miles and reappear in Castleton, 600 feet beneath. Whether they unite into one or two large streams, which form considerable chambers and caverns in the inaccessible region beyond the farthest known parts of Speedwell and Peak Caverns, is an interesting question, that tempts one to answer boldly in the affirmative, since the action of underground streams in Somerset and Yorkshire seems to justify the assumption, if we take into account the extent of the vertical joints eaten away by the water in its descent of 600 feet, and the effects of periodical floods. In Somerset, in a situation exactly similar, two caves of 600 feet fall and 2000 feet horizontal measurement have recently been discovered by opening similar swallet-holes. Is there any hope of finding such hypothetical cavern or caverns here by exploring, and if necessary opening artificially, any of the swallets between Perryfoot and Giant's Hole? The investigations recently carried out by a friend and myself do not make us hopeful that if there are such caverns they will ever be made accessible. We began our work at Giant's Hole, which opens in the bottom of a little gorge between Peak's Hill and Middle Hill. The brooklet that runs in at the cave mouth was very low, and we passed almost dryshod over the rough stones that cover the stream-bed for some 60 feet. Giant's Hole has an arched entrance about seven feet high, and the first part of the cave retains the same form. Then the walls contract, and the cave takes the shape of a deep and narrow canyon, cut through solid rock, with the stream coursing along at the bottom over little falls and waterslides and through pools that are not easy to pass without a wetting. One hundred and fifty feet from the entrance to the cave is a lofty rift, near the top of which an upper gallery turns west, the general direction of the main passage being southerly. Passing this, we followed the stream downhill for another fifty or sixty yards, and were then brought to a standstill by a partial choke. At this point a quantity of stones and gravel comes within two feet of the roof, and the water is dammed back in a pool a foot deep, so that there is barely a foot of clear space between water and roof.