A pot is truly simmering when you can see only an occasional bubble breaking the surface.
Bubbles are little pockets of water vapor, created at the bottom of the pot where the temperature is highest. They then rise, but most of them revert to liquid and collapse as they cool down on the way up, never reaching the surface. The only ones we consider “real bubbles” are those that make it all the way.
Several cookbooks attempt to define a simmer by stating specific water temperatures, often widely diverging ones, somewhere below 212 °F (10o°C). But the exact temperature of a simmering pot will depend on the characteristics of the burner, the pot, and its contents, not to mention the altitude of your kitchen and the weather.
At low barometric pressures, water boils at a lower temperature. And if you’re shooting for a specific simmering temperature, where are you supposed to measure the temperature of a stock? Near the bottom of the pot, where it’s hottest, or somewhere higher up, where it’s cooler?
So forget about trying to achieve a certain temperature and use the small number of occasional bubbles as your criterion for a proper simmer.
French cooks sometimes make a distinction between the simmering of soups or stews that contain solids, and the simmering of liquids such as water, milk, or thin sauces. In the former case, they use the verb mijoter, which is more or less equivalent to the English verb simmer. But when the entire surface of a pot of liquid is clearly visible to the cook, undisturbed by icebergs of meat and vegetables sticking up, there is a discernible pre-simmer or pre-bubble stage that the French call frémirr, meaning to quiver or to tremble.
If you look closely at a pot of heating water as it approaches a simmer and before any bubbles break the surface, you will see the surface quiver, or, as some would have it, smile. The quiver is caused by convection currents, plumes of hot water rising through zones of cooler water, giving up some of their heat to the air when they reach the surface, and then, being a bit cooler than before, falling back down. The slight disturbances of the liquid’s surface as these plumes reverse their direction creates a visible quivering effect.
An egg may be coddled or minimally cooked by frérnissernent (frêmir-ing it) rather than by mijotement (mijoter-ing it), because it is completely submerged in the water. The average temperature of the cooking water will be slightly less than at a simmer.