APPENDIXThe conditional probability distribution of cos (q~h+ %+q~-h-Z)Let the vector h be fixed and assume that k ranges uniformly throughout reciprocal space. Denote by P(xl IEkl, IEh+kl) the conditional probability distribution of the random variable X= cos (~h + ~k + 9-h-k),given that I~1 and IEh+kl have specified, fixed values. Crystal data for estriol (C18H2403) are: a= 9.270, b = 23.001, c= 7.560 A, p= 110.90. Space group P21 with two molecules in the asymmetric unit. The structure was solved from a set of phases derived initially by application of a phase determining formula of the type KIEIE2E3I cos (~,, +~,2+,,3) = ((If,d"-) (If,,,+,,l'-) (lf-,,3+,,l ~°-)>,,+ R and extended by application of the tangent formula. The structure was refined by block diagonal least-squares with anisotropic thermal parameters for the non-hydrogen atoms, to R= 5.6%. All hydrogen atoms were located. Standard deviations of non-hydrogen distances and angles are 0.007/~ and 0.4 ° respectively.Differences in hydrogen bonding, packing environment and intramolecular sterie effects cause the two molecules in the asymmetric unit to be non-identical. The two molecules are hydrogen bonded head-to-tail via the 3-hydroxyl oxygen of one molecule and the 16or-hydroxyl hydrogen of another, in such a way that the 18-methyl group of the first lies under the A ring of the second, producing distortion of this aromatic ring. Steric hindrance between the C ring equatorial hydrogen atom at C(11), and the hydrogen atom at C(1) produces twisting about the C(9)--C(10)bond, in opposite directions in the two molecules, causing the B ring to take up a half chair conformation in the first and a twist boat conformation in the second.The molecules pack with molecules of the first kind and molecules of the second kind, hydrogen bonded in separate chains parallel to b. These chains are cross linked via the asymmetric unit and via weaker hydrogen bonds involving all three hydroxyl groups. Three distinct types of hydrogen bond exist in which the O...H-O angles are 159-177 °, 136 °, and 128 °.