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Quartz wall clocks:  Quartz wall clocks, like any quartz clock, has it's accuracy controlled by a quartz crystal.  A precisely trimmed quartz crystal is used to generate an electrical timing signal that regulates the speed of the clock.  Quartz wall clocks may gain or lose around one second per day, and the drift rate may depend somewhat upon temperature.

Auto setting wall clocks:  Auto-setting wall clocks are a relatively new technology.  They are available under a number of names, depending on the manufacturer.  Auto-setting wall clocks are built with a quartz crystal to regulate speed, and a built in integrated circuit that knows the approximate time, and the date.  Although they can gain or lose time like any quartz clock, they have one advantage.  They know about, and will automatically adjust for  daylight savings time.

Atomic wall clocks, or Radio Controlled wall clocks:  The United States Government National Institute of Standards and Technology  maintains a radio station, WWVB, in Ft. Collins, Colorado.  This radio station transmits highly accurate time information.  Atomic, or Radio Controlled clocks receive this signal when they can, and set themselves.  These will maintain time accurate to a fraction of a second as long as they are placed in a location where they can receive the signal.  Like any radio receiver however, they may not be able to receive the signal if they are in a building with a lot of steel in the structure, near computers or cordless phones that may generate interference, or if the weather is unsuitable.  Please note.  The signal they receive does not propagate well during the day.  That's the nature of the signal, not the clock.  These clocks are designed to catch the signal when they can, generally in the middle of the night, calibrate themselves, and then run quite accurately for days until they can catch another signal.  When you first put in the batteries, they will most likely not set themselves until the middle of the night.  The analog clocks generally tick for a few seconds, advance to 4:00, and wait.  The digitals display various things while they wait.  That's normal.  By morning, weather permitting, it should be correct.