resistance of transversely split cylinder

$\mathrm{d} G = \frac{\mathrm{d} S}{\sigma l}$

$G = \int_{r_1}^{r_2} \frac{\sigma h}{\pi r} \mathrm{d} r = \frac{G h}{\pi} \ln{\Big(\frac{r_2}{r_1}\Big)} = \frac{1}{R}$

$R = \int_{r_1}^{r_2} \frac{1}{\sigma \pi r h} \mathrm{d} r = \frac{1}{\sigma \pi h} \ln{\Big(\frac{r_2}{r_1}\Big)}$

$R = \frac{h}{\sigma S} = \frac{2 h}{\sigma \pi (r_2^2 - r_1^2)}$