“For instance, let an organism at birth be capable of giving N reactions (a, b, c, ... N) to a definite stimulus S and let only one of these reactions be appropriate. If only one reaction can be given at a time and if the one given is determined by the state of the organism at the time S is received, there is one chance in N that it is the appropriate reaction. When the appropriate reaction is finally given, the other reactions are not called into play, S may cease to act, but until the appropriate reaction is given let the organism be such that it runs through the gamut of the others until the appropriate reaction is brought about. As there are N possible reactions, the chances are that the appropriate reaction will be given before all N are performed. At the next appearance of the stimulus, which we may call S₂, those reactions which were in the last case performed, are, through habit, more likely to be again brought about than those which were not performed. Let _u_ stand for the unperformed reactions. Then we have N - _u_ probable reactions to S₂. Habit rendering the previously most performed reactions the most probable throughout we should expect to find the appropriate reaction in response to S₁ contained in N. S₂ contained in N - _u₁_. S₃ contained in N - _u₁_ - _u₂_. ... S_ₙ_ contained in N - _nu_, which approaches _one_ as a limit. Thus the appropriate reaction would be fixed through the laws of chance and habit. This law of habit is that when any action is performed a number of times under certain conditions, it becomes under those conditions more and more easily performed” (_Journal of Comparative Neurology and Psychology_, 1908, Vol. XVIII, pp. 503-504). This hypothesis is, like Professor Jennings’, adequate to account for only the one special case, and is adequate to account for that only upon a further limitation of the number of times that the animal may repeat any one of his varied responses to the situation before he has gone through them all once, or reached the one that puts an end to the situation. The second limitation may be illustrated in the simple hypothetical case of three responses, 1, 2 and 3, of which No. 2 is successful. Suppose the animal always to go through his repertory with _no_ repetitions until he reaches 2 and so closes the series. Only the following can happen:— 1 2 1 3 2 2 2 3 1 2 3 2 and, in the long run, 2 will happen twice as often as 1 or 3 happens. Suppose the animal to repeat each response of his repertory six times before changing to another, the remaining conditions being as above. Then only the following can happen:— 1 1 1 1 1 1 2 1 1 1 1 1 1 3 3 3 3 3 3 2 2 2 3 3 3 3 3 3 1 1 1 1 1 1 2 3 3 3 3 3 3 2, and in the long run 2 will happen one third as often as 1 or 3 and, though always successful, must, by Smith’s theory, appear later and later, so that if the animal meets the situation often enough, he will eventually fail utterly in it!