THE KANSAS CITY BRIDGE. 99

Hixperiments indicated the coefficient of friction of dressed oak on sand to
be .475, but in calculations it was generally assumed to be .5, which, substituted
in equation (c¢.), gives for the friction corresponding to each horizontal foot of
caisson ;—calling the friction F .

| F = 451 h2; (e.)

or, substituted in equation (d),
F = 8.56 h?. (f)

The average weight of saturated sand, however, did not exceed 125 pounds to
the cubic foot, and the coefficients of friction adopted have been slightly ex-
cessive ; the decimals may therefore be omitted, and the formula reduced to the
convenient form :—
P= Sh. (g.)

The average friction in pounds on each superficial foot of caisson in contact
with the sand may therefore be considered as eight times the average depth in
feet of the cutting edge below the surface of the sand. This formula of course
varies with the material, and in its present form is applicable only to the Mis-
souri River.

The sand pressure on the caisson at Pier No. 5, when sunk twenty feet into
the sand, that being the depth of sand immediately around it when the sinking
was completed, computed by formula (c.), which would properly be used in this
case, as the external water pressure, whether through sand or water, was bal-
anced by an equal internal water pressure, was 3,608 pounds on each horizontal
foot, or, estimating the perimeter as 155 feet, 559,240 pounds on the entire
caisson ; this was less than two-fifths of the water pressure on the caisson used
at Pier No. 1, and was easily carried by internal braces. The sand pressure at
No. 3 was never so great as this. In proportioning the inverted caisson for Pier
No. 4, the timber-work was made strong enough to withstand the thrust of the
sand, without the assistance of the beton. The formula by which the pressure
should be computed in this case is :—

P = 9.02 (h?—h’?). . (h.)

in which / denotes the total depth of sand, and A’ the depth above the top of the
inverted caisson. Assuming i = 40 and /’ = 28, this equation gives for the