Besides perfect stability, a boring through the solid rock would present another most important advantage over any other method of orienting the base of the pyramid. In the case of an inclined direction line above the level of the horizontal base, there would be the difficulty of determining the precise position of points under the raised line; for manifest difficulties would arise in letting fall plumb-lines from various points along the optical axis of a raised tubing. But nothing could be simpler than the plan by which the horizontal line corresponding to the underground tube could be determined. All that would be necessary would be to allow the tube to terminate in a tolerably large open space; and from a point in the base vertically above this, to let fall a plumb-line through a fine vertical boring into this open space. It would thus be found how far the point from which the plumb-line was let fall lay, either to the east or to the west of the optical axis of the underground tunnel, and therefore how far to the east or to the west of the centre of the open mouth of this tunnel. Thus the true direction of a north-and-south line from the end of the tube to the middle of the base would be ascertained. This would be the meridian line of the pyramid's base, or rather the meridian line corresponding to the position of the underground passage directed towards the Pole-star when immediately under the pole.
A line at right angles to the meridian line thus obtained would lie due east and west, and the true position of the east-and-west line would probably be better indicated in this way than by direct observation of the sun or stars. If direct observation were made at all, it would be made not on the sun in the horizon near the time of spring and autumn, for the sun's position is then largely affected by refraction. The sun might be observed for this purpose during the summer months, at moments when calculation showed that he should be due east or west, or crossing what is technically the _prime vertical_. Possibly the so-called azimuth trenches on the east side of the great pyramid may have been in some way associated with observations of this sort, as the middle trench is directed considerably to the north of the east point, and not far from the direction in which the sun would rise when about thirty degrees (a favourite angle with the pyramid architects) past the vernal equinox. But I lay no stress on this point. The meridian line obtained from the underground passage would have given the builders so ready a means of determining accurately the east and west lines for the north and south edges of the pyramid's base, that any other observations for this purpose can hardly have been more than subsidiary.