Several striking coincidences between the details of these works and others of the same class are worthy of notice. The diameter of the circle, the perfect form of which has been noted, is nearly identical with two others forming parts of remarkable groups in the Scioto valley, one of them seventy miles distant. The square has also the same area as a rectangular enclosure belonging to the “Hopeton Works,” where it is attached to a circle 1050 feet in diameter, and to an avenue constructed between two parallel embankments 2400 feet long, leading to the edge of a bank immediately over the river-flat of the Scioto. A like coincidence in the precise extent of the area enclosed has been noticed in the octagon of a group, called the High Bank Works, on the same river-terrace; and in another, at the junction of the Muskingum and Ohio rivers. The authors of the elaborate surveys embodied in the Smithsonian Contributions to Knowledge, remark generally that the figures of the Scioto valley earthworks are not only accurate squares and perfect circles, but are in most cases of corresponding dimensions; each square being 1080 feet a side, and the diameter of each of the larger and smaller circles a fraction over 1700 and 800 feet. This they observe is “a coincidence which could not possibly be accidental, and which must possess some significance. It certainly establishes the existence of some standard of measurement among the ancient people, if not the possession of some means of determining angles.”[84] It is no less important to note that it establishes the use of instruments. A standard of measurement could not otherwise exist, still less be applied, on so large a scale in geometrical construction; and the very simplest instruments that we can conceive of, constitute no less certain evidence of a condition of intellectual development attained by this ancient people very different from anything achieved by the most advanced Indian tribes. Varied, moreover, as the combinations of their singular groups of earthworks are, traces are clearly discernible that certain well-defined plans of construction, and a proportionate scale of parts, guided their builders. Justly estimating the importance of such coincidences, and the still greater value of the evidence of the construction of geometric figures on so large a scale, the authors of the surveys have detailed their method of procedure, in order “to put at once all scepticism at rest, which might otherwise arise as to the regularity of these works.” This important point rests accordingly on the most satisfactory evidence;[85] nor are even the imperfections observed in the construction of some of the rectangular figures without their significance, as a test of the extent to which geometry had been mastered by the ancient builders.