This implies that variations below _U_ (the lower limit of the area of exemption) and above _O_ (the upper limit) can occur, but do not survive and leave descendants, and we can therefore easily understand why characters, of which different degrees arise with equal ease from the constitution of the species, must gradually develop a symmetrical curve of frequency because of the constant crossing. Obviously those individuals which stand just upon the borders of admissible variation will, other conditions being equal, leave behind them fewer descendants than those which approximate to the middle of the area of exemption; for as the characters concerned can vary in the offspring in both directions, there will always be at the lower end some of the descendants of a pair which will fall below the limits of exemption, and at the upper end some which will rise above it. This will happen even when pairing takes place between parents at the middle or at the other end of the abscissa, for there are always cases of the preponderance of one parent in heredity. A higher percentage of the descendants of individuals on the borderline will therefore be eliminated, and their frequency _must therefore be less_. Even if at the beginning of the series of observations a condition obtained in which all the ordinates of the area of exemption were equally high, those nearest the boundaries would of necessity very soon become lower, and this in proportion to their distance from the boundary, and the frequency-curve, which at first would be a straight line (according to our assumption, which of course does not tally with natural conditions), would become a symmetrical curve, highest in the middle and falling equally at either side. Ammon has worked out the hypotheses on which the curve of frequency would become asymmetrical. Firstly, when the fertility is greater towards the upper or lower limit of the area of exemption; secondly, when germinal selection forces the variation in a particular direction, upwards or downwards; and thirdly, 'when natural selection intervenes diversely at the upper or lower limit.' Of these three possibilities the first two must be acknowledged as quite probable, but the third, it seems to me, could only cause a temporary asymmetry of the curve, lasting, that is, only until a state of equilibrium has again been reached; but that may in certain conditions take a long time. Asymmetrical curves of frequency (Fig. 120, _B_) therefore arise, for instance, when the intra-germinal conditions (the 'constitution of the species') more easily and therefore more frequently produce extreme variations. In this case the area of exemption can only extend on one side, and must remain in this state. In _Caltha palustris_, the marsh marigold, we may find, according to De Vries, among a hundred flowers, those with five, six, seven, and eight petals, in the following proportions:-- Petals 5 6 7 8 Number of flowers 72 21 6 1