For 99 Years, Oxford English Dictionary Got It Wrong
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The force that makes water want to go from one end to the other of the siphon is gravity. However what pushes the water up the siphon is atmospheric pressure. And if the middle of the siphon is too high for atmospheric pressure to push water up to the middle, then the siphon won't work no matter what height differential exists between the two ends.
So both gravity and air pressure are involved.
The falling water causes a vacuum in the tube, which "pulls" the water up behind it (since water has almost no tensile strength).
And vacuum doesn't really pull, atmospheric pressure pushes.
But fluids that do have some tensile strength could flow without air pressure, so the siphon as a concept is all about gravity.
The cup experiment is showing gravity, not hydrostatic pressure. There is more water in the lower tube, so it's heavier than the water on the other side.
In a typical siphon setup, arms of uneven length, hydrostatic pressure (a result of gravity, as explained above) is what pulls the water down. There will be greater hydrostatic pressure in the longer arm of the siphon. This is the same as what you said above.
In a siphon with arms of equal lengths, the hydrostatic pressure (due to the weight of the water, if you want) in each arm is equal, but the arm in the full container has higher hydrostatic pressure at the bottom of the tube than the arm in the empty container. It is the hydrostatic pressure from the container water that pushes the water up the arm. Otherwise, the water would sit motionless in the tube, since the water pressures in the arms balance each other out. (I did this experiment in my kitchen just to make sure I wasn't crazy.)
For others: If it were due to atmospheric pressure, the water should actually run the other way, since the atmospheric pressure is slightly higher at the lower end.
So if one container is less full, then the arms are NOT the same length - the arm in that container is longer. And yes, the length of the arms changes as the water moves.
The hydrostatic pressure does NOT push the water up the arm! The hydrostatic pressure can not move the water any higher than the top of the water.
Basically, for a siphon any water below the surface essentially does not exist. You could have a mile of water - it doesn't make any difference. The only thing that matters is the relative heights of the TOP of the water.
Try it. Get a very tall container, and a short one. Position the containers so that the top of the water level is the same for both, and see what happens when you move one up or down.
Nice catch.
Anyone have the ability to run a siphon and pull the middle up about 50 feet in the air? If atmospheric pressure is key, it should stop working at something like 30 feet high. If tensile strength is key, it should go several times that height.
Edit: I accidentally said that the tensile strength of water was said to be irrelevant, not relevant.
1. http://dl.dropbox.com/u/404957/siphon_with_a_large_leg.jpg
2. I realize is impossible because it would end up moving water from a lower reservoir to a higher one, but proof by contradiction doesn't count - I'm trying to understand what's happening at the point of the cap (in [1]).
The reason is that it's only height that matters - not width. The weight of that very wide ocean is supported by all the water under it.
It's the same in a siphon. All the water in that wide leg is supported by the water in the bottle.
The difference in height however is not. Maybe think in terms of pressure. The bottom of a tall column of water is under higher pressure than the bottom of a short one. The width of the water however doesn't matter. Pressure is pounds per area, so while there are more pounds at the bottom, there is also more area, so area cancels out.
Well, no one except the physicists :).
Apparently chemists encounter a similar thing when studying chemical bonds - every new academic year you are told that what you learned the previous year was such a gross simplification that it's basically wrong.
If you know a little about it's history, it's pretty easy to see how mistakes were made. Wikipedia has mistakes too.
One of my life dreams is to add a word to the OED. I would definitely be happy with adjusting an existing definition as well !
There have been intervening editors since Noah Webster's time.
http://www.1828-dictionary.com/d/search/word,siphon
A device, consisting of a pipe or tube bent so as to form two branches or legs of unequal length, by which a liquid can be transferred to a lower level, as from one vessel to another, over an intermediate elevation, by the action of the pressure of the atmosphere in forcing the liquid up the shorter branch of the pipe immersed in it, while the continued excess of weight of the liquid in the longer branch (when once filled) causes a continuous flow. The flow takes place only when the discharging extremity of the pipe ia lower than the higher liquid surface, and when no part of the pipe is higher above the surface than the same liquid will rise by atmospheric pressure; that is, about 33 feet for water, and 30 inches for mercury, near the sea level.
It seems the error traces back to Noah (but he correctly points out the receiving side must be at a lower elevation). Johnson's definition is simply "a pipe to convey liquors through".