A standard cell of 1.20 V balances on a potentiometer wire at 340 cm…

The gradient is $k = \dfrac{IR_w}{L}$, and the potential at a distance $l$ is $V = kl$. At balance $E = kl$, so $\dfrac{E_1}{E_2} = \dfrac{l_1}{l_2}$. A balance with the cell open and with $R$ across it gives $r = R\,\dfrac{l_1 - l_2}{l_2}$. A voltmeter of resistance $R_v$ across a cell reads $V = \dfrac{ER_v}{R_v + r}$.