Political apportionment is the allocation of an integer number of seats to each of a number of subunits into which a legislature is divided. This paper introduces the theoretical issues. and then applies the theory to the apportionment of parliamentary scats in the United Kingdom. It shows that the outcome is defective by comparison with desirable and achievable standards, and that the, defects lead to predictable biases of representation in favour of certain parts of the country. The defects have arisen partly through manipulation for party advantage, but largely because of a failure of all concerned to understand the theory of apportionment.