Re: Why does the spark on a Jacob's ladder rise, thus becoming longer?

You are correct: electricity follows the path of least resistance.  But 
there's something else to consider: warm air rises.  So let's see what 
happens to that "path of least resistance" as a Jacob's Ladder operates.

Initially a spark forms at the gap at the bottom of the Vee.  The high 
voltage supplied to the legs of the Vee break down the insulating ability 
of the air by ionizing the air and allowing it to conduct electricity.  At 
the same time, the air is heated to very high temperature, forming a plasma 
(a fourth "state of matter" that's in addition to the usual three: solid, 
liquid, gas).

The little bridge of air, being hot, begins to rise.  However, it's been 
ionized, so it remains the path of least resistance, so the electricity 
conduction path follows along as well, maintaining the high temperature.  
Eventually, the spark rises high enough so that the distance to be bridge 
is so long that one of at least four things happens:

1. There is insufficient voltage to maintain the arc, the spark dies out, 
and the cylce repeats with a new arc at the bottom of the Vee.

2. There is insufficient current to maintain a strong, stable arc, an a 
random air current blows out the arc, and the cycle repeats.  

3. the arc rises to the top of the Vee and a stable arc is maintained.

4. the arc rises to the top of the Vee, continues to bow out, and is 
extinguished (for reasons 1 or 2, above), and the cycle repeats.

By the way, if the gap at the bottom of the Vee is too short, the arc never 
rises; instead a stable arc is formed that just sits there in rather boring 
 fashion.

Steve Czarnecki