\¢ ls? ee mn | 
pea yt) (eet Eee 
nad. BAD ) (7) 
D 
thea „ te) 
i) Zr == — UE Xy ll 
§ 3. After Poyntinc had first given considerations about the 
changes of the dimensions in a twisted wire, which he had to relinquish 
later on, a supposition is made in his more recent consideration, which 
is not evident from the standpoint of a third degree potential energy. 
If we transform a cube ABCD by a shear over an angle & to 
ABKL, the line GB. which undergoes the greatest contraction will 
. . . . é 
get into BH after the deformation, so that angle ABH = 45° + ie 
The line Af, which has been most stretched, will make an angle 
6 é 9 ad $ En : ; 
Senn with 45. This holds for terms up to € inclusive. PoYNrinc’s 
supposition now runs that only a normal pressure acts on AQ, and 
only a normal tension on BQ, and that therefore no tangential 
stresses exist along AQ and BQ, not of the 2"¢ order either. PoyntinG 
introduces two new elasticity constants p and g; he does so in the 
following way. The pressure on AQ will amount to ue + pe in 
2¢ approximation, that on BQ will have a value — we + pe’, and 
the pressure normal to the plane of drawing ge’. 
The problem raised is the following one. A long, thin cylindrical 
rod is twisted over an angle 9 without being pressed sideways or 
on the end planes. Required is the increase in length, the decrease 
in thickness, and the shortening of the radius at any point in a 
