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Abstract Horse methaemoglobin crystallizes with two molecules in a face-centred monoclinic unit cell (space group C2), in which rigid layers of molecules parallel to (001) alternate with layers of liquid. The crystals can be made to swell and shrink in a series of steps involving changes in d(001) and in the angle β. It appears that only the distances between the molecular layers change, but not their internal structure. The lattice changes allow the modulus of the molecular Fourier transform to be sampled along lines of constant h and k. When k = 0 the transform is real and the sampled values of |F| describe a series of loops and nodes. Part I of this series dealt with the principles of deciphering these and established the absolute signs of the 00l reflexions. In part II the absolute signs of certain 20l reflexions were derived from the changes in intensity produced by the substitution of salt solution for water as the liquid of crystallization. In this paper the transform is measured for all values of h and l up to λ/d = 0·24, comprising nine layer lines in all. The absolute signs of layer lines with h 2 are left in doubt, but many sign relations are established within each of them. It is difficult to assess exactly the number of sign relations found by the transform method, but it is estimated that the number of alternative sign combinations is reduced from 296 to 218. The remaining uncertain ties are cleared up by the isomorphous replacement method described in part IV .
M. F. Perutz (Tue,) studied this question.