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TO DETERMINE THE HORIZONTAL THICKNESS OF ABEARING WALL OF A BRIDGE.

(Commonly called a Bearing Pier.)

Make BB'* in the springing line FEB' of the arch, Fig. 12.continued equal to the semiparameter of the para-bola GK 'K equal 2 AV, then BB' is the width of thebearing pier at that level.

Bisect BB ; in J. J is a point in the axis of thebearing pier, and in the axis of a logarithmic curve,whose subtangent equals CV, the radius of curva-ture of the arch at the vertex of the extrados V, andJB is an ordinate to that curve, from which US maybe obtained, and any other ordinate RT, If UJ bebisected in R, then RT is a mean proportional toBJ and SU. And by bisecting RU in r, the meanproportional rt to TR and SU will be had.

Take UZ in UJ, continued equal to CV, and drawSZ, which is the tangent to BS at S ; in like manner,by setting up the height CV from any point R in theaxis, the tangent to the corresponding point T in theordinate will be obtained.

CALCULATION.

Put BJ = AV - n C V = c

JU

Log. US ~ log. n -f „

D b T Cx 2.302585

JU = c x 2,302585 (log. US — log. n.)

When R bisects JU, then RT =r ^BJ x US

* Perronet says in his Memoire sur 1’Epaisseur des Piles, page620. “ Les meilleurs constructeurs, et ceux qui ont fait les plusgrands ponts, tant en France qu’ailleurs, n’ont point donne, a