Solution to Problem 222 Poisson's Ratio

$\nu = -\dfrac{\varepsilon_y}{\varepsilon_x}$

$\varepsilon_y = -\nu \, \varepsilon_x$

$\varepsilon_y = -\nu \, \dfrac{\sigma_x}{E}$

$\dfrac{\delta_y}{d} = -\nu \, \dfrac{-P}{AE}$

$\delta_y = \dfrac{Pd}{\frac{1}{4} \pi d^2 \, E}$

$\delta_y = \dfrac{4P \nu}{\pi Ed}$       (okay!)