Neutron scatter studies have been made on gently prepared chicken erythrocyte chromatin over a range of ionic strength. At low ionic strength the mass per unit length of the '10 nm nucleofilament corresponds to one nucleosome per 8--12 nm and a DNA packing ratio of between 6 and 9. From the contrast dependence of the cross-section radius of gyration of the nucleofilament the following parameters have been obtained; RgDNA' the cross-section radius of gyration (Rg) when DNA dominates the scatter; RgP, the cross-section Rg when protein dominates the scatter; Rc, the cross-section Rg at infinite contrast and alpha, the constant which describes the dependence of the cross-section Rg on contrast variation. From our understanding of the structure of the core particle, various arrangement of core particles in the nucleofilament have been tested. In models consistent with the above parameters the core particles are arranged edge-to-edge or with the faces of the core particles inclined to within 20 degrees to the axis of the nucleofilament. With increase of ionic strength the transition to the second-order chromatin structure has been followed. This gave the interesting result that above 20 microM NaCL or 0.4 mM MgCL2 the cross-section Rg increases abruptly to about 9 nm with a packing ratio of 0.2 nucleosome/mn and with further increase of ionic strength the Rg increases to 9.5 nm while the packing ratio increases threefold to 0.6 nucleosome/nm. This suggests a family of supercoils of nucleosomes which contract with increasing ionic strength. In its most contracted form the diameter of the hydrated supercoil has been found from the radial distribution function to be 34 nm. Models for the arrangements of core particles in the 34-nm supercoil are discussed.