TORSIONAL OSCILLATIONS OF WIRES. 443 



The total loss of energy is therefore 



irkva?(aO) s+lx |. m 



(3 + /x) (5 + /*) i [m(m+L)f+* 



If this loss is a small fraction of the whole energy we may write it proportional to 

 Bdd/dx, and, by integration, obtain, in the former notation, the result 



The theory therefore indicates that n is greater or less than unity, according as groups 

 breaking at large distortions are more or less numerous than groups breaking at small 

 distortions. 



We can easily, as above, determine the more general relation which connects set with 

 torsion, but it is sufficient to note that the preceding considerations justify, from the 

 point of view of theory, the adoption of the approximate expression used in the first 

 paper on this subject, and that they are therefore justified, in turn, by the experimental 

 confirmation therein given. 



It is not to be supposed that the agreement of the results of the above theory 

 with the results of observation necessarily proves the truth of the particular assump- 

 tions therein made. The object of the investigation is rather to show how well a 

 theory based upon simple and reasonable assumptions concerning molecular statistics 

 can account for general phenomena exhibited by imperfectly elastic solid media. 



Note. Added 6th October 1898. 



It is of interest to determine the general law of motion at all stages of the inward 

 motion. Let 6 and (p have the same meanings as formerly, and take 



r9-=(l+p)r<f> 

 with the condition 



l 



- = p + A , 

 V 



where m is a whole number and X is a proper fraction. Consider the various stages 

 r<pj(m + 1 ) to rcp/m, where m is a whole number. 

 A group which breaks at 



+ x- 



m+ 1 ' m(m+ 1) 

 has its (m+ l) th break at 



rcb + x- 

 m 



