It is well known that de Vries himself considered fluctuating variations and mutations as something quite different. The former he considered as nothing new, only as augmentations or diminutions of something previously existing; and he regarded fluctuations as due to the action of the environment, following in their distribution the laws of chance.[30] Mutations, on the other hand, were something quite new. Now future analysis of variability will not, we think, bear out the validity of this distinction. It is far more likely that a fluctuation is a variation which is the result of some causes the action of which is variable. (We are regarding variability now as subject to “causation” in the physical sense, for only by so regarding it can we attempt its analysis). As a rule this process results in a fluctuation, but if its extent, or degree of operation, exceeds a certain “critical value” a mutation is produced. We may, following the example of the physicists, illustrate this by a “model.” [30] See Appendix, p. 351. [Illustration: FIG. 23.] This model is a modification of Galton’s illustration of the degrees of stability of a species. It is a disc of wood rolling on its periphery. We divide it into sectors, and the arcs _ab_, _cd_, _ef_, and _gh_ have all the same radius, 10, 20, 30, and 40. Then we flatten the sectors _bc_, _de_, _fg_, and _ha_, so that their radii are greater than are those of the other arcs. Now let us cause the disc to roll about the point 8 as a centre. It will oscillate backwards and forwards about a mean position 8. Let us think of these oscillations as fluctuations. Suppose, however, that we cause the disc to roll a little more violently, so that it oscillates until either of the points 3 or 4 are perpendicularly beneath the centre _O_. In either of these positions the disc is in a condition of “unstable equilibrium,” and an infinitesimal increase in the extent of an oscillation will cause it to roll beyond the points 3 or 4. But if it does pass either of these critical points it will begin to oscillate about either of the new centres 5 or 7, thus rolling on one of the arcs, _ha_ or _de_. This assumption of a new condition of stability we may compare with the formation of a mutation.