Q.Describe how a potentiometer is used to compare the emfs of two cells by the combination method.

[!TLDR] Wire the cells through four keys so closing $K_1,K_3$ gives the sum ($\varepsilon_1+\varepsilon_2$) configuration and closing $K_2,K_4$ gives the difference ($\varepsilon_1-\varepsilon_2$) configuration; the two balancing lengths gi …

This is potentiometer Method II of Section 9.4.2. When two cells are joined negative-to-positive (as in an ordinary series battery), their emfs ADD, giving an effective source $(\varepsilon_1+\varepsilon_2)$ -- the sum method. When they are instead joined LIKE-terminal-to-like-terminal, their emfs OPPOSE, giving an effective source $(\varepsilon_1-\varepsilon_2)$ (with $\varepsilon_1$ the larger) -- the difference method. A potentiometer circuit wires both cells through four keys $K_1,K_2,K_3,K_4$: closing $K_1$ and $K_3$ together selects the sum configuration, and closing $K_2$ and $K_4$ together (with $K_1,K_3$ open) selects the difference configuration, both sharing the same wire, galvanometer and jockey. In the sum mode, the null point at length $l_1$ gives $\varepsilon_1+\varepsilon_2 = k\,l_1$; in the difference mode, the null point at length $l_2$ gives $\varepsilon_1-\varepsilon_2 = k\,l_2$. Dividing these, …

Set up the sum and difference configurations via the four-key switching, write both balance equations, then …

Mixing up which key pair gives the sum mode and which gives the difference mode, or forgetting $\varepsilon_1$ must be the larger emf for the difference-m …