Louisa S. Cook, Geometrical Psychology or the Science of Representation: an Abstract of the Theories and Diagrams of B. W. Betts, George Redway, 1887


In figure 18, an Ond in arithmetical progression, common difference 1, the right side of the form, the positive ideation, is governed by the scales E G. A compromise is effected between the scale of five terms and that of seven terms. Mr. Betts draws five circles of differentiation and seven radii of realized activity arranged according to the scale of comparison. Thus the realised activity, though equal in amount, is more limited in extent than it would have been if it had been perfectly developed in the scale of G. The two circles of differentiation which have been suppressed through the lower necessity would have afforded the perfect realisation of the higher law of the nature. The contour of the experience manifests three stages of progress, one of decline, and three of progress again, 1+1+1-1+1+1+1=7. It might equally well have been 1+1-1+1+1+1+1=7—i.e., any total of sevel links, whether ascending or descending. The left side of the figure, the negative ideation, is governed by the scales D F in a similar manner. The contour is 1+1+1-1+1+1=6. The counterpart form, figure 19 [right], has similar indentations.