The height of the Pillar having been finally fixed at 138·5 feet, and the radius of the base, at the level of about 4 feet above high water, at 21 feet, I next proceeded to consider the details of its proportions. Of the whole height of 138·5 feet, 18 were to be absorbed in a suitable capital for the Pillar, consisting of a parapet for the Lantern, an abacus, a cavetto, and a belt separating these from the shaft. The internal void I determined should be 12 feet in diameter, as the size most suitable for the reception of the lantern and apparatus; and this, combined with the choice of about 13,000 cubic feet of void already mentioned, fixed the height of the solid frustum at the base of the Tower at about 26 feet above the foundation. Having farther decided that the thinnest part of the walls, immediately under the belt-course which separates the capital from the shaft, should not be less than 2 feet thick, as necessary to give due solidity and strength to the walls, and prevent, by the breadth of the joints, the percolation through the walls of the water which might be furiously dashed against them in storms, I had nothing farther to do but to determine the nature of the line which should connect the extremities of the top and bottom radii of the Pillar. As I had already concluded that this line must, as in the Eddystone and Bell Rock, be a curve line, concave to the sea, I next proceeded to try the effects of various curves traced between these points, in giving a convenient and advantageous disposition of the materials, with regard to both the thickness of the walls and the mass of the solid frustum at the base of the Tower. These two points, as will be better understood by means of the accompanying diagram (No. 2), are separated from each other vertically 120·25 feet, and are horizontally distant from each other 13 feet, which is the excess of the bottom radius over that of the top of the shaft, or the consequent amount of what may be called the _aggregate slope_ of the wall. The solid generated by the revolution of some curve line about the vertical axis of the building then becomes the shaft of the pillar. For this purpose I tried four different curves, the Parabola, Logarithmic, Hyperbola, and Conchoid, figures of which, upon the same scale, will be found in Plate, No. IV., with the position of the centre of gravity, which was carefully calculated, marked on each. The logarithmic curve I at once rejected, from its too near approach to a conic frustum, and the excessive thickness of the walls which such a figure would produce, where the hollow cylindric space for the internal accommodation commences at the level of 26 feet above the base. The parabolic form displeased my eye by the too rapid change of its slope near the base; and I had some difficulty in reconciling myself to the condition of the exterior ring of stones at the base, too much of the outer portion of each stone being left without the advantage of direct pressure from