I now propose to apply a somewhat similar method to a problem which has always been regarded as at once highly interesting and very difficult, the question of the purpose for which the pyramids of Egypt, and especially the pyramids of Ghizeh, were erected. But I do not here take the full problem under consideration. I have, indeed, elsewhere dealt with it in a general manner, and have been led to a theory respecting the pyramids which will be touched on towards the close of the present paper. Here, however, I intend to deal only with one special part of the problem, that part to which alone the method I propose to employ is applicable--the question of the astronomical purpose which the pyramids were intended to subserve. It will be understood, therefore, why I have spoken of applying a somewhat similar method, and not a precisely similar method; to the problem of the pyramids. For whereas in dealing with the origin of the week, I could from the very beginning of the inquiry apply the _à priori_ method, I cannot do so in the case of the pyramids. I do not know of any line of _à priori_ reasoning by which it could be proved, or even rendered probable, that any race of men, of whatever proclivities or avocations, would naturally be led to construct buildings resembling the pyramids. If it could be, of course that line of reasoning would at the same time indicate what purposes such buildings were intended to subserve. Failing evidence of this kind, we must follow at first the _à posteriori_ method; and this method, while it is clear enough as to the construction of pyramids, for there are the pyramids themselves to speak unmistakably on this point, is not altogether so clear as to any one of the purposes for which the pyramids were built.