The potentiometer works on the principle that the potential drop across a length of a uniform wire is directly proportional to its length ($V \propto l$). When used to compare the EMF of two cells, the ratio of their EMFs is equal to the ratio of their balancing lengths: $\frac{\varepsilon_2}{\varepsilon_1} = \frac{l_2}{l_1}$. Substituting the given values: $\varepsilon_2 = \varepsilon_1 \times \frac{l_2}{l_1} = 1.25 \text{ V} \times \frac{63.0 \text{ cm}}{35.0 \text{ cm}} = 1.25 \times 1.8 = 2.25 \text{ V}$.