In the vicinity of Chapel-en-le-Frith is a steep hill, rising to the hight of more than a hundred feet, immediately beneath which this natural phenomenon lies. It is of an irregular form, but nearly approaching to a square, from two or three feet in depth, and about twenty feet in width. Its ebbings and flowings are irregular, and dependent on the quantity of rain which falls in the different seasons of the year; when it begins to rise, the current can only be perceived by the slow movement of the blades of grass, or other light bodies floating on the surface; notwithstanding which, before the expiration of a minute, the water issues with a gurgling noise, in considerable quantities, from several small apertures on the south and west sides. The interval of time between the ebbing and flowing is not always alike: consequently the proportion of water it discharges at different periods, also varies. In the space of five minutes flowing, the water occasionally rises to the hight of six inches; and, after remaining a few seconds stationary, the well assumes its former quiescent state. The cause of the intermittent flowing of this well may be satisfactorily explained, on the principle of the action of the siphon, and on the supposition of a natural one communicating with a cavity in the hill, where the water may be supposed to accumulate; but for the phenomenon of its ebbing, no satisfactory reason has been assigned. The opinion of a second siphon, (which is ingeniously advanced by one tourist,) that begins to act when the water rises, is inconsistent with the appearance of the well, and therefore can not be just. ST. ANNE’S WELL. This well, the usual resort of the company who frequent Buxton to drink the waters, has been classed among the wonders of the peak, on account of this singularity, that within five feet of the hot spring by which it is supplied, a cold one arises. This is not, however, the only well of the kind, since hot and cold springs rise near each other in many parts of England, and in other countries. The water is conveyed to the well, which is an elegant classical building, in the Grecian style, from the original spring, by a narrow passage, so close and well contrived as to prevent it from losing any considerable portion of its heat, and is received in a white marble bason. It is not so warm as the Bath water, its temperature being about eighty degrees of Fahrenheit. THE CRYSTALLIZED CAVERN. The crystallized cavern, the new wonder of the Derbyshire Peak, was discovered some years ago in the vicinity of the village of Bradwell. We extract the following particulars of this singular and beautiful natural excavation, from Hutchinson’s tour in the High Peak.