|MLA Citation:||Bloomfield, Louis A. "Question 1518"|
How Everything Works 19 Jun 2018. 19 Jun 2018 <http://howeverythingworks.org/print1.php?QNum=1518>.
The force pushing mercury back down the column as it cools is tiny in comparison. Mercury certainly does contract when cooled, so that the manufacturer is telling you nonsense. But just because the mercury contracts as it cools doesn't mean that it will all flow back down the column. The mercury needs a push to propel it through its narrow channel.
Mercury is attracted only weakly to glass, so it doesn't really adhere to the walls of its channel. However, like all liquids, mercury has a viscosity, a syrupiness, and this viscosity slows its motion through any pipe. The narrower the pipe, the harder one has to push on a liquid to keep it flowing through that pipe. In fact, flow through a pipe typically scales as the 4th power of that pipe's radius, which is why even modest narrowing of arteries can dramatically impair blood flow in people. The capillaries used in fever thermometers are so narrow that mercury has tremendous trouble flowing through them. It takes big forces to push the mercury quickly through such a capillary.
During expansion, there is easily enough force to push the mercury up through the capillary. However, during contraction, the forces pushing the mercury back down through the capillary are too weak to keep the column together. That's because the only thing above the column of liquid mercury is a thin vapor of mercury gas and that vapor pushes on the liquid much too feebly to have a significant effect. And while gravity may also push down on the liquid if the thermometer is oriented properly, it doesn't push hard enough to help much.
The contracting column of mercury takes hours to drift downward, if it drifts downward at all. It often breaks up into sections, each of which drifts downward at its own rate. And, as two readers (Michael Hugh Knowles and Miodrag Darko Matovic) have both pointed out to me in recent days, there is a narrow constriction in the capillary near its base and the mercury column always breaks at that constriction during contraction. Since the top portion of the mercury column is left almost undisturbed when the column breaks at the constriction, it's easy to read the highest temperature reached by the thermometer.
Shaking the thermometer hard is what gets the mercury down and ultimately drives it through the constriction so that it rejoins into a single column. In effect, you are making the glass accelerate so fast that it leaves the mercury behind. The mercury isn't being pushed down to the bottom of the thermometer; instead, the glass is leaping upward and the mercury is lagging behind. The mercury drifts to the bottom of the thermometer because of its own inertia.
You're right that the glass tube acts as a magnifier for that thin column of mercury. Like a tall glass of water, it acts as a cylindrical lens that magnifies the narrow sliver of metal into a wide image.