Mercury thermometers are not as common today, with electronic thermometers everywhere, and higher consciousness about the dangers of mercury. (When I was a kid we broke one and had no idea that we had a toxic spill on the floor that today would call for a HazMat team.) But when I was a kid, my mom would take out the thermometer, and then shake it to get the mercury back down before taking my temperature.
Why does shaking it lower the reading? Is the mercury being compressed? Why will it do this without regard to what temperature it is?
Why doesn’t the mercury return without help to show room temperature after you take it out of your mouth?
How can a mercury thermometer possibly be accurate if you can change the reading just by shaking it? How does it renormalize its calibration to show a correct temperature when it starts out showing the wrong temperature?
WAG: Mercury is slightly odd stuff, and when it cools down (lowering in volume) it doesn’t always nicely fall down towards the bottom ‘bell’ of the thermometer like it’s supposed to. Droplets and chunks of mercury keep clinging to the sides of the thermometer where they are. The volume has decreased, but it appears not to because you don’t see all the little holes where the mercury isn’t any more. “Shaking it down” will slowly push the mercury droplets back towards the bell.
It also will tend to accelerate conduction of heat betwee the bell and the surrounding air, so that if the bell was at a different temperature than air temperature, the shaking will accelerate calibration. This probably isn’t a significant effect tho.
It has nothing to do with any “odd properties” of mercury, but more due to the design of a thermometer used for medical readings. It may not be easy to read it in situ, so it is obviously desirable to have some “persistence of reading” after removal from the person or animal whose temperature is being taken. The capillary means that the maximum value of the temperature is held long enough to be read, but the mercury then needs to be shaken back past the capillary before a new reading is taken.