This paper considers the design and construction of a large permanent magnet for use in cosmic ray studies. It is shown that there is an optimum distribution of the magnetic material in order to obtain either a maximum field, H, or a maximum line integral, integral from -infinity to +infinity of Hdy for a given pole face area and gap size. It has been shown that a good value of the leakage factor for use in the design calculations for magnets with rectangular pole faces can be predicted theoretically. Detailed comparison between results predicted by this theory and those obtained in practice with the present magnet and other large permanent magnets suggest that these calculations can be usefully applied to magnets with pole faces of any shape. These comparisons also show, in agreement with Andrew and Rushworth, that demagnetization curves for small specimens of magnetic material are not reliable where large blocks are considered.