SL 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 :— 
Additional Young's 
Original Stress Stress Elongation per Modulus, 
(grms. persq. ' (grms. per sq. unit length. (abs. C.G.S 
cm.) | cm.) | units). 
108 x 
| 
1354 ' 789 .0618 Dees 
1354 | 1574 .1397 1.05 
1354 | 2529 . 2449 | 9.73 
| 
1354 se | 3424 .3342 | 10.05 
These sueeantions | 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 
