44 J. O. Thompson — Law of Elastic Lengthening. 



Experiments with Silver Wire. 



The following table gives the mean result of eight series of 

 measurements. 



p- 



x observed. 



x calculated. 



Observed-calc. 



kg. 



ram. 



mm. 



mm. 



0-2 



7'898 



•896 



+ 0-002 



0-4 



15-820 



•822 



- 2 



0-6 



23-775 



•776 



- 1 



0-8 



31-758 



•756 



+ 2 



1-0 



39-762 



•762 



± 



Mean temperature, 14° 

 Cross-section of wire, 0*0687 mm. 2 

 Length of wire, 22690 mm. 

 Specific gravity of wire, 10-00 

 Initial load, 0-593 kg. 



The figures in the third column were calculated according 

 to the equation 



x = 39-4030 p + 0-3905 p* — 0-0313 p* 



This wire was not so free from curves as the others, and 

 consequently it was necessary to begin with a comparatively 

 heavy initial load. 



The influence of the after-effect was as a rule so slight that 

 it could not be measured. After each release of the wire the 

 mark returned quickly to the zero-point, and the sinking of the 

 zero-point was explained almost entirely by the gradual rise in 

 temperature in the tower. 



Calculation of the True Modulus of Elasticity. 



From the results given above it follows that the modulus of 

 elasticity is not a constant, but in every case a function of the 

 tension. From the equation 



x = ap -j- 2>j» 2 + cp s 



which gives the relation between the elastic lengthening and 

 the stretching weight we obtain 



±=a + ** + *? 



and with the help of this latter equation we can compute the 

 modulus for any tension whatever. 



The almost perfect agreement between the observed and cal- 

 culated values of x makes it extremely probable that, inas- 

 much as the initial load was slight, we may extend the applica- 

 tion of this equation backwards to an initial load of zero. 



