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XV. On an Anomalous Variation of tlie Rigidity of Phosphor 

 Bronze when in the form of Strips. By Harold Pealing. 

 M.Sc., Lecturer in Physics at /South African College, Cape 

 Town, late Oliver Lodge Fellow, University of Liverpool* . 



METALS when in the form of very fine wires or ex- 

 cessively thin strips or blades show variations in their 

 elastic constants. An extreme case of this behaviour is 

 shown by phosphor-bronze strips 0*005 cm. thick or less. 

 In the Phil. Mag. for March 1913 I gave an account of the 

 variations of torsional rigidity of phosphor-bronze strips of 

 that thickness when subjected to different tensions. These 

 variations I attributed to overstrains given to the strips 

 during the process of manufacture. Now it has been urged 

 that this variation in the restoring couple per unit angle of 

 displacement with different tension, which I considered to 

 be wholly due to variation in the torsional rigidity, may be 

 due to a bifilar action of the strip t • Indeed, it has been 

 said quite explicitly that a bifilar effect ought to have been 

 observed in the strips on which I experimented \. 



Now there are no grounds, from a theoretical point of 

 view, for supposing that we would get a bifilar action for 

 small oscillations. Searle has given a fairly complete treat- 

 ment of the subject §. He finds that when a blade (or strip) 

 is twisted about its central filament that the central plane 

 becomes a helicoid, and all filaments in the central plane of 

 the untwisted blade remain unchanged in lenyth when the 

 blade is twisted. 



Applying this result, we see that when the couple is applied 

 by means of a moving inertia bar, the axis of the inertia 

 bar will be in the same horizontal plane at all phases oi' the 

 oscillations, and therefore there can be no restoring couple 

 due to bifilar action. Searle also gives experimental evidence 

 in proof of this||. From this it is clear that there is 

 abundant evidence both theoretical and practical against the 

 view that we should expect a bifilar action in phosphor- 

 bronze strips. The object of this investigation was to try 

 to show by experiment that there was no bifilar effect in 



* Communicated by the Author. 



t Campbell, Proc. Phys. Soc. April 1913. 



X Buckley, Phil. Mag. December 1914. 



§ Searle, 'Experimental Elasticity/ p. 63 &c. 



'I Searle, ' Experimental Elasticity,' p. 132. 



