curve to its asymptote is continually decreasing, it is here just the reverse; this rate is continually increasing. Hence the two, viz.[ TN: space] the curve and the axis of x, appear to the eye, after a very short time, to merge into one another.
6 As by Quetelet: noted, amongst others, by Herschel, Essays, page 409.
7 Proc.[ TN: space] R. Soc.[** TN: space] Oct. 21, 1879.
8 We are here considering, remember, the case of a finite amount of statistics; so that there are actual limits at each end.
9 It must be admitted that experience has not yet (I believe) shown this asymmetry in respect of heights.
10 The above reasoning will probably be accepted as valid at this stage of enquiry. But in strictness, assumptions are made here, which however justifiable they may be in themselves, involve somewhat of an anticipation. They demand, and in a future chapter will receive, closer scrutiny and criticism.
11 A definite numerical example of this kind of concentration of frequency about the mean was given in the note to § 4. It was of a binomial form, consisting of the successive terms of the expansion of (1 + 1) m . Now it may be shown (Quetelet, Letters , p. 263; Liagre, Calcul des Probabilités , § 34) that the expansion of such a binomial, as m becomes indefinitely great, approaches as its limit the exponential form; that is, if we take a number of equidistant ordinates proportional respectively to 1, m , m ( m −