1878.] 



Strain in a Glass Fibre. 



151 



Experiment VI. — Twisted for 121 minutes. 



t J 1 2 3 4 5 7 



Scale divisions . 191 170 148 136 126£ 119£ 108£ 



f 10 15 30 65 90 120 589 



Scale divisions . 97 84J 631 411 34 28 3j 



It should be mentioned that the operation of putting on the twist 

 and of releasing each occupied about two seconds, and was per- 

 formed half in the second before the epoch t = 0, and half in the 

 second after or as nearly so as could be managed. The time was 

 taken by ear from a clock beating seconds very distinctly. 



3. The first point to be ascertained from these results is whether or 

 not the principle of superposition, assumed by Boltzmann, holds for 

 torsions of the magnitude here used. 



If the fibre be twisted for time T through angle X, then the torsion 

 at time t after release will be X {yjr (T-\-t)—yjr (£)} where 



f (0 =/0 (0 dt 



If now T = £ x + t % + t 3 + • • . we may express the effect of one 

 long twist in terms of several shorter twists by simply noticing that 



X{f(0-^ + T)}=X[{f(0--fG + ^i)} + {^(^ + ^)-f (t + h + U)} 

 + {f(t + h + L)-^(t + h + t 2 + t i )} + , &c] 



Apply this to the preceding results, calculating each experment from 

 its predecessor. Let xt be the value of ^ (T + £)— ifr (£), that is, 

 the torsion at time t, when free, divided by the impressed twist 

 measured in same unit ; we obtain the following five tables of com- 

 parison. 



Results for T = 2 compared with those from T=l. 



t 1 2 3 4 5 7 



^observed 0'00195 128 092 077 066 051 



^calculated... 0*00199 112 082 064 051 040 



t 10 20 40 



x t observed. ... 041 023 018 

 x t calculated . . 029 016 



Results for T = 5 compared with those from T = 2 and T=l. 



t 1 2 3 4 5 7 10 



a* observed.... 0-00328 262 212 182 164 136 110 

 x t calculated. . . 0*00323 233 181 156 136 108 193 



t 15 22 58 151 



ce* observed 087 072 036 010 



x t calculated. . . 066 047 



m 2 



