770 THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1951 



Abstract — A two-dimensional theory of flexural motions of isotropic, 

 elastic plates is deduced from the three-dimensional equations of elasticity. 

 The theory includes the effects of rotatory inertia and shear in the same 

 manner as Timoshenko's one-dimensional theory of bars. Velocities of 

 straight-crested waves are computed and found to agree with those obtained 

 from the three-dimensional theory. A uniqueness theorem reveals that 

 three edge conditions are required. 



Growth of Germanium Single Crystals Containing P-N Junctions. G. K. 

 Teal\ M. Sparks^ and E. Buehler^ Letter to the editor. Phys. Rev., 

 V. 81, p. 637, Feb. 15, 1951. 



A Mechanical Determination of Biaxial Residual Stress in Sheet Materials.* 

 R. G. Treuting^ and W. T. Read, Jr.' References. J I. Applied Phys., 

 V. 22, pp. 130-134, Feb., 1951. 



Abstract — A method is given for determining the residual stress in a 

 sheet material by removing successive uniform layers of material from the 

 surface of a test specimen and measuring the resulting curvature. From the 

 condition of equilibrium of a free specimen, a stress vs curvature relation 

 is derived which holds over the depth to which material has been removed. 

 The method applies when the stress is constant in the plane of the specimen 

 and varies through the thickness. An experimental technique is described 

 which is believed to satisfy the essential requirement that the removal of 

 surface layers should not affect the stress in the remaining material, and a 

 practical example is given. 



Improved Methods for Measuring Ultrasonic Velocity.* G. W. Willard^ 

 References. Acoustical Soc. Am., Jl., v. 23, pp. 83-93, Jan., 1951. 



Abstract — Some improved sound wave interference methods for measur- 

 ing the lo gitudinal and transverse ultrasonic velocity in opaque as well as 

 transparent solids may be simply carried out by using the ultrasonic light- 

 diffraction system (as arranged for making sound beams visible on a screen). 

 The sonic unit of the system is arranged to produce two individual traveling- 

 wave sound beams, by use of two generators or by splitting a single beam. 

 Three simple arrangements are described in detail. In Case A one beam 

 travels entirely in a reference liquid, while the other beam travels a parallel 

 path in an immersed transparent test specimen. In Case B one beam travels 

 entirely in a reference liquid, while the other beam travels an adjacent course 

 through an immersed, transparent or opaque test prism, and on into the 

 liquid at an angle to the first beam. In Case C the two beams are generated 

 at the equal edge faces of a transparent or opaque isosceles test prism (only 



* A reprint of this article may be obtained on request. 

 ' B. T. L. 



