THIS problem, proposed by Prof. Karl Pearson in the current number of NATURE, is the same as that of the composition of n iso-periodic vibrations of unit amplitude and of phases distributed at random, considered in Phil. Mag., x., p. 73, 1880; xlvii., p. 246, 1899; (“Scientific Papers,” i., p. 491, iv., p. 370). If n be very great, the probability sought is
