192 V Professor Cornu on the [May 16? 



the substance, or an invariable one, and equal to J as given by the 

 Navier's and Green's theories. 



Double difficulty. 1. Is the body really homogeneous and iso- 

 tropic ? 



The metals are always annealed or crystallized : homogeneous 

 glass is one of the bodies approaching nearest to theoretical isotropy. 



2. The transversal contraction is extremely small. 



Necessity of using any indirect mode of deformation to determine 

 accurately the transversal contraction. 



Mode of Experiment : Circular Flexion of a Bectangular Bod. 



The upper surface, primitively plane, becoming curved with two 

 opposite curvatures (and not cylindrical, as commonly supposed), like 

 a horse saddle. The ratio of the main radii of curvature is, according 

 to a theorem due to Mr. De St. Venant, precisely the ratio in 

 question. 



[Illustration of this general fact with an indiarubber plate.] 



Optical Methods for Testino the Defoemation of the Surface 

 OF Elastic Bodies. 



1. Variation of Focus of a Beam of Light Beflected from the Polished 

 Surface of the Elastic Body. 



2. Use of the Newton's Coloured Bings. 



Newton's rings are produced by illuminating with white or with 

 monochromatic light the thin film of air comprised between a fixed 

 sui'face and the exterior surface of the elastic body. 



Extreme sensitiveness of this method, according to the small 

 difference of thickness, corresponding to the successive rings. 



The lines of equal intensity of the rings corresj^ond to the lines of 

 equal thickness of the film of air. The successive rings correspond to 

 a difference of thickness of about ^ of a thousandth of a millimeter (a 

 hundred thousandth of an inch). 



If the fixed surface is a plane one, the appearance of the rings is 

 exactly the topographic map of the deformed surface, of which the 

 scale of elevation is the small length above defined. 



In a small part of the field, the rings coincide, in form, with conic 

 sections, concentric with the indicatrix curve of Ch. Dupin. 



Illustration of various forms of Newton's rings — circular, elliptic, 

 hyperbolic — with monochromatic light (sodium vapour in electrical 

 arc). 



Optical Method of Testing the Circular Flexion. 



A piece of jdate-glass is used. The Newton's rings, before 

 flexion, more or less regular according to the perfection of polish, 



