Why is the temperature of the ice/water bath not dependent on the barometer pressure, as was the temperature of the boiling-water bath? Part of a laboratory experiment question set.
Why is it that the known temperature of the boiling bath can be accurately determined from the days atmospheric pressure but the atmospheric pressure is not considered when determining the temperature of the ice bath for the calibration of thermometer? 
 A: The required change in pressure for a change in melting point can be found from the phase diagram of water. The typical variations in atmospheric pressure are negligible, just as you neglect the additional water pressure experienced in the lower parts of the ice bath.
I will leave it up to you to find the factor involved - it is the slope of the water/ice boundary in the phase diagram.
A: In order for water to boil, it must become a vapor.  Bubbles rising from boiling water contain water molecules that have enough kinetic energy to separate themselves from the less-energetic liquid molecules that remain in the liquid state.  It's easier for vapor to form in a low pressure environment because there is less total kinetic energy outside the liquid in a low pressure environment. Therefore, the temperature required to impart kinetic energy to water molecules sufficient to differentiate themselves from liquid under low pressure is less than required under high pressure.
Look at this phase diagram of water: http://schools.birdville.k12.tx.us/cms/lib2/TX01000797/Centricity/Domain/912/ChemLessons/Lessons/Phases%20and%20Changes/image022.jpg
You will notice that the "triple point" at which ice, liquid, and gaseous water are in thermodynamic equilibrium is 100 degreesC away from the boiling point of water, but only 0.01 degreesC away from the freezing point of water at normal atmospheric pressure.  A given increase or decrease in atmospheric pressure has a much greater effect on the boiling temperature of water than on its melting temperature.  This is reflected in the steepness of the boundary line between the liquid and ice phases of water, compared to the more gradual slope of the liquid/gas boundary, as Floris pointed out in his succinct answer.
Therefore, it's easier accurately to determine the temperature of boiling water from the pressure than it is accurately to determine the temperature of ice from the pressure.  The difference in pressure required to produce a given effect on melting temperature is too small to be easily measured.
