People assault the flinty rock with their hands and lay bare the roots of the mountains.
Is there any evidence that mountains have such deep roots? Yes, there is abundant evidence from measurements of gravity over and near mountain ranges. Let's first digress briefly to the equation that specifies the force of gravitational attraction between two masses that are separated by a distance r.
F= G * m1 * m2 / (r * r)
Here, G is a constant (the universal gravitational constant), and m1 and m2 are the masses of objects 1 and 2. The equation thus indicates that as the distance between two objectsincreases, the gravitational attraction between them decreases as the square of the distance.
If the earth were perfectly spherical (i.e. no topography) and lacked any variation in density, then a mass that is hanging from a string (a plumb bob) would always point directly toward the earth's center. In the 18th century, French scientists on an expedition to South America to measure the distance of a degree of latitude noted that the great mass of the Andes mountain belt represented additional mass that would exert its own gravitational pull on a plumb bob that would deflect the plumb bob from "vertical" toward the mountain range. They thus estimated the mass of the mountain range and then predicted how much the vertical deflection should be. To their surprise, they found that the mass was not deflected as far as they predicted - they thus postulated that a "deficit" of mass beneath the mountain range had to exist. The mass deficit was a buoyant crustal root that extended down into the denser surrounding mantle.
Since the 18th century, many more gravity surveys of mountain ranges have been completed and they indicate that mountain ranges are often (but not always) accompanied by a mass deficit. For example, if one measures the gravitational attraction at many points in or above a mountain range and one then corrects the measured gravity signal for a variety of effects, one of which includes the contribution from topography above sea level (this is done by estimating the gravitational attraction that results from a given volume of material with a density equivalent to that of continental crust), the gravity field over a mountain range should be the same as the gravity field for flat regions that flank the mountain range. Instead, the corrected gravity field over the mountain range typically has values lower than the surrounding flat regions. This gravity "deficit" is evidence for a mass "deficit" beneath the mountain range - such a deficit can only occur if the density of material beneath the range is lower than the density of the material beneath the flat-lying regions. Thus, less dense or buoyant material underlies many mountains - this buoyant material is the "root" that is predicted to exist based on Archimede's principle.