A 
Yorsion of Lead Wire beyond the Hlastic Limit. 555 
No doubt with more care in the determination of the 
constants a, p and q, a closer fitting equation could be obtained. 
There seems, however, to be no convenient method of deter- 
mining them except by trial and error. 
The type of law which fits in with our experiments is 
surprisingly at variance with what one would from analogy 
expect, and indeed with what has actually been deduced from 
theoretical grounds. Professor Natanson *, who has thrown so 
much light on the question of overstrain, arrives at the 
a} 
expression II=II,e7 for the stress required to preserve con- 
stant strain, where I], is the initial pressure and T, following 
Maxwell, is the time of relaxation f. 
Our experiments with lead on the contrary, as we have 
seen, agree so long as the time is small with an expression 
cid é ee et L 
e « =t-+c¢,or to remove that restriction €« = ; 
Tae 
All the more obvious considerations which suggested them- 
selves have been found to lead to an expression of the 
wrong type. For instance, one may picture the material 
as being composed partly of viscous and partly of elastic 
components interdependent on each other. These may be 
arranged in a variety of ways, which all ultimately lead, 
however, to the wrong form of expression. A model was 
actually constructed on such lines before the true law was 
appreciated. Two thin rubber bands hanging from above 
helped to support a crossbar to which a weight could be 
attached. Between these in the centre, fixed upright on the 
crossbar, was a long cylinder filled with a thick oil. A piston 
hung from above by a strong rubber band worked in this 
cylinder f. 
The action on attaching a weight below is to immediately 
pull out the thick rubber band which carries the piston an 
amount corresponding to the weight put on, the piston for 
instantaneous movements being fixed in the oil, and the 
thin bands hardly affording any help at this stage. As the 
piston slowly draws out, more and more weight is thrown on 
the thin bands, which accordingly continue to stretch. Ulti- 
mately they carry the whole weight. 
* Bulletin de ! Académie des Sciences de Cracow, Oct. 1902, p. 512. 
+ Experiments made with pitch show that the above form for the 
law is inadmissible for this substance also. Phil. Mag. vol. vil. p. 347, 
1904. 
{t The weight of the cylinder and oil was eliminated by means of 
balance weights acting by cords over pulleys. 
