I. Preliminary Observations. This Cave, or rather series of enlarged fissures in the Devonian Limestone, was discovered in January 1858 whilst quarrying the rock on the slope of the hill which rises above the small fishing-town of Brixham, near Torquay, in Devonshire. The owner of the quarry had the excavation carried sufficiently far to show that the cave had several branches, and contained bones both on the surface of the stalagmite and in the red loam beneath it. Mr. Pengelly visited the cave soon after its discovery, and, believing it likely to prove of much interest, opened negotiations with the proprietor, with a view to secure the right of exploration. There were, however, obstacles which then prevented this object being carried into execution. Shortly afterwards the late Dr. Falconer, while on a visit to Torquay, was informed of the discovery, and, after a careful inspection of the cave, he was so impressed with the opportunity here afforded of working out completely a new and untouched bone-cavern, that on his return to London he addressed the following letter to the Geological Society. This letter is given at length, as showing the state of the cave question at that period, and the objects to be attained by the exploration of the Brixham Cave.