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Find T, M, K, as before.

From B, the point of contact, draw BN equal andparallel to EF, N is a point in the intrados.

Let BN be in the radius of curvature of any curve,

BaA the extrados of an arch, BW being the tangentat B, and from any point a in the extrados KB a A,let fall the vertical line ab, and draw be horizontal,cutting the radius of curvature to the point a in c.Through VcNM draw the intrados.

It is manifest that if any semi-lunular VIT MNFVbe supposed, and a component part, the arch will bestrengthened thereby.

An abutment wall resisting an uniform horizontalforce, such as that of the wind.

If the opposing side GD be a vertical line, the Fig. 10other side will be a parabola GK; the modulus ofhorizontal thrust at any part equals GF the focal dis-tance, the parabola GK limits the range of any para-bola whose vertex is any point g in GD and focaldistance equal GF.

An abutment wall supporting a fluid or bank of earth.

If the opposing side GD be a vertical line, the Fig. 11other side will be an inclined plane, the angle of in-clination varying as the slope, the fluid or earth na-turally assumes from the limit a vertical line, at whichstone will naturally stand, to the limit a horizontalline which a perfect fluid naturally assumes.

An inclined plane limits the parabolas which willpass through GD at a given angle.

When the pressure is from a fluid, the vertices ofthe parabolas are in GD, and the angle of inclinationof the wall or of thrust GKD will be 45°.

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