Water Clocks

 Again, still working underground, the question is, "How do you tell time?"  If you're living close to the surface, it could be a simple system of relays to note sunrise, sunset, noon and so on.  Mister Salvatore invented a massive pillar lit once per day by a master wizard character, which told the time for all who could see it.  In essence, time of day doesn't matter much to those who live underground.  It's always feeding time in the dark.  However, to make a more advanced society work, you probably need some mutually agreed upon method to measure time so that work shifts can be measured and you can all arrive for meetings more or less simultaneously. Obviously the sundial won't work, so we move on to the water clock.

http://romantech.wikispaces.com/A+-+Water+Clock

    There are two basic forms of water clock: inflow and outflow.  Both depend upon a consistent flow of water.  An outflow clock is filled with water, which escapes at a uniform rate, with markings along the side which can be read to tell the passage of time.  An inflow clock has a second container (with the markings) that collects that water.  A second version of the inflow clock has the inflow bowl floating in water, so that the sinking of the inflow vessel would mark the time.  These two simple concepts were a good start, but generally not very accurate (difficult to maintain a constant water pressure) or precise (difficult to make perfect graduations to mark time). 
    The Greeks and Romans advanced water clock design with mechanical components.  Through the use of gearing and escapement mechanisms (when a vessel fills to a certain point it tips, activating a pulley, empties and resets).  These were connected to bells, gongs and even automated figures (think cuckoo clocks).  These clocks were designed even more elaborately in the Arabian world, involving astronomical/astrological elements (though these are obviously not very interesting for those who live underground).  The Chinese, as well, built some incredibly complex mechanisms.  It wasn't until the 17th Century that the more accurate pendulum clocks replaced water clocks in Europe.
    The implications for a subterranean people are simple.  As long as you have a steady supply of water, you can have a water clock.  You might not be reading off the gradations on said clock, but you could set up a vertical series of buckets to count the hours of the day.  It's possible to set up a more complex mechanization to turn a waterwheel whose rotations mark off the hours.  You can design all kinds of bells and whistles to sound in response to the passage of time as well.  With a little ingenuity you don't need eyesight to tell time.  The real beauty is that you don't even need to worry about seasonality or being in time with the outside world, as long as you are internally consistent.  
   


General - http://www.factmonster.com/ipka/A0855491.html
Wiki - http://en.wikipedia.org/wiki/Water_clock
The Basics - http://www.ancient-origins.net/ancient-technology/ancient-invention-water-clock-001818
klepsydra - http://www-groups.dcs.st-and.ac.uk/history/HistTopics/Water_clocks.html