298 
Proceedings of the Royal Society of Edinburgh. [Sess. 
In writing out the stresses from the above it must be remembered 
that the equivalent of the term — pgr cos (fi — 6) must be added to xx and yy. 
When y is small tan 20 is small, and tan 2 0 is negligible in comparison 
to unity, and we get 
dy/dx = xy/(xx - yy ) , 
and this is of the form 
dy/dx = ■*- yj {a x x - a 2 y) 
at either face. The primitive of this equation is 
y a \(ci l + l)a; - a 2 y] = constant. 
Assuming /3 = a = 18° and pg / P = 2*30, the curves are as follows : — 
Near front face . . . xy 0 ' 3136 - 3 , 368/y 1 ' 3136 = constant. 
Near back face . . . xy*'* 65 - 1 "51 0?/ 5 ' 865 = constant. 
The curves have been drawn for the foregoing case, and are shown 
in fig. 3 below. 
O 
Diagram shewing lines on which normal pressure exists due to the weight of 
THE WEDGE lSPG-2 30; AND WATER PRESSURE ON THE VERTICAL FACE igg-36°> 
(11) From the foregoing the solution for a truncated wedge can be 
obtained to a high degree of approximation, provided the part cut off or 
the part added, as the case may be, is not a large part of the whole. 
