THE DEVIATION OF THE OSCILLATIONS 



OF A VISCOUS SOLID FROM THE 



ISOCHRONOUS LAW 



THE fact of the distinct departure from isochronism of the 

 torsional vibrations of a metallic wire has been known since 

 the classical researches of the Russian physicist Kuppfer 

 were published in the middle of last century. And that fact, 

 amongst others, exhibits the essential difference existing 

 between the origin of the internal dissipation of energy in 

 this case and that which is effective in cases of true viscosity, 

 in spite of the other fact, established by Kelvin and very 

 rigidly corroborated by Tomlinson, that the logarithmic 

 law applies to the decay of the small oscillations of a metallic 

 wire. 



When the oscillations are large the logarithmic law of 

 decay is widely departed from, and the range of oscillation y 

 is, to a high degree of approximation, related to the time x by 

 the condition 



y n (x+a)=b, 



where n, a, and b are constants throughout a large series of 

 oscillations (see Mr. Ritchie's paper in this volume, p. 113). 



Further, the departure from the sine law during any single 

 oscillation is very marked. The time of inward motion from 

 the maximum elongation to the zero point is greater than the 

 time of outward motion from the zero point to the maximum 

 (Trans. Roy. Soc. of Edin., 1896). In this note I propose 

 merely to indicate, by the aid of a diagram, the nature and 

 extent of these deviations ; a full descriptive and theoretical 



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