Figure 46 is the S. 3 W. 1 line, bearing 198° 26' 5.82"; here the dark slope angle of the pyramids with the sun to the eastward occupies half of the apparent half base. Figure 47 is the S. 5, W. 2 line, bearing 201° 48' 5"; here Cephren and Mycerinus are in outside slope line. Figure 48 is the S. 7 W. 3 line, bearing 203° 11' 55"; here the inside slope of Cephren springs from the centre of the apparent base of Mycerinus. I must content myself with the preceding examples of a few pyramid lines, but must have said enough to show that from every point of the compass their appearance was distinctly marked and definitely to be determined by surveyors acquainted with the plan. § 11. DESCRIPTION OF THE ANCIENT PORTABLE SURVEY INSTRUMENT. I must now commence with a single pyramid, show how approximate observations could be made from it, and then extend the theory to a group with the observations thereby rendered more perfect and delicate. We will suppose the surveyor to be standing looking at the pyramid Cephren; he knows that its base is 420 cubits, and its apothem 346½ cubits. He has provided himself with a model in wood, or stone, or metal, and one thousandth of its size--therefore his model will be O.42 cubit base, and O.3465 cubit apothem--or, in round numbers, eight and half inches base, and seven inches apothem. This model is fixed on the centre of a card or disc, graduated from the centre to the circumference, like a compass card, to the various points of the compass, or divisions of a circle. The model pyramid is fastened due north and south on the lines of this card or disc, so that when the north point of the card points north, the north face of the model pyramid faces to the north. The surveyor also has a table, which, with a pair of plumb lines or mason's levels, he can erect quite level: this table is also graduated from the centre with divisions of a circle, or points of the compass, and it is larger than the card or disc attached to the model. This table is made so that it can revolve upon its stand, and can be clamped. We will call it the _lower limb_. There is a pin in the centre of the lower limb, and a hole in the centre of the disc bearing the model, which can be thus placed upon the centre of the table, and becomes the _upper limb_. The upper limb can be clamped to the lower limb.