IQ Art. 6.— S. KUSAKABE : 



third teaches us that the dissipation above stated increases more and 

 more when the amplitude of the cycle becomes greater and greater. 

 This increase of the dissipation must necessarily be due to the im- 

 perfect elasticity of the specimen. The fourth means that the 

 specimen becomes less and less rigid when it is twisted further and 

 further. Thus, the ordinary conception of the modulus of rigidity is 

 necessarily vague and uncertain. In future, the actual resistance 

 to the deformation in any state whatever, be it elastic or plastic at 

 that state, will be taken as the measure of rigidity at that state. 

 Hence : The Rigidity- Modulus of a substance in a given state is 

 measured by the increase of stress required to give a unit increase of deforma- 

 tion to the substance in that state : i.e. the trigonometrical tangent of the 

 angle which the tangent to the stress-strain curve at a point 

 corresponding to that state, makes with the strain axis. 



The following" numerical calculations show the above facts 

 quantitatively : — The equation of the representative straight line is 

 either a+ßM=d or ß{M-y} = o ; 



where M and d being the effective mass and the corresponding deflec- 

 tion of the image respectively, « is proportional to the residual twist 

 surviving the couple which is proportional to M, and ß is inversely 

 proportional to the rigidity-modulus of the specimen at that state : 

 while T is the effective mass which is required to bring the specimen 

 into the state of no torsion. The couple required to detort the 

 specimen is, as G. Wiedemann -* noted in his experiment on metallic 

 wire, obviously less than the couple which produced that tort. The 

 following table giving the relation between «, ß, y and 6 proves the 

 above statements. 



(1) G. Wiedemann. Pogg. Annalen. Bd. CVI. 1859. 



