I have paid little attention to the inside measurements. I take it we should first obtain our exoteric knowledge before venturing on esotoric research. Thus the intricate internal measurements of Cheops, made by various enquirers have been little service to me, while the accurate measures of the base of Cheops by Piazzi Smyth, and John James Wild's letter to Lord Brougham, helped me amazingly, as from the two I established the plan level and even bases of Cheops and Cephren at plan level--as I have shown in the preceding pages. My theory demanded that both for the building of the pyramids and for the construction of the models or subsidiary instruments of the surveyors, simple slope ratios should govern each building; before I conclude, I shall show how I got at my slope ratios, by evolving them from the general ground plan. I am firmly convinced that a careful investigation into the ground plans of the various other groups of pyramids will amply confirm my survey theory--the relative positions of the groups should also be established--much additional light will be then thrown on the subject. Let me conjure the investigator to view these piles _from a distance_ with his mind's eye, as the old surveyors viewed them with their bodily eye. Approach them too nearly, and, like Henry Kinglake, you will be lost in the "_one idea of solid immensity._" Common sense tells us they were built to be viewed from a distance. Modern surveyors stand _near_ their instruments, and send their flagmen to a distance; the Egyptian surveyor was _one of his own flagmen_, and his instruments were towering to the skies on the distant horizon. These mighty tools will last out many a generation of surveyors. The modern astronomer from the top of an observatory points his instruments direct at the stars; the Egyptian astronomer from the summit of his particular pyramid directed his observations to the rising and setting of the stars, or the positions of the heavenly bodies in respect to the far away groups of pyramids scattered around him in the distance; and by comparing notes, and with the knowledge of the relative position of the groups, did these observers map out the sky. Solar and lunar shadows of their own pyramids on the flat trenches prepared for the purpose, enabled the astronomer at each observatory to record the annual and monthly flight of time, while its hours were marked by the shadows of their obelisks, capped by copper pyramids or balls, on the more delicate pavements of the court-yards of their public buildings.