A new rotational method, particularly appropriate when a positive manifold can be assumed, is presented in theory and in computational detail. It is applied to a five-dimensional factorial matrix in which a simple configuration is known to exist. The new technique is much more efficient in yielding the simple configuration than are the methods formerly used. Landahl's transformations can be combined with this method to advantage.

An initial transformation for facilitating the analysis of a factor problem is discussed. Such a transformation is used in the rotational procedure developed by L. L. Thurstone in an accompanying article.

The theory of discrimination learning developed in Part I* of this paper is extended to more complex learning situations such as those used for differentiating relative from absolute habits. The greater difficulty of learning an absolute discrimination than of learning a relative discrimination is predicted. The theory is also extended to cover cases of transfer. It predicts that under the ordinary training conditions transfer to new stimulus situations will be on a relative basis, and it predicts the type of transfer to be expected under other training conditions. A number of additional established facts of learning and transfer can be deduced from the theory. Methods of testing the adequacy of the theory by new and more crucial experiments are suggested.

On the basis of previous mathematico-biophysical studies, a theory of visual perception is outlined. The theory is applied to the aesthetic values of polygonal patterns and found in fair agreement with experimental results.

A circuit of mutually exciting neurones capable of approaching and maintaining a state of permanent excitation has been described by Rashevsky as a possible mechanism for the production of conditioned reflexes. The mode of approach of such a circuit to the steady state is examined in some detail under slightly more general assumptions, and an estimate is made of the order of magnitude of the time required to reach this state.

In previous formulations the assumption has been made that the intensity of excitation or inhibition varies with distance. In this paper the simple case of a series of identical neurones is treated. The development shows five possible relations. In future theoretical formulations it is no longer necessary to postulate arbitrary relations in case any of the derived forms can be used.