On the Physical Characteristics of the Hydra Cluster of Nebulae.

which is impossible since r is a primitive root of I and the exponent is odd. 1 Proc. Nat. Acad. Sci., 15, 45 (1929). 2 We say that an ideal p belongs to an exponent n when p" is a principle ideal but pd is not a principal ideal for 0 < d < n. Trans. Amer. Math. Soc., 31, 632 (1929). Duke Math. Jour., 5, 419-420 (1939). 6 Trans. Amer. Math. Soc., 31, 632-633 (1929). 6 Dickson, Jour. fair. Math., 135, 134-141 (1909). 7 Proc. Nat. Acad. Sci., 16, 303 (1930). 8 Landau, Math. Zeitschrift, 2, 52-154 (1918). 9 Hasse, Jahresbericht Deutschen Math.Verein, Erganzungsbiinde VI, 61 (1930). 10 Hasse, loc. cit., p. 112.