A Duality in Interpolation to Analytic Functions by Rational Functions.

omission and to say whether its correction will lead only to a new interpretation of the constants of our equations or to an actual change of their form. Another simplification is the neglect of polar and excited states: While there is reason to assume that their influence is small, its exact estimate is still lacking. Further inaccuracies were discussed in our preceding paper: The use of Bloch's periodicity condition in place of the actual border conditions, the restriction to interactions between adjacent atoms and to first order perturbations. With these omissions the mathematical side of the theory becomes simple and elegant and, as the preceding sections show, it is sufficient to represent the actual conditions at low temperatures. However, the prospects of carrying this treatment to a higher degree of approximation are not very favorable. The mathematical simplicity is lost and the theory becomes rather cumbersome because one has to increase the accuracy in so many different directions, For determining the Curie point one should, perhaps, try a different approach to the problem, for instance, that recently outlined by L. Brillouin'1 although it seems that this method, too, is difficult to be carried through without considerable idealizations. 1 R. I. Allen and F. W. Constant, Phys. Rev., 44, 228 (1933). 2 p. S. Epstein, Phys. Rev., 41, 91 (1932). 3 P. Weiss, Phys. Zeits., 9, 361 (1908). 4 W. Heisenberg, Zeits. Physik, 49, 619 (1928). 5 F. Bloch, Ibid, 61, 206 (1930). 6 R. Forrer, Journ. Phys. et le Rad., 1, 49 (1930). 7 F. Bitter, Phys. Rev., 37, 91 (1931). 8 A. Preuss, Thesis of Zurich (cited by Forrer). 9 We infer this from the fact that our formula (8) with a suitably chosen constant represents well the saturation curves obtained by Weiss and his pupils for heterocrystalline materials. 10The formula given by Bloch (note 5) leads to a still much slower decline than ours. 11 L. Brillouin, Journ. Phys. et le Rad., 3, 373, 565 (1932); 4, 1 (1933).