1339 
this quantity is found if, after differentiating in (22) under the signs 
of integration we substitute the value (28) and then perform the 
integrations. 
The result is 
9 
rr 
né 
S—=2all[AR’q + 2(À + u) A's] + zr Ge + a + b) R' 
Q= al [(à + 2) Bq 4 ARB] 4 
p(w + a) Re. 
If no stretching forces act on the ae of the wire, nor any forces 
on the surface, we have Q=0, S=0O, so that 
YR R? 
ES an — (pp a B) ee SM) 
Ter 
(4 + 2u)q-+ 228 = ris: es nd Vilalta bo) te! op NU) 
When the coefficients of elasticity 2, u and the coefficients a and 5 
are given, we can derive from these equations the changes | in 
length and diameter (q and s) caused by a torsion. 
§ 14. We shall use formulae (29) and (30) to calculate the 
coefficients a and 6 from Poyntina’s measurements. 
PoyntinGc has worked with two steel wires and one copper wire, for 
and 
which he has determined in the first place Youne’s moduius — ats 
2u 
À 
Poisson’s ratio BĲ) From these quantities we can calculate 2 and yu. 
Further he has measured g and s, so that a and 5 can be found. 
The results are given in the following table, in which everything 
has been expressed in C.G.S. units. The length of the wire was in 
all cases 
/=160,5 em 
and the numbers given for g-and s refer to the value @ = 2,7; so 
they indicate by what part of the original value the length and the 
diameter change, if one end of the wire is once twisted round. 
Steel 1 
Steel 2) 
Copper 
NE eg 
0,0493  2,12.10!2 0,270 9,77. 10'18,35. 10!1|1,71.10—6|—3,19. 10-7 —5,03. 1012, 0,58. 1012 
0,0605 | 2,12. 1012 0,287 11,09. 1011.8,24. 1011/2,90, 10-6 —5,24. 10-7 —5,70. 1012, 0,10. 1012 
0,06095 | 1,31. 1012 0;331 | 904. 1011492. 10114,25.10-6 ,75.10-6 —3,94. 1012 3,37. 1012 
