fissures likely open as a result of bulging of the rock beds above a magma chamber that is being filled with magma from deeper in the crust. However, open fractures can exist only near the surface. Magma deeper in the crust must force its way through the rock, always opening a path along a plane normal to the minimum principal stress. This is the direction in which the crust is under the weakest compression and so requires the least work to fracture. At shallow depths, where the rock is brittle, the pressurized magma progressively fractures the rock as it advances upwards. Even if the magma is only slightly pressurized compared with the surrounding rock, tremendous stress is concentrated on the tip of the propagating fracture. In effect, the magma wedges apart the brittle rock in a process called hydraulic fracture. At greater depths, where the rock is hotter and less brittle, the magma forces the rock aside along brittle shear planes oriented 35 degrees to the sides of the dock. This bulldozer-like action produces a blunter dike tip. At the greatest depths, the shear planes become ductile faults, angled 45 degree from the sides of the dike. At depths where the rock is completely plastic, a diapir (a rising plug of magma) forms instead of a dike. The walls of dikes often fit closely back together, providing strong evidence that the dike formed by dilatation of a fissure. However, a few large dikes, such as the 120-meter-thick Medford dike in Maine, US, or the 500-meter-thick Gardar dike in Greenland, show no dilatation. These may have formed by stoping, in which the magma fractured and disintegrated the rock at its advancing tip rather than prying the rock apart. Other dikes may have formed by metasomatism, in which fluids moving along a narrow fissure changed the chemical composition of the rock closest to the fissure. There is an approximate relationship between the width of a dike and its maximum extent, expressed by the formula: Here is the thickness of the dike; is its lateral extent; is the excess pressure in the magma relative to the host rock; is the density of the host rock; and is the P-wave velocity of the host rock (essentially, the speed of sound in the rock). This formula predicts that dikes will be longer and narrower at greater depths below the surface. The ratio of thickness to