281 
Physics. — “On the use of Third Degree Terms in the Energy of 
a Deformed Elastic Body.” By J. Trusiine. (Communicated 
by Prof. H. A. Lorentz). 
(Communicated in the meeting of May 27, 1916). 
§ 1. We shall indicate the deviations to which a point 2, y, 2 
of an elastic body is subjected in a deformation by §, 4, &. 
It is easily shown’) that this change of form can be obtained 
by making the dimensions in 3 definite directions normal to each other 
resp. 6,,6,,6, times smaller, and by then rotating the body. If we 
RE Bn 
write S; for —, the three values of S; are determined as the three 
Oi 
roots of the equation: 
S° — (34-27,) S*H3HAT, HAJ) S — (1-2, HAJ, +8) = 0 
in which: 
Jit e tT 5 
J, — 838: str 836, a ë,€, at (yy “i Yo" te Ya) 
J, — 818263 =F bias Fi EY Enk Ever ar EsYs') 
and the ¢,...y, are the following functions of the 9 differential 
hed 
he 
quotients a Aerle: 
3 ce 
08 fae)? (au? (08) 
Ei doe le a & a 5) | 
ROR) 
En SS oO =— = hs —— i ao 
dy (3; dy y 
o¢ EN? 07)? dE: 
ae ag aes 5 | wee 
i z Ô J el 3 Ie i ey | 
oy 05. § 0§.0§ Anon: (0506 
be de" dy + Oy Ox Oy 022 On Oe 
0s 0¢ 0808 dy dy 0506 
SOT da as de de Be Ob te EDs 
05 On Of 05 dn! eos 
en dy he a da Oy Ow Oy Ag da dy" 
The .J/,,-/,,-/,; are invariant in case of axial rotation. The free 
energy of an elastic isotropic body will be a symmetrie function 
OF 64,035) 0;,: 
If we confine ourselves to terms which are of the 2"¢ and 3rd 
1) Dunem, Recherches sur |’élasticité, 1906. 
