XXXll 



PROCEEDINGS. 



Mr. Macdonald did not intend at the outset, to make any deter- 

 minations of Young's Modulus ; but his observations may be used for 

 two" purposes, viz., to determine (1) how the value of this modulus for 

 a cord under a constant original stress varies with the magnitude of the 

 increment of stress to which it is subjected, and (2) how the value of 

 the modulus for a cord under different original stresses, and elongated 

 by approximately equal increments of stress, varies with the magnitude 

 of the original stress. In the determinations given below, Young's 

 Modulus has been taken to be the increment of tensile stress divided 

 by the corresponding increment of length per unit of the length immedi- 

 ately before the stress was increased. 



(1) The observations requisite for the first purpose were made only 

 in a few cases ; and even in those cases in calculating the increment of 

 tensile stress, it is necessary to assume (the requisite measurements not 

 having been made) that the radius of the cord would not appreciably 

 vary with the small variations of length under the permanent load 

 an assumption which is doubtless permissible. The following table 

 gives the results : 



These determinations would thus seem to show that for the smaller 

 additional stresses to which the cord was subjected, the value of Young's 

 Modulus diminished as the additional stress increased, that for the larger 

 additional stresses, it increased with the additional stress, and that there 

 was a certain additional stress for which Young's Modulus had a 

 minimum value, this additional stress being of such a magnitude as to 

 produce an elongation of about 0.25. This result is in agreement, 

 qualitatively, with Mallock's observations, which showed that Young's 

 Modulus, statically determined, " diminishes with the extension until 

 the stretched length is about 3/2 times the natural length." As Mallock's 



