Recent experiments have indicated that at least one important magnetic compass used by many animals for navigation may be located in the eye. Here it is shown that a very sensitive magnetic compass is formed by the incorporation of a small quantity of ferrimagnetic single-domain crystals in a droplet of nematic liquid crystal. Optical detection of the compass output is illustrated by experiment and the predicted properties of a biological compass, based upon these principles, are compared with the known properties of the natural compass. Some experiments that could test the model are described.