$2\mathrm{.}7.$ A circular$-$arc gage $[10]$ with resistance $R($shown in Fig. P$2\mathrm{.}7)$ is mounted on the surface

of a specimen in the biaxial strain state. Determine $\frac{R}{R}$ in terms of $lo{n}_{x}lo{n}_y,$ and ${}_{xy}.$ The

radius of the circular arc is $r.$

FIGURE P$2\mathrm{.}7$