Herodotus tells us that in his time the great pyramid of Cheops was coated with polished stone, in such a manner as to present a smooth surface on all its sides from the base to the top; in the upper part of the pyramid of Cephren the casing-stones have remained in their places to the present day. No American pyramid with smooth sides has as yet been discovered, and of this fact those who reject the Egyptian theory have not failed to avail themselves.[I-124] It is nevertheless probable that many of the American pyramids had originally smooth sides, though, at the present day, time and the growth of dense tropical vegetation have rendered the very shape of the structures scarcely recognizable.[I-125] It is further objected that while the American pyramids exhibit various forms, all are truncated, and were erected merely to serve as foundations for other buildings, those of Egypt are of uniform shape, "rising and diminishing until they come to a point,"[I-126] and are not known to have ever served as a base for temple or palace. It is, however, not certain, judging from facts visible at the present day, that all the Egyptian pyramids did rise to a point. Again, it is almost certain that the American pyramid was not always used as a foundation for a superimposed building, but that it was frequently complete in itself. In many of the ruined cities of Yucatan one or more pyramids have been found upon the summit of which no traces of any building could be discovered, although upon the pyramids by which these were surrounded portions of superimposed edifices still remained. There is, also, some reason to believe that perfect pyramids were constructed in America. As has been seen in the preceding volume, Waldeck found near Palenque two pyramids, which he describes as having been at the time in a state of perfect preservation, square at the base, pointed at the top, and thirty-one feet high, their sides forming equilateral triangles. Delafield[I-127] remarks that a simple mound would first suggest the pyramid, and that from this the more finished and permanent structure would grow; which is true enough. But if we are to believe, as is stated, that the American pyramids grew from such beginnings as the Mississippi mounds, then what reason can there be in comparing the pyramids of Teotihuacan with those of Gizeh in Egypt. For if the Egyptian colonists, at the time of their emigration to America, had advanced no further toward the perfect pyramid than the mound-building stage, would it not be the merest coincidence if the finished pyramidal structures in one country, the result of centuries of improvement, should resemble those of the other country in any but the most general features? Finally, pyramidal edifices were common in Asia as well as in Northern Africa, and it may be said that the American pyramids are as much like the former as they are like the latter.[I-128]