285 
section. If the three formulae have been found for this, the first two 
will make it possible to derive the valnes of p and q from the 
observed change ot the dimensions. The third formula is a relation 
that is not practically controllable. 
We now first examine what relation there is between the quanti- 
ties p, q, and those which we have above introduced. Poyntine 
calculates from his suppositions that a normal pressure (4 u + p) & 
acts on AB, and a normal pressure (— 4+ pe’ on AD, the 
tangential stresses ge existing hesides. This appears to agree entirely 
with our equations (7), and the relation between the elasticity con- 
stants of Poynting and ours is expressed by 
Oss keton Ds A 
ETEN TV TRC 
With these values of p and g we can follow the reasoning of 
Poyntinc. The result can be represented as follows in another 
notation. A rod of a length / and a section with the radius F, on 
being twisted over an angle 6, and not subjected to any external 
pressure, becomes longer in the ratio of 1 to 1 + y, its radius 
changes in ratio of 1 to 1 +6. A point at a distance 7 from the 
axis will get at a distance 7(1-+ s) from it. The quantities y, 5, 
and s are found from: 
Ork? 
2ay+4(44+ w)o=— PTS (u—2 p—2 4) | 
(4+ 2u) 7 + 240= VT (u + 2p) Hire zak 165) 
TE up 6 
Rn 
"Te PE 2u 
(formulae (8), (9), and (10) in the cited paper by Poyntine). 
Observed were o and 7. The two first formulae gave the possibility 
to find the quantities p and q for a definite steel wire. For that 
wire 2= 9,77 Xx 10; w= 8,35 Xx 10*'. The values for pand q were 
then: "p==1.67 # 10"; ¢g—— 0,70 X 10", hence: D= 13,6 < 10%: 
H=—14,5 « 10", all this expressed in C, G, S unities. 
Prof. Lorentz treats the same problem, for which other con- 
stants of elasticity a and 5 are introduced. The three equations 
(29), (30), and (28) in his paper can, however, not be made to 
agree all at the same time with the equations (8) by a suitable 
connection between p, g on one side, and a, 6 on the other side. 
The coefficients a and’ b-introduced by Lorentz occur as follows. 
When a body which has undergone the dilatations «3,7 in the 
