From Memphis he undertook, with the assistance of Erbkam’s technical knowledge, to investigate the architectural system employed in the construction of the pyramids. The results were recorded, even before the close of the journey, in a dissertation in which the subject was treated in the most fundamental manner.[50] These conclusions have been maintained against all attacks, and even against the attempt to modify them made by the excellent Perrot. In this work Lepsius confirms and explains the statement of Herodotus that the pyramids were completed from above downwards, and were built “in successive steps.” The work cited also contains a well considered and convincing answer to that other question which presents itself to the thoughtful observer of these remarkable monuments. As soon as a Pharaoh ascended the throne he began the construction of his mausoleum. It was at first of modest dimensions, since he erected, as a nucleus of the whole, a truncated pyramid with steep sides, and in doing so often took advantage of the natural rocks. When he was overtaken by death, the pinnacle was first placed upon this nucleus, and its inclined sides were then continued to the ground. If time and power were still left after the completion of the first nucleus and before the pinnacle was set on, the truncated pyramid was invested with a new outer layer in the form of steps, and so it was continued until a point was reached where each new addition constituted of itself a gigantic labor. Whenever the time came to bring the monument to completion it was always necessary first to set on the pinnacle; the steps lying nearest to it were then filled out, and finally those at the bottom. There are pyramids of all sizes, and what we have said explains how it came to pass that one king erected for himself a monument of prodigious dimensions, while another was contented with one much smaller; why we can only point to two unfinished pyramids, and how Cheops, the builder of the largest pyramid, found courage to undertake a work for the execution of which the average duration of a reign would in no wise suffice, while yet the completion of it could not be exacted of his successors, who would have their own mausoleums to provide for. Everything is made clear, if we assume with Lepsius that the size of the pyramid was regulated by the duration of its builder’s life, and that the latter had it in his power at any time to complete the work.