XVIII. W. H. WARREN. 
Let A, denote the area of the portion oee, 
» As ” ” ” ” eeymm 
, 
” A; ” ” ” ” mmrr 
Then these areas may be expressed as follows :— 
A, = 4 LedAl 
A, = a Lm (Al, — Al) 
A, ae p Lm (A1,, sh Al.) 
Where «a and p are coefficients depending on the shape of the 
diagram. 
The total work applied to the test piece up to the moment when 
fracture occurs is— 
A=A,+A,+4A,;=} Le Al + Im (Al, - Al) +p Lm (Al, - Al) 
The elastic elongation A/ is very small, and moreover does not 
depend upon the ductility of the material, 7.¢., it has no reference 
to the total elongation at rupture, it may therefore be neglected. 
Again (Al,,—Al,) is not large even in ductile materials, and 
approaches zero as the material bécomes more brittle, hence we 
may write approximately— _ 
Al, = Al, = Al and Lm = Lr 
The expression for the work done then becomes— 
Az=alLlmAl 
If 7 denotes the length of the test piece in millimeters and 
the area of the section in square millimeters, = work done per 
unit of volume will be— 
Im Al 
xl 
a=a 
aed 
where f is the load per unit of area of section and X the elonga- 
tion per unit of length. Now a can be determined experimentally, 
and Professor Tetmaier has proved by a numerous series of experi- 
ments that for the same class of materials the value of a is very 
sensibly constant. It follows then that the coefficient— 
ec = BX 
