Question
I'm sorry if I described the system inaccurately when I said LARGE. Your right, MASSIVE is a better description. Here's the thing: the system has a pressure switch that will turn the pump off if system pressure reaches 70psi, and will not allow it to start again until pressure is down to 40psi. This switch is located just after the 3" pump outlet. The switch is tied into a tee, and the tank is plumbed in to that same tee. If this was an on demand system like in a house I would understand, but is not. The system does not tie into anything other than the irrigation. As you guessed, the pump is started and stopped by the clock and a pump start relay. It seems to me that the switch is the safety. Does the tank work with the switch? Upon further investigation here locally I have been told that the tank prevents short cycling, but I still do not understand how or why.
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Followup To

Question -
As I said, it is a LARGE system. I pull from a pond. Rise from suction to pump is about 12'. Length of suction is about 40'. At the system's furthest reaches I push about 1/2 mile to an average of 50 heads using 75GPM. I just cannot for the life of me figure out why I need this pressure tank.
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Question -
I have a large irrigation system with a 15hp pump that pulls water from a retention pond. The system has a pressure swith and a pressure tank installed after the pump. I understand that the switch will turn the pump off if the system overpressures. What does the tank do? I ask because the tank has rusted out, and should be replaced, but even my local irrigation store cannot tell me why I need it!  

Answer
jason,
the pressure tank does exactly that. keeps the pump from cycling on and off. you want at least one minute of run time on the pump to prevent premature failure. you can try to bypass the tank with some piping and run the system and see how the pump behaves. if it doesn't seem to be short cycling then you don't need the tank. i can't physically come down there and look at it. so i assume you know how to bypass it. But that is what the tank is doing is acting as a reservoir to stabilize the pressure in the system. it may have been installed later to remedy a pump problem. maybe the pump is oversized and the tank is there to act as a buffer.      thanks Jim