The purpose of the present investigation was to explain a nature of error which occures when subjects are required to repeat the multiplication table, on the basis of the reproduction law underlying the recall of a single number. The experimental procedure was as follows : Subjects were requested to write any digit between 0 and 9 in response to a stimulus digit (digits used as stimuli ranged from 0 to 9). Instruction was given to avoid mere repetition of a presented digit and foreward or backward sequence responses.
The intervals between the stimulus digit and the response digit was examined with special attention to the frequency of occurence of each interval.
Many years ago, Obonai and Ito, analized the causes of errors in the repetition of the multiplication table. It was demonstrated that the majority of errors were caused by replacing one of the component numbers. For instance 2×6=14, in this case the 6 was replaced by 7 yielding an erroneous answer, 14.
In the present study, we proceeded a step further and investigated the relation between the tendency to reproduce an associated digit when the stimulus digit was a single unit and when the stimulus digits were composed of compounds as in the multiplication table. The results were as follow; (1) Subjects were requested to respond freely with a digit between 0-9, when a stimulus digit was given. Inspection of Fig. 1 in Jap. text shows that there is a considerable tendency for subjects to reproduce an adjoining digit in their response when the stimulus digit is a single unit. Only a small percentage gave responses which were as much as 4, 5, 6, …… intervals removed from stimulus digit.
(2) Inspection of Figs. 3 and 4 shows that in multiplication error the strength of replacement of digit declines with the increasing degree of remoteness of two digits. Therefore, it is clear that the cause of error in multiplication results from remote association, i.e. induced reproduction, of a single digit.
(3) Fig. 5 shows the various degree to which the latter factor effects error in each stimulus digit. Different digits show different reproductive tendencies. Digit 7, for instance, shows the most marked tendency to induce an adjoining digit, digits 8, 9, 6, and 2 follow in that order as regards strength of their induction tendencies. The similarity in pronounciation of 4 and of 7 in the Japanese language makes the former a special case.
(4) Number replacement occurs more often in the multiplicand than in the multiplier. (Fig. 3) This, to the writer's belief, is due to the retroactive inhibitory effect of the multiplier which results in a failure to reproduce the multiplicand.
(5) As regards the size of the reproductive error, a larger number error occures among small digits, and the reverse holds true for larger digits (Fig. 8). The same phenomenon is also seen in the free reproduction experiment when single digits are used as stimuli (Fig. 2). Thus, we can say safely that a source of error in the multiplication table is the reproductive tendency associated with use of single digits as stimuli. The phenomenon we have described here resembles a central tendency that is seen in the process of perception and judgement and seems to have the same underlying mechanism.

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Many authors have referred illusions of direction to a tendency to overestimate acute angles. However, they have not proved that acute angles are in fact overestimated but merely supposed it as the cause of these illusions.
The writer attempted to determine whether the seen direction of either side of an acute angle differs from its objective direction. A rotatable disk, on which a line was drawn, was set at a little distance from the vertex of an angle and was so adjusted that the line on the disk appeared to be in a straight line with one side of the angle. The amount of deviation of the adjusted line from the objective direction of that side of the angle was measured.
By this means, it was found that The sides of an acute angle were always seen as deflected outwards. Such deflection of side lines could also be found even when the ends of the side lines were a little separate from each other and no longer formed a perfect angle. The amount of the deflection (D) decreased regularly with the increase in the separation (d) between the two sides provided that the objective direction of each side was kept constant (see Fig. 5). The exact relation of D to d was established in a logarismic equation as follows :
D=a-b·log d
where a and b are constants.
This fact makes us suppose that some stress, which causes the deflection of lines, must be produced in a certain area around a Figure. The writer would like to call such an area a Vector-Field after BROWN. The stress is strong in the center and is weak at the periphery of the Field. The amount of deflection of the line depends upon the strength of the stress in the Vector-Field. On this assumption the fact of overestimation of acute anglesand there-fore illusions of direction can be explained as the effect of some stress in the Vector-Field.

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Using Skinner box, we examined the behavior of white rats in the learning of barpressing habit by the partial reinforcement procedure at fixed ratios.
Sixty-five rats were divided into 13 groups and trained to learn bar-pressing responses under predetermined schedules (Number of reinforcements / Number of responses : 24/24, 48/48, 96/96, 36/48, 48/64, 96/128, 24/48, 48/96, 96/192, 12/48, 24/96, 48/192, and 0/0), and then extinguished. We analyzed the results in regard to three aspects : number of reinforcements and responses, and ratio of reinforcement.
And then we examined the methodological problem of criterion of socalled resistance to extinction, which had hitherto been determined arbitrarily.
Findings were as follows :
1) The acquisition of the habit was, as Jenkins and Stanley report, more difficult by the procedure of partial reinforcement in the early stage of training, but with the progress of training the difficulty decreased, and at last about the same level of performance was attained as by the procedure of continuous reinforcement.
2) The after-effects of the differential acquisition training on the socalled resistance to extinction were :
a) In regare to the aspect of the same ratio of reinforcements, the more the responses (therefore reinforcements) in acquisition, the more the responses were emitted in the first extinction session. This suggests the functioning of the principle of effect.
b) In regard to the aspect of the same number of reinforcements, the more the responses in acquisition, the more the responses were emitted in the first extinction session. This suggests the functioning of the principle of expectancy or substitution.
An interesting fact to us was :
c) In regard to the aspect of the same number of responses, the less the number of reinforcements, the responses emitted in the first extinction session showed increasing trend rather than decreasing.
It is impossible to interpret this fact by the hypothesis of secondary reinforcement, not to speak of the hypothesis of generalization of after-effect of reinforcement and of response unit.
Rather it is supposed that the principle of substitution, particularly the principle functioning in the phenomenon named positive reciprocal induction by Pavlov was powerfully at work.
On the problem of the criterion of the socalled resistance to extinction, the following were made clear by computing the coefficients of correlation among the number of responses up to the criteria of 3, 5, and 10 minutes of non-response in two extinction sessions after 24 and 48 hrs. of acquisition training.
1) The number of responses emitted in the second extinction session (spontaneous recovery after 24 hrs. of the first extinction session) was little affected by the differential conditions of acquisition training.
2) The coefficients of rank correlation of the number of responses emitted in the first extinction session was the higher, the longer the time of the criterion of resistance to extinction. According to these results, it will be necessary and adequate to take the criterion of 10 minutes of non-response to make the number of responses in extinction session the index of effects of differential training conditions.

