152 



Dr. Hopkinson on Torsional 



[Dec. 12, 



Results for T = 10 compared with those from T = 5. 



t | 1 2 3 4 7 10 



x t observed.... 0-00544 435 338 292 253 192 159 

 ^calculated 469 398 339 300 236 197 



t 15 25 45 120 170 



^observed.... 125 092 067 036 031 

 x t calculated. . . 161 130 088 



Results for T = 20 compared with those from T = 10. 



t 1 2 3 4 5 7 10 



x t observed. . . . 0-00580 470 398 358 327 276 234 

 ^calculated... 0-00587 483 430 384 356 312 266 



t 15 25 40 60 80 100 



^observed.... 188 140 111 085 072 066 

 x t calculated. . . 217 167 135 100 084 



Results for T = 121 compared with those from T = 20. 



t | 1 2 3 4 5 7 



^observed... 0-00979 871 758 697 648 612 556 

 ^calculated.. .. 1070 950 880 830 780 730 



t 10 15 30 65 90 120 589 



^observed... 497 433 325 212 174 144 18 

 ^calculated.. 670 600 500 380 350 



Iu examining these results it must be remembered that those for small 

 values of T are much less accurate than when T is greater, for the 

 quantity observed is smaller but is subject to the same absolute error ; 

 any irregularity in putting on or releasing from the stress will cause 

 an error which is a material proportion of the observed deflection. 

 For this reason it would be unsafe to base a conclusion on the experi- 

 ments with T = l and T=2. The three last tables agree in indicating 

 a large deviation from the principle of superposition, the actual effect 

 being less than the sum of the separate effects of the periods o stress 

 into which the actual period may be broken up. Kohlrausch finds 

 the same to be the case for india-rubber, either greater torsions or 

 longer durations give less after-effects than would be expected from 

 smaller torsions and shorter periods. 



4. Assuming with Boltzmann that 0(£) = 4: J we have at time t 



t- 



after termination of a twist lasting time T, 



a?,=A{log(T + 0-log*}, 

 the logarithms being taken to any base we please. The results were 



