282 
degree with respect to the 9 differential quotients, we may write 
for that free energy : 
pdr =([(4.4 + w) J? — 2aJ, + CIS + DJ, + EJ) dr, 
in which dr is the volume element of the undeformed body. In 
strained condition it is dr’. 
The variation of energy after a virtual transformation from a 
strained condition amounts to: 
dg dg 
— de, +..,..+ — dy, 
de, 1) SR 
The virtual transformation is determined bv its 6 strain compo- 
ents DD Ar Ger Xb ae 
The de, ...dy, can be expressed linearly in these. The variation of 
energy amounts to: 
(XD, + Y,D, + ZD, 4+ 2 Y.G, +226, + 2 XG) dr 
in which 
bere = a8 \* dy IE 08)" 0g 
OR Bn a =) de, Es de, t (= de, a 
i 9 W895 0% fs 5 95 14 ae ata =| 
Oy de Oy, Oz du) OY, da / Oy OY, 
with two analogons for }, and Z.. 
dn OS 0g òn\dsdp Ay OE 0p 
—(1+J,)Y:= —- ti l+— J——+—/14—)]—- 
abd Oa Ow de, i. ( r =) Oy de, Oz ( 35 de) de, | 
ay 06 Ond) Op (0 d8 zi is | dp 
- 1+ — +. - - — aad (ig | = 
; ( : DIe a) "02 dy ) 
dy,” lOzde | de dy," 
B18 (14 28) 26) Oe 
Ow Oy Oy / Oa) Oy, 
with two analogons for Z, and X,.. 
They give the stress components as sum of differential quotients 
of the y with respect to the strain components. 
Oz 
§ 2. In $ 1 we have placed side by side the formulae of DunEM, 
which we shall require for the comparison of two papers *) on the 
changes which take place in the dimensions when a strained steel 
wire is twisted. In this § we shall give the results of their applica- 
tion in some special cases. 
Let us give to a body a dilatation «@, 8,7, resp. in the a, y, and z 
1) H. A. Lorentz. The expansion of Solid Bodies by Heat. Verslag Kon. Ak. Oct. 
1915 p. 671. Poynrine. On the changes in the Dimensions of a Steel Wire when 
Twisted and on the Pressure of Distortional Waves in Steel. Proc. Royal Soc. 
(A) 86, 1912, p. 534. 
