Let A F and B E be drawn perpendicular to the radii A D, and B D, and
tangent to the curve A W B. I'ake E g equal to the weight ( W) of water pressure
on a belt of the. dam one foot in breadth, and the length of the chord.
From (g) draw g h and g i parallel to F B and E A. Then will E hgi
become a parallelogram of forces, and E h equals one component, normal to the
voussoir joints at A. and equals the total pressure (p) on that joint.
The triangle E h g is similar to the triangle A D B, their sides being perpen-
dicular to each other, therefore A B : E g : : A D : E h, or C : W : : R : p, and p= ,

'IMie radius, weight and chord, or span, being known, the ])ressure p is found by



8

this formula, which being divided by the area of the joint in square feet gives the
average pressure per square foot.
This formula proves the fact that, with a given radius, the total pressure on
each of the voussoir joints is equal and remains the same to all lengths of span,
from the length of a voussoir, to the total length of the dam, and that the pres-
sure on voussoir joints increases as the length of radius increases. If we assume
a value for (p), we can find the value of R by the above proportion, which becomes
p C. p.
