Starting from some of these cracks, a segment with an are of thirty feet was cut from the base, and a cavity was made in the shaft itself about ten feet wide, seven high, and five deep. No one doubts that this was done artificially. I have attempted to ascertain how long a time has elapsed since it was done. The right edge of the incision runs underneath a stalagmitic wrapping eight feet wide and ten inches thick at its thickest part. Inspection shows that drippings like those now healing this wound were at work before it was inflicted, and that the cut was primarily made through a mass like that by which it is now overlapped. The region above ground is still covered by forests. Hence, as there has been no change of conditions, there has been constancy of stalagmitie growth. A series of experiments has established the fact that in the immediate vicinity of the pillar stalactites grow at the rate of one inch in twenty-five years, but that stalagmites grow only one quarter of an inch in that period, or an inch in one hundred years. At this rate of increment, it must then have required one thousand years for the wrapping to have attained its present thickness of ten inches; and that length of time has therefore elapsed since this alabaster quarry was worked. Confirmatory of this calculation is the fact that some of the fragments thrown out from the pillar are cemented over cavities where clusters of exquisite stalactites have had time to form. Further search by me, in 1878, revealed the implements with which the ancient quarrymen wrought; namely, round or oblong bowlders of granitic rock, extremely hard, and of a size (from four to ten inches) suitable to be wielded by hand, or twisted in a withe and swung as a maul. Rothrock, who has been familiar with the cave from boyhood, denies having at any time carried any such stones into it, or of any one else having done so to his knowledge. The customary tool for gathering specimens is a hammer or hatchet; and these clumsy stone-pounders would be used only by those who had no better tools.

The theory that these pebbles were swept in by an underground stream is untenable: first, because barometrical observations show the place to be twenty feet higher than the entrance; then, there are here no beds of sand or gravel, or other indications of recent fluviatile action; and, moreover, the entire region lies below the line of glaciał drift. Professor Collett, the State geologist, informs me that the entire cave is at least one hundred feet below any drift yet discovered in Crawford County. It is certain, therefore, that these small bowlders were brought by hand from a long distance. Although nothing

has been done by art to modify their natural proportions, they seem to have been carefully selected with reference to their fitness for use. Hard as the material is, the ends are whitened and battered by much pounding. My conclusion, therefore, is well grounded that these were the implements used by the Indians, more than one thousand years ago, in breaking from this alabaster quarry blocks of a portable size.

Quite probably the spot was resorted to by successive generations for material to be made into amulets, ornaments, disks, and images; such as we are told by Dr. Joseph Jones have been repeatedly exhumed in the Southern States, and also, according to Professor S. F. Baird, from tumuli in Illinois. If not found abundantly in Indiana, the reason may be that, although this kind of alabaster is hard and durable when not exposed to the elements, it is fibrous in its structure and liable to decay amid atmospheric vicissitudes, as was proved by fragments found in a crumbling condition just outside the cave.

The

As remarked, there are other alabaster quarries in the newer portions of Wyandot Cave. One of these is in the stalagmitic mass crowning Monument Mountain, an eminence 135 feet high, rising under a dome 205 feet high and 1,000 feet in circumference. stalagmite is 25 feet in diameter at its base, pyramidal in shape, and sustains three statuesque figures, the tallest of which is 8 feet high. I observed, what it is a little singular no one has remarked upon before, an incision in the base and side of this alabaster pyramid, precisely like that in the Pillar of the Constitution. Searching amid the débris below, I found similar fragments of alabaster and granitic pounders.

In the south arm of the cave a different quarry was noted in what is called the " Pillared Palace." Here the alabaster was obtained by felling the smaller columns, from 3 to 7 feet in height. Some were broken up, while others are still nearly entire. Granitic pounders, again, were found lying under adjacent limestone ledges, as if secreted there.

It should be added that, in all cases, the fractures, instead of showing a sharp edge and bright surface, like those made by recent visitors, have a discolored, corroded appearance befitting their antiquity.

THE FLINT MINE AND WORKS. The proprietor of Wyandot Cave is impressed by the notion that it was once a favorite resort for bears. Here and there are "bear slides," which I suspect were really worn smooth by Indians clambering over the rocks. In like manner,

for twenty-five years he has pointed out some "bear wallows "not far from the Pillared Palace. These are circular depressions, twenty or more in number, each a yard wide and a foot deep. A thin crust of clay covers them, and their appearance agrees well with their name. About two years ago, however, I had the satisfaction of proving them to be the remains of ancient flint-works. Happening to remove the clay crust from a bear-wallow, I found a pile of ashes and cinders on one side and a quantity of flint chips on the other. On examination this proved true of each wallow. Further removal of the crust brought to light hundreds of flinty prisms with parallel faces, and averaging four inches in length by one and a half in width and half an inch in thickness.

The mine is near by, abounding in flint nodules, lying in rows in the cave walls, and occasionally in bands or belts. Each nodule has a coating of some grayish mineral, perhaps discolored flint, and between them is usually a soft, chalky substance, easily cut by a knife. Freshly fractured, a bright black surface appears, in contrast with the dingy, faded blocks by the wallows. This change of hue is due to the gradual removal of the traces of iron found with the silex. Many of the blocks were rejected on account of flaws or imperfections. The nodules are easily split into this form, which is convenient for transportation. Arrow-head making, however, was carried on here to a considerable extent, as appears from the chips. Pounders like those in the alabaster quarries were found along with the flints, showing the means of breaking the nodules.

The only manufactured article dug up in this spot was a little stone saucer, containing a soft black substance. This may have been a rude lamp.

Search at the mouth of the cave unearthed quantities of flint chips, and also finished arrow-heads. The question has been raised why the Indians should delve for flint balls amid subterranean darkness, when quantities of such spheres are found along the beds of streams and elsewhere in the open air. The reason is that the latter, having been exposed to the elements, have deteriorated in quality; they also break with irregular cleavage. Hence the Indians sought to get flints fresh from the strata where they were originally deposited; and which, because of their moisture, readily part into quadrangular prisms under the hammer.

Since making known the existence of this flint mine in Wyandot Cave, I have learned of flint-pits dug along Indian Creek and else

where in Harrison County, Indiana; and Professor Collett's observations on their peculiarities confirm my own conclusions, independently arrived at, as to the probable date of these works, the nature of the implements used, and the final disposition made of the materials obtained.

SOME OBSERVATIONS ON GEOMETRIC BEAUTY, CONSIDERED AS CONSISTING IN ANGULAR RATHER THAN IN LINEAR RATIOS. By S. EDWARD WARREN, of Newton, Mass.

[AESTRACT.]

THE object of this paper was to present some results of a fresh study of the general proposition that, if one geometrical form is beautiful, and another not so, there is a discoverable geometrical reason why the former is so, which reason, being known, would facilitate ornamental geometrical design, the definition having been ventured that beauty in general consists in spontaneous expression of excellence of some sort; that is, of some form of good, as, for instance, of some worthy purpose.

Three abstract principles of beauty were then mentioned and illustrated unity, whereby a whole, consisting of parts, is made one by the possession of one aim or use; uniformity, by which parts, while evident and appropriate components of a whole, are alike; harmonious variety, by which parts may be unlike, and yet each, in its own appropriate way, may contribute to the perfection of the whole; freedom, by which was meant wholes of different design for the same purpose, yet each so self-consistent throughout, and so consistent with surrounding circumstances, as to be agreeable.

Next, passing from purely abstract principles to quantity in general, elementary numerical representatives of the foregoing principles were found in 1, as the representative of unity; 2 = 1+ 1, as that of uniformity; 3 21, as that of variety; 5 23, as that of the combination of the last two; and 7, as that of freedom, owing to the number of ways in which it embraced the preceding.

Next, lest the foregoing, being abstract, should be deemed only fanciful, it was rehearsed that musical chords are based on the numbers 1, 2, 3, 5, and rarely on 7, and on multiples of these.

Next it was argued, from the admitted unity of nature, that if beauty

of sound is demonstrably founded on the numbers mentioned, beauty of form might be so also. But here exists the alternative between supposing beauty of form to consist in ratios between the lengths of its determining lines, or between its angles. It was argued that form and size were distinct elementary geometrical ideas, size depending on the number of points in a magnitude (considering a point not now as an absolute zero of magnitude) and form, on their arrangement. Direction was considered as being to form what distance is to size; that is, as more fundamental to the idea of form than distance is; and, as an angle is generally defined as difference of direction, it was argued that ratios between the angles of a magnitude, and founded, as in the ratios in musical chords, upon the numbers 1, 2, 3, 5, and perhaps 7, are the secret of purely geometric beauty. Some illustrations from rectilinear objects were then given, preferring rectangular ones as most frequent and practically important.

For example: A parlor being 24 feet long, shall its width (being not arbitrarily chosen) have a certain simple ratio, as or, to its length, or shall it depend on the ratio between the angles into which its floor diagonal divides a corner right angle? Upon the latter, on the principles of the paper; and, accordingly, making these angles 36° and 54°, with a ratio, the width would be 17': 6′′; or, if these angles were 30° and 60°, giving the ratio, the width would be 13':10′′. In either case a longer wall diagonal, dividing the rectangular corner into angles of 221° and 671°, having the ratio, would give the harmonious, as well as practically suitable, height of 9' 9 feet.

Passing to the more intricate subject of curvilinear beauty, the superiority of ovals, or egg-curves, to bi- or multi-symmetrical curves (ellipse and circle), was mentioned, and the distinction between natural curves, formed according to a uniform law, and artificial curves, composed of arcs of more elementary curves, was noticed; and then a method of constructing ovals indefinitely varied in form, from the most compressed (or turnip-shaped) to the most elongated (or spindle-shaped) was shown, consisting in making various sections of a right conoid (warped surface) of circular base, by planes parallel to its line of strietion (rectilinear directrix), with an attempt to connect these ovals systematically with certain governing angular ratios.

The paper concluded with a few applications of such ovals to the design of house and garden vases, fruit dishes, gas shades, etc., and a hope that attention might be more generally directed to a subject possessing so much, both of philosophical and industrial interest.