336 REPORTS ON THE STATE OF SCIENCE, ETC. 
The distances of scale from indicating mirrors are the same in the present 
tests as in those made four years ago, and are— 
For bending strain apparatus. ; ; - 165 cm. 
5, torsional  ,, re 4 4 7 =p hOBy gh 
For bending, the mirrors registered a scale displacement proportional to the 
angle between the tangents at the ends of the specimen. ‘I'he actual value of 
this angle is 
‘Range of Strain’ in cm. _Ry (say) 
“22x 165 660 
As mentioned on page 331, the mirrors were fixed to the square shoulders of 
the specimen, and the length 7 over which this angle is measured is not known 
accurately. If 7 be regarded as an equivalent length® of specimen, and if 
r stands for the (outside) radius of specimen, then the maximum fibre strain 
will (provided the strains have a linear distribution and are proportional to 
distance from axis of specimen) be 
; (angle between tangents) = = 
The angle of twist over length 7 will be 
‘Range of Strain’ in cm. _R, (say) 
2x 2x 155 620 
ar 
620 
and the shear strain will be accordingly o 
In the Preliminary Dead-weight Tests (see Table IV.), in which the 
material is elastic, the bending strain 
SEG Ty Apa) eS OE 
where +p, is the range of stress which gives the range of elastic strain R. (cm.), 
and H=Young’s Modulus. 
The shear stress in torsion similarly 
Say CR mp ey Sia 
where +g, is the range of shear stress giving the range of elastic strain 
eRy (cm.), and C is the modulus of rigidity. 
If we consider a specimen on which preliminary dead-weight tests were made 
both in bending and torsion, and if we assume that the fillet at the shoulders 
affected the bending and twisting stresses and strains in the same proportion, 
then— 
R, e 
Pe e*Yb ‘ 
E / qe = 660 Rr ; 
Cc 620 j 
Fy 
De eRy 660 
; 
de ey 620 2 
Dd 
or 
I 
2 
C 
8 Equivalent in the sense that the angle of bending over a parallel-turned 
length 7 is to be the same as that measured on the length between the square” 
shoulders. ry 
