The "_closing_" of one pyramid over another in bringing any of their many lines into true order, must even now be very perfect;--but now we can only imagine the beauties of these great instrumental wonders of the world when the casing stones were on them. We can picture the rosy lights of one, and the bright white lights of others; their clear cut lines against the sky, true as the hairs of a theodolite; and the sombre darkness of the contrasting shades, bringing out their angles with startling distinctness. Under the influence of the Eastern sun, the faces must have been a very blaze of light, and could have been seen at enormous distances like great mirrors. I declare that the pyramids of Gïzeh in all their polished glory, before the destroyer stripped them of their beautiful garments, were in every respect adapted to flash around clearly defined lines of sight, upon which the lands of the nation could be accurately threaded. The very thought of these mighty theodolites of the old Egyptians fills me with wonder and reverence. What perfect and beautiful instruments they were! never out of adjustment, always correct, always ready; no magnetic deviation to allow for. No wonder they took the trouble they did to build them so correctly in their so marvellously suitable positions. If Astronomers agree that observations of a pole star could have been accurately made by peering up a small gallery on the north side of one of the pyramids only a few hundred feet in length, I feel that I shall have little difficulty in satisfying them that accurate measurements to points only _miles_ away could have been made from angular observations of the whole group. § 10. HOW THE PYRAMIDS WERE MADE USE OF. It appears from what I have already set forth that the plan of the Pyramids under consideration is geometrically exact, a perfect set of measures. I shall now show how these edifices were applied to a thoroughly geometrical purpose in the true meaning of the word--to measure the Earth. I shall show how true straight lines could be extended from the Pyramids in given directions useful in right-angled trigonometry, by direct observation of the buildings, and without the aid of other instruments. And I shall show how by the aid of a simple instrument angles could be exactly observed from any point. This Survey theory does not stand or fall on the merits of my theory of the Gïzeh plan. Let it be proved that this group is not built on the exact system of triangulation set forth by me, it is still a fact that its plan is in a similar shape, and any such shape would enable a surveyor acquainted with the plan to lay down accurate surveys by observations of the group even should it not occupy the precise lines assumed by me.