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This article is an attempt to know how, while in Braille reading, the blind supplements his defect in visual sense by making a fairly efficient use of vibratory sense in addition to the tactile sense and pressure sense, and also to know what sort of function is being rendered by the vibratory sense in the process of Braille reading. Our experiment has been conducted by reference to the opinions of Von Frey, Katz and Geldard on the theory of vibratory sense. The experiment was divided into three stages.
The first experiment dealt with the pressure, pain, cold and warm spots from four surfaces of the skins which were the surface of the skins in the Braille reading, the left side, the right side and the tip of the first finger, in both hands.
The needle of the vibratory-sense measurer was applied to these sensation spots to measure the sensitivity of the vibratory sense.
In the second experiment, the amplifier and oscirograph for E. E. G. was used to analyse the wave types of the finger search movement during Braille reading. The piezo-crystal was used at the contact point of the finger. The results of the two experiments were studied comparatively.
In the third experiment, the actual searching movement was recorded by fixing a pen to the tip of the finger.
Our findings are as follows :
1) As far as the subjects in these experiments were concerned, the vibratory sense of the left first finger was more acute than that of the right first finger, and the surface of the skins of the left first finger was the most sensitive in Braille reading.
2) The vibratory sense of the pressure spot of the left and right first finger was more sensitive than the pain, cold and warm spots.
3) The pressure on the Braille was very weak with those whose vibratory sense was sensitive, but strong with those with whom it was not sensitive. (cf. Piezo-crystal experiment in the text)
4) When the sensation spots of both first fingers were above 1280 cy. in the stimulus threshold and below 0.13 in the relative descrimination threshold, the finger search movement did not appear. This movement was observed when stimulus threshold was below 896 cy.
5) At the stimulus threshold of 640 cy., the wave types of the finger search movement was with frequency 5-9 cy. and amplitude 4-16mm. on the left first finger, and with frequency 3-10 cy. and amplitude 3-18mm. on the right first finger.
The Braille pressure on the Braille was weak in the second experiment for those with whom the vibratory sense was acute in the first experiment. In this case the finger search movement did not appear. Even when it happened, the frequency and amplitude of that wave type was unexceptionally small.
Thus, we found that a very close relationship exists between the sensitivity of vibratory sense and the finger search movement during the Braille reading by the blind.
We are led to conclude that the vibratory spots are placed on the pressure spots.

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1. The purpose of this study is to analyse and understand the vicious environments which make up neurotic children in early childhood. In this study, I presume that the essential elements which form neurotic needs are basic anxiety and neurotic anxiety as described by K. Horney.
2. The method adopted for the study is case analysis, which makes use of the sources of understanding utilized by the social worker, the clinical psychologist and the child psychiatrist in the child guidance approach.
3. The subjects are 6 to 7 -year-old boys : A, B, C, and D, who had strong neurotic needs.
4. The main, direct environmental factors in the formation of neurotic needs of these 4 children were as follows. The neurotic needs in child “A” are caused by : a) his mother's affectionate protection for him while he was suffering from some diseases on the one hand and her attitude toward her son in trying to correct his left-handedness on the other, and b) the stress which this only child felt in his social life. The neurotic needs in child, “B” were caused by : a) his mother's nervous nursing of this eldest child ; b) constantly insecure life environments, and c) the scoldings that his father occasionally put upon his behavior. Child “C” 's neurotic needs were caused by : a) the rejection given him by his grandmother, uncle and aunt ; b) his mother's over-affection for this eldest child on the one hand and her several desertions of the child on the other, and c) the very limited life space. Child “D” 's neurotic needs were caused by the over-affection of his mother or grandmother on one side and their strict discipline they put on him on the other.
5. Particularly, the following points were noted in the results obtained from the four case analysis. 1) All members of the three families and the majority of the rest show strong interests in bringing up these children as if they were princes. Therefore, most members of these four families cause direct anilety to them, only a few member of one family causing him anxiety by their hostility. 2) These four children get security by depending upon their neurotic mother, and at the same time severe anxiety on their part is caused by their mother's attitude. Thus their mothers play an important role in the formation