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. 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. The arc AK is built on a curve of 107·8 feet radius; and if a circle be drawn as described with a radius of 169·3 feet, it will determine the length of the chord of the arc at 107 feet, and the distance between the two arcs measured on the middle radius will be 5·45, which is equal to the diameter of the little tower. The arc KB treated in the same way, with a curve of 84·6 feet, and with a distance of 17·17 feet (the diameter of the great tower) between the intersecting circle and the arc, has the length of its chord fixed at 129½ feet. These two lengths of 107 and 129½ feet agree to within six inches with our actual measurement of the wall itself. If we apply our system to the arc BC in an exactly similar manner, but with the distance between the circle and the arc made equal to the radius of the great tower, we find that the length of its chord should be 111 feet; and this also agrees closely with our measurements. The arc of the eastern temple on the hill has a radius of 42·3 feet, and if a circle of 169·3 feet be applied to it with a distance of 17·17 feet between the circle and the arc, we find that the length of its chord should be 72 feet; and this is exactly what we make it on our plan. This also explains the hitherto inexplicable position of the eastern doorway. In a similar way we determine the length of the chord of the great wall in the western temple to be 140 feet; but as the ends of this wall are in a ruinous condition, and as the present outer face is not of the original period, we cannot say whether this was the actual measurement or not.