Compressor cycles on and off

OK, car is a 1971 Duster with factory air, all stock components. I replaced the dryer and expansion valve, evacuated and charged system until sight glass ran clear. The pressure on high and low side is fine. The system is working fine, nice and cold even on a hot FL day. The low pressure switch is not cutting power to the compressor. The power coming from inside the car going to the low pressure switch is going on and off. Tell me more about this thermostat..