Abstract
In a former paper on this subject which the author presented to the Royal Society, and which is published in the 'Proceedings’ (vol. xv. p. 182), he obtained formulæ for calculating the thrust of a spherical dome of uniform thickness, by supposing it to consist of a number of thin ribs, each of which is formed by two vertical planes intersecting at the axis of the dome, and making a small angle with each other; and then treating each rib as forming, with the corresponding one of the opposite side, a complete arch. In the present paper the author applies the same method to domes of other forms than the spherical. The following are the kinds for which the formulæ are investigated:— A. The Gothic dome, of which that of the cathedral at Florence is a splendid example. This kind has for its section a pointed arch formed by two segments of circles, the centre from which each is struck being on the springing line, but not in the axis of the dome. The author denotes by a the angle between the vertical and a line drawn from this centre to the point, near the crown of the dome, where its axis is intersected by a circle drawn around that centre with a radius equal to the mean of the radii of the circles which generate the outer and inner surfaces of the dome, and reduces his results to numbers for three different values of the angle a .
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