358 Mr. Tred gold’s experiments on the elasticity 
formula you have given in your Nat. Phil. ( Vol. II. p. 48 ) is, 
according to the first experiment, - - 8,827,300 feet. 
And according to the second experiment 8,810,000 feet. 
Now the height of the modulus, as you had determined 
it for steel by Experiments on Vibration, is 8,530,000 feet. 
(Nat. Phil. II. p. 86.) The modulus for cast steel calculated 
from Duleau’s experiments (Essai Th^orique et Experi- 
mental sur le Fer Forge, p. 38 ) is 9,400,000 feet, and for 
German steel 6,600,000 feet. 
The force which produces permanent alteration is to that 
which causes fracture in hard steel, as 350: 580 ; or as 1 : 1.66 
in the same steel of a straw yellow temper as 150 : 385, or 
as 1 : 2.56. 
When the tension of the superficial particles at the strain 
which causes permanent alteration, is calculated by the for- 
mula given in my Essay on the Strength of Iron, p. 146, 2nd 
Edition, it is 45,ooolbs. upon a square inch in tempered steel ; 
and the absolute cohesion ii5,ooolbs. Mr. Rennie found the 
direct cohesion of blistered steel to be i33,ooolbs. (Philoso- 
phical Transactions for 1818. ) 
But in the very hard bar, the strain which produced perma- 
nent alteration was 5i,ooolbs. for a square inch, and the ab- 
solute cohesion only 85,ooolbs. 
From these comparisons I think it will appear, that in the 
hardening of steel, the particles are put in a state of tension 
among themselves, which lessens their power to resist ex- 
traneous force. The amount of this tension should be equal 
to the difference between the absolute cohesion in different 
states. Taking Mr. Rennie’s experiment as the measure of 
cohesion in the soft state, it will be 133,000 — 115,000 = 
