[1] The heights have been obtained with aneroid and boiling-point thermometers, and with the exception of that of Zimbabwe, where we stayed some time, are only approximate. [↑]
APPENDIX C
Addenda to Chapter V
By R. M. W. Swan, Esq.
Since writing the preceding pages ([Chapter V].) it has been found to be possible from the measurements made at Zimbabwe to determine the radius of another curve of the outer wall of the great temple. This part of the wall extends from B in a north-westerly direction for 111 feet, to a point which we shall call C. The radius of its curve is 133 feet, so that the diameter of the circle of which it is a part is equal to one half of 17·17 × 3·143, and the centre of the curve (which we shall call W) is situated on the meridian line from the altar through the main doorway. The middle point of this arc B C, the S.S.E. doorway of the arc G, the centres G and W, all lie in one and the same straight line. This line cuts the meridian at an angle of 30°, and when produced will pass over the outer wall at a point which is marked by a step which is built across the top of the wall. A line drawn in a similar way from the middle of the arc K B through the centre of the great tower, the altar, and P, also cuts the meridian at an angle of 30°, but from its other side. As the original wall no longer exists at the point where this line would pass we cannot say if its position was marked on the wall.
These lines of sight seem to have been used, like the meridian lines, for the observation of stars, but of stars off the [[402]]meridian. It could hardly have served any useful purpose to observe several stars crossing these lines unless they all had the same polar distance; for stars with different polar distances would cross the lines at different lengths of time before and after their culminations. Nor, in the latitude of Zimbabwe, would any individual star cross the lines at any important time in its daily circuit. But if we suppose that this temple is built on the model of one in the parent country in the northern hemisphere, it is easy to imagine a useful purpose which these lines may have served. In the latitude of Southern Arabia, for instance, an observer facing north would see the North Pole elevated about 15° above the horizon. If we compare the northern portion of the sky to a watch dial, the stars will represent the moving hands, the pole the centre of the dial, the meridian the XII. and VI. hour-points, and the III. and IX. hours will be marked by a horizontal line passing through the pole east and west. When stars cross this line they may be said to be at their east or west elongation. Now it seems probable that the two lines in question would be used in the parent country to observe a star having a north polar distance of 30° when it was at its east and west elongations and six hours from the meridian.
We have before remarked that none of our trigonometrical functions seem to have been recognised by the builders of Zimbabwe, and that the angular values of the arcs are of no special importance when measured in our way. But they must have been of importance to the builders of the temples. The locating of the centres of the arcs on the several meridian lines, supposing the meridian lines were first laid down in planning the temples (as the central one undoubtedly was in the great temple), does not really determine the intersecting points of the arcs; for, were the centre moved along the meridian lines in either direction, the points of intersection would change their positions and the lengths of the arcs would be altered. [[403]]
The lengths of the arcs seem to have been determined by the intersections of circles of radii different from those of the arcs themselves, but the lengths of whose radii were determined by the same system as those of the arcs. The centres of the intersecting circles are situated on the radius of the arc which lies midway between its extremities, and the distance between the arc and the intersecting circle measured on the same radius produced is equal to the diameter of one of the towers.