214 
MR. a. H. DARWIN ON THE STRESSES 
If however a permanent set begins to take place before the wire breaks, this product 
should be less than the tenacity. I do not see how it can ever be greater, unless 
there be a marked departure from Hook’s law “ut tensio sic vis;” or different sets of 
experiments with the same class of material might make it seem greater. In some of 
the results given by Sir William Thomson the product of modulus and elastic 
extension is however greater than tenacity. 
Ordinary experience would lead one to suppose that such materials as lead and 
copper would undergo a considerable stress beyond the limits of perfect elasticity, 
before breaking. It is surprising therefore to see how nearly identical this product is 
to the tenacity—indeed in the case of lead absolutely identical, as may be seen in the 
table below. 
With regard to the earth we require to know what is the limiting stress-difference 
under which a material takes permanent set or begins to flow, rather than the stress- 
difference under which it breaks; for if the materials of the earth were to begin to 
flow, the continents would sink down and the sea bottoms rise up. 
It will be seen from the definition of tenacity given above that it is the rupturing 
stress-difference for tensional stresses. There is no word specially applied to rupturing 
stress-difference under pressure. 
I am inclined to think that for the purposes of this investigation these tables in 
most cases rate the strength of materials somewhat too highly; for it seems probable 
that a permanent set would be taken, if a material were subjected for a long time to a 
stress-difference, which is a considerable fraction of the limiting value. We are likely 
to know more on this point in some years time when the wires hung by Sir William 
Thomson in the tower of Glasgow University have been subjected to several years of 
tension. However this may be I give the results of some of the experiments as 
collected and quoted by Sir William Thomson and the late Professor Pankine. 
The first table of tenacity, except the results denoted by the letter E, are taken from 
Sir William Thomson. The second table of crushing stress-difference is taken 
entirely from Eankine. The multiplications and reductions to different units I have 
done myself. 
