This is a plot of some experimental data conducted on sodium chloride. That is table salt. The idea was to figure out the melting curve as a function of temperature and pressure. We have pressure here on the x axis in kilobars. We have temperature in Celsius on the y axis. This curve connecting up these experimental data points is the melting curve. The way to read this plot is that everything to the left of the curve is when sodium chloride is in a liquid phase. Everything to the right of this curve is in the solid phase. If these people had been geologists, they might have plotted pressure on the y axis and started with zero at the top and went positive downward because that would have been analogous to depth in the Earth. But they were physicists so they did not do it that way. We can still think of it that way if we want to, though. Just to orient you, seventy kilobars is approximately equal to being at a depth of about two hundred twenty kilometers. Zero kilobars is approximately equal to being at the surface of the Earth. This is the way decompression melting works. Let us say that you are a piece of table salt and you are sitting at thirty kilobars and nine hundred degrees Celsius. That is right here. If you want to melt there are two ways you can do it. You can increase the temperature and you will finally melt at this very high temperature up here. Or, you can decrease the pressure without adding any heat at all. And if you do that, then this point begins to move this way. And at some point it will intersect the melting curve and it will melt right here where it is at this much lower pressure but the same temperature. All this has been accomplished without adding any heat at all. All that has happened is that we have decreased the pressure. At an atomic scale, the way you can think of this is that liquid is a more disordered state and each atom is farther away and can move around a lot more. As you increase the pressure it is harder to get to that disordered state. You have to add a lot more heat to it because pressure squeezes the solid and makes it more compact and makes it less likely to be in that disordered state. This is a decompression melting path. This is equivalent in the Earth to moving to a shallower and shallower depth without losing or gaining heat. At some point the rock will intersect its own melting curve and it will melt. This is how you form magma at a mid-ocean ridge.