478 REPORTS ON THE STATE OF SCIENCE. — 1919. 



As, however, K' = ^ K, in the case of rectangular bars y' = ky accurately, 

 and it is not unreasonable to suppose that y' will generally be of the order 

 hf. (Note for similar sections y'=^]cy also.) 

 Thus, we may take the case of rectangular bars as fairly typical. 



We have then ^ = ^, and 



greatest stress in model : greatest stress in full size 



= E':E. 



That is : 



greatest strain in model = greatest strain in full size. 



Hence, the greatest strain to which the material of the full size is 

 subjected in the case considered must not break down the material of the 

 model. 



If the model is made of miich more yielding material than the full size, 

 the iiiaterial of the model will, as a rule, stand a much greater strain than 

 that which would break material of the corresponding full-sized member. 



Xylonite is a much more yielding material than wood. So that if the 

 full-size spar is of wood and the model of xylonite, the conclusions of the 

 last paragraph hold good. Loads on the xylonite model will still usually 

 be well within the safety limit, even when the corresponding loads on the 

 full-sizo wooden member exceed the safety limit, a point of great value in 

 investigating dangerous stresses. 



The Soap Film Method of Stress Estimation . 

 By A. A. Griffiths. 



The use of soap films in the determination of elastic stresses and strains 

 depends on the mathematical similarity between certain forms of the 

 general equations of elasticity and the equation of the surface of a soap 

 film slightly displaced from a plane. 



The latter equation may be taken to be 



8a;^+a«/2+ 2s~~ 



where the plane is that of x, y, p is the pressure difierence between the two 

 sides of the film, and s is the surface tension. Any two-dimensional 

 elastic problem in which the dilation, or the sum of the principal stresses, 

 is a known function of x and y may, by known mathematical methods, be 

 made to depend on the solution of an equation of this type. This is the 

 most general form of elastic problem which can be solved directly by means 

 of soap films. 



The solution is obtained by forming a film, which satisfies the conditions 

 of the problem, and taking the required measurements from it by means 

 of special appliances. The most useful of these are 



{a) The spherometer, which is a needle, moistened with soap solution, 

 which can be moved at will in any desired plane parallel to the plane of 

 X, y. This is caused to touch the film at a series of points, whose positions 

 are recorded by a simple copying mechanism. In this way a complete 

 contour map of the film surface may be obtained. 



