are runners on base and the ball is dropped and does not cross either foul line -- then that is a balk. See NF 6-1-4.

In situation #1 below, since there were no runners on base and the ball did not cross the foul line, then this is a "no pitch".


2. Is the umpire's call different if there is a runner on third base when the ball is dropped in the situation above?
 
Call
Situation #2 below is a balk, since the ball did not cross the foul line and there was a runner on 3rd base.