372 THOMAS GRAY ON THE EFFECT OF PERMANENT ELONGATION 
In determining the moduluses of elasticity, the method of direct elongation 
was adopted for the Youne’s modulus, and the method of torsional vibrations 
for the rigidity modulus. The arrangement adopted in the case of the length 
modulus is shown in fig. 2. The wire to be experimented on W, together with 
another wire w, soldered to it at the upper end, were fixed firmly between the 
jaws of a vice. 
To the lower end of the wire w a frame F was attached. This frame 
formed part of a pulley and index arrangement for multiplying the elongation 
of the wire ; the whole of this arrangement was held straight by two heavy balls 
BB. The multiplication produced by the arrangement was exactly 20, as 
found both by measurement and by experiment. A wire, 4 metres long, 
could thus be tested for elongation with as great accuracy as one 80 meires 
long, when the elongation is observed directly. I have found this mode of 
observation very satisfactory, and certainly much better than the method of 
direct observation, either with the naked eye or by means of a cathetometer. 
The latter instrument, when used to measure elongations by means of a scale 
graduated on itself, is worse than useless. 
The modulus of rigidity was determined by attaching to the lower end of 
the wire W a cylinder of sheet brass (according to the method adopted by 
THomson), and observing the period of torsional vibration. Having determined 
the period, the rigidity is obtained from the equation 
3 
where T is the period, 7 the length of the wire, V its volume, and p» the 
moment of inertia of the vibrator. 
In the cases of two iron wires, one copper, and one German silver wire, 
the moduluses were determined, both before and after stretching. The results 
of these observations are given in the following table ; the first column gives a 
description of the specimen referred to, the second gives the weight per metre 
of the wire, the third the percentage conductivity of pure metal, according to 
JENKIN’s table, the fourth the percentage elongation, the fifth the modulus of 
rigidity, the sixth the length modulus, and the seventh the ratio of the lateral 
contraction to longitudinal extension as derived from columns five and six, and 
the density of the wire. 
Perhaps the most curious point connected with these results is the direc- 
tion of the change of rigidity produced by stretching. This subject was first 
treated by THomson (“ Proc. Roy. Soc.,” 1865), but the direction of change 
was in the cases given by him uniformly a diminution. With the exception 
of the iron, No. 3 specimen, my results give the opposite change. I hope to 
go into this more fully at a future opportunity, with special arrangements for 
that alone. 
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