292 Proceedings of the Koyal Society of Edinburgh. [Sess. 
XXVI. — Plane Strain in a Wedge, with Applications to Masonry 
Dams. By S. D. Carothers, A.R.C.Sc.I. Communicated by The 
General Secretary. 
(MS. received March 6, 1913. Read July 7, 1913.) 
(1) It has been shown * that in the case of plane strain the stresses in a 
body can be obtained from a single stress function ^ satisfying 
Vi 4 X = 0 > (!) 
where 
2 _d 2 d?_ 
Vi ~d& + w' 
Solutions of equation (1) will be applied to obtain the stresses in an 
infinitely long wedge-shaped cylinder, having normal force varying accord- 
y 
ing to some integral power of the distance from the angle applied to the 
plane faces, and the same at all corresponding points along the length of 
the cylinder. The conditions which will be supposed to exist at the curved 
boundary subtended by the angle will be taken to be similar to those 
which exist at points nearer to the angle. 
The case of a triangular dam having its free edge in the surface of 
water and subjected to water pressure on one face will be dealt with in 
some detail, and a solution for a truncated wedge partially subjected to 
water pressure will be given. 
The notation adopted will be that of Love’s Elasticity , 2nd edition. 
The axes of reference will be selected as shown in fig. 1, the axis of z 
being the line of intersection of the plane faces. 
* A. E. H. Love, Elasticity , 2nd edition, p. 201 ; or J. H. Michel], Proc. Lond. Math. Soc ., 
vol. xxxi. p. 100. 
