I. Introduction. The area described in this paper is shown on Sheet 196 (uncoloured edition) of the 1-inch Ordnance Survey map, and on Sheet 56 S.W. of the (Old Series) 1-inch Geological Survey map, and also on the following 6-inch maps:—Brecònshire, viii N.W., N.E., S.W., S.E.; x N.E., S.E.; and xi N.W., S.W. The district lies north-west of the Irfon, a tributary of the Wye, and mainly in the basin of the Chwefru, which flows southeastwards through the northern portion to join the Irfon near Builth. Murchison dismisses most of the tract as containing ’hardly a single bed of solid stone’, and compares it with the Radnorshire area, where the ‘Upper Silurian’ lies, without the intervention of the Caradoc and Llandeilo groups, on the ‘Cambrian’. The rocks of Pen cefn-ty-mawr, Allt-y-elyêh, and Dol-y-fan are definitely referred to the ‘Cambrian’. His plate (facing p. 346) illustrates this arrangement, as do also the map and section. In ‘Siluria’ (5th ed. 1872) the strata west of the previous boundary-line of the ‘Lower Silurian-Cambrian’ were included as ‘Lower Silurian’. The area was first surveyed by the officers of the Geological Survey, W. T. Aveline & Andrew Ramsay, and the map was published in 1850. The section (Sheet 5, Sect. 1), on the scale of 6 inches to the mile, shows the relationships of the Wenlock, ‘Tarannon’ (Pale) Shales, and Upper and Lower Llandovery. The occurrence of ‘sandstones and shales with fossils distinct from those of the Upper Llandovery, Rhynchonella angustifrons, Atrypa marginalis, Pentamerus undatus