-t76 PROFESSOR MOSELEY, ON THE THEORY OP 



- Pa sin <I> 



S8 = 



ia^ — Pcos't" 



Eliminating therefore P sin <t>, and P cos <I>, between this equation 

 and equations (33), and calling fl, the width of the pier to distinguish 

 it from the depth of the arch, we have 



.^^;""4 (34). 



tr — et] 



7. Let it now be supposed that the forces P are impressed upon 

 all the points of the face BC (Fig. 2) of a mass, and that the plane 

 of intersection is horizontal. Let moreover all these forces P be parallel 

 to one another, and let them be represented respectively in magnitude by 

 tlie values of a function P of ::, continuously from Z to z; 



.-. 2P cos * = cos ^j'Pdz, SPsin <t) = sin 't> ^ P(k, 



2 + Pk cos <l> = / ' P{yi cos 4) - a sin <1>) d%. 



These substitutions being made, the equation (4) to the line of re- 

 sistance gives the following: 



1 Hyl — yf)d% + %sm.(^ f'Pdz + J'P (1/2 cos <t> - s! sin $) dz 



y=- -^ -^ (35). 



cos <1> / Pdz + / (^1 — y-i) dz 



Jz -'0 



or y = — ° ; — ^ '— (36).- 



cos ^ j'Pdz + j'{y^ — y2)dx 



8. Dykes and Embankments. 



Let the forces P be the pressures of a fluid mass upon the face of 

 an embankment, supposed a plane, inclined to the vertical at the angle a,, 



