182 Mr. Horace Lamb on the 



For the majority of substances, then, an increase in the 

 dielectric constant similar to that which I have found in the 

 substances investigated might be expected ; and it appears to 

 me that in experimenting with slow swings there is more 

 chance of success, since in that case, proceeding as Schiller or 

 Colin and Arons have done, the causes of error can be more 

 easily eliminated from the experiments or allowed for in the 

 observations. 



Vienna, May 1890. 



XXIII. On the Flexure of a Flat Elastic Spring. 

 By Horace Lamb, M.A., F.R.S* 



IT is a well-known consequence of the ordinary theory of 

 flexure that when a bar of (say) rectangular section is 

 slightly bent by opposing couples in a plane parallel to one 

 pair of faces, so as to form a circular arc of radius p, the 

 remaining faces take an anticlastic curvature cr/p, where 

 a is " Poisson's ratio ; " and this fact has been made the 

 basis of ingenious experimental methods of determining cr, 

 by Cornuf and MallockJ. It appears to have been first 

 remarked by Thomson and Tait (' Natural Philosophy,' § 717) 

 that this tendency to anticlastic curvature imposes in certain 

 cases a limit to the degree of flexure, beyond which the 

 theory in question will not apply. " For unless the breadth 

 of the bar (or diameter perpendicular to the plane of flexure) 

 be very small in comparison with the mean proportional 

 between the radius \_pjo~] and the thickness, the distances 

 [in any cross section] from [a line through the axis per- 

 pendicular to the plane of flexure] to [one pair of corners] 

 would fall short of the half-thickness, and the distances to 

 [the other pair] would exceed it by differences comparable 

 with its own amount. This would give rise to sensibly less 



10 per cent, of sulphuric acid has been added. With Hertz oscillations 

 on the other hand, the distilled water, used in the same trough, behaved 

 as if it had a dielectric constant of about 300. If a few drops of sulphuric 

 acid were then added to it, the oscillations either entirely ceased or at any 

 rate were no longer visible by my method. The insertion of such thick 

 layers would be of advantage, insomuch as one could compare the large 

 dielectric constants not with air, but with a dielectric constant oo . This 

 mode of procedure cannot unfortunately be directly applied to Hertz 

 oscillations, since the insertion of a conductor 27 centim. long alters the 

 length of the path of the oscillations by too great an amount. 



* From the Proceedings of the Manchester Literary and Philosophical 

 Society, April 29th, 1890. Communicated by the Author. 



t Comptes JRendus, August 2, 1869. 



1 Proc. Roy. Soc. June 19, 1879. 



