value to the numbers; but, such as they are, they were obtained as follows.

Standing in Al Mamoon's hole, towards its western side, you can see, looking eastward, a part of the upper or southern end of the portcullis; and also part of the entrance passage vertically under it ; but you cannot drop a plumb-line from one to the other, for there is much projecting masonry between : neither can you see the whole length of portcullis, for the lower part thereof is buried still in solid surrounding masonry: and this state of things is shown in our large Plate VI., in elevation; and partly in plan, in the upper figure of Plate v.

The difficulty of the plumb-line was overcome, by making use of two,-one hung upon the portcullis itself, and the other from the end of a square, whose base was on the portcullis surface, and whose rectangular arm was so long, horizontally, as to carry the plumb-line clear of the obstructing matter below. It was then tolerably easy to bring the eye into the plane of the two plumb-lines, and see where that, being produced optically, would cut on the roof line of the entrance passage below, or at the point c.

e;

Now, that point c, was measurable by rods from the point A, or at where the roof surface of the upper passage met the roof of the lower one ; and such length a C, must be geometrically equal to A B, the angles of the passages being assumed equal and opposite. But A B being thus obtained, and found = 1805; we must evidently, in order to get the