The Heudeshope beck is a small feeder of the Tees, running swiftly down a steep valley into the main stream, at Middleton Teesdale. It is wholly in the lead-measures (Carboniferous limestone), which are here nearly horizontal, undisturbed by trap, and shew only a few faults, so small as not to affect the surface. The great Teesdale fault operates on the other side of the main valley. The Heude beck flows north and south. Its source is in the table-land, forming the water-shed, between Weardale and Teesdale, whence four or five streams issue in different courses. It is unobscured by the drift beds, which characterize the opposite lower slopes of the Tees valley. It is excavated down to the solid rock, the banks have been quite undisturbed by cultivation. It passes through forty-three distinct alternations of grit, shale, and limestone, to each-of which the miners have given a distinct name; it falls about 1,000 feet in the six miles of its course, In the hope that a tramp down by side of its brawling rivulet, during the short hours of a winter day, might illustrate some theory of valley-formation, I devoted one of the last days of the year to the task.