The aim of the present study consists in analytical consideration of the learning mechanism of pupils, which is observed chiefly in the relation between the educational action (S) and educational effect (G), or, the mechanism which is represented by function (f) in f (S)=G In the present report, description will de made of the learning mechanism mainly in terms of the readiness to learn. In the present study, the learning mechanism, or function (f), was constituted with the model of the readiness to learn, and the various properties concerning the readiness to learn were analysed by means of the model (f). The process of analysis was as follows. 1. The point of the readiness to learn (Rα) was defined exactly at the point where the pupil was found ready to learn the subject matter (α). By analytical manipulation of this model, the point of the readiness to learn (Rα) was educed from the actual data. 2. On the assumption that erroneous answers indicate a systematical condition in the neighborhood of the point of the readiness to learn, analysis of the point of the readiness to learn was undertaken by dint of the erroneous answers in each stage of ability. The results obtained in 1 and 2, were as shown in (8) and (13) formulas, respectively. The (8) formula defines the point of the readiness to learn (Rβ) as follows : Max__j{P_β (G_j)-P_β (G_j-1)} where G_1, G_2, ---, G_n are the group to be defined on the continuum X_β. G_1 is the group of the lowest ability, in respect to ability β, and G_n, the group of the highest ability. P_β (G_j) is the percentage of the correct answer to the problem, in respect to ability β. When j satiafied (8) formula : R_β⊂G_j or R_β⊂G_j-1 And, (13) formula is : Max__lMax__j'Q_rj' (G_l)/Σ^^m__j=0 Q_rj (G_l) where Q_rj' (G_l) is the ratio of erroneous answer to the problem, inrespect to ability γ. j=0 denotes absence of answer. j'=1, 2, ----, m When l, j' satisfies (13) formula, and if k≒1 (where, R_γ⊂G_k), j', the erroneous answer, is presumed to be due to inadequate preparation. Because, however, this result was considered on unidimensional space, it wa pregnant with the possibility of scalability. Accordingly, it was magnified multidimensionally. The results, thus obtained, are (18) and (22) formulas. (see p. 147, 148 in the text.)