176 ROYAL SOCIETY OF CANADA 



very well with the measured diameter, and even in that case the differ- 

 ence is only a little over one per cent. 



The curves shown in this part of the work are increase per cent, 

 resistance on increase per cent stretch. Above the elastic limit, on 

 account of the slow pulling out of the material, it cannot be said that the 

 stretch is proportioned to the load; consequently, the increase of resis- 

 tance is not plottted on a load base in these curves. 



Below the elastic limit the extensions are proportional to the loads, 

 so that this part of the curve would not be altered in either method of 

 plotting. 



Assuming that the specific resistance p does not change as stretch- 

 ing o^oes on, and that the volume of the wire remains constant, — then if 

 B, is the resistance, I the length, and A the cross-sectional area before 



stretching we have 



p I 



/= I 



For any extension S of the wire, 



R = 'i. (IJr S) 



But I . A 



^1 



I -f *Sf 



I A 



p S' 



A ^ I 



Increase of Resistance = R^ — R 



P S' 

 = - (2 S -\ ) 



A ^ r 



Increase of Eesistance -^ f2 S -\- j-j 



P 



Increase of length '^ 



S I pi SB iS 



(2 + _) = (2 + -) = - (2 -f -); 



A I I A I I . I 



Increase of Resistance 



Original Resistance S 



or =^=_. = 2 + -^ 



Increase of length 



Original length 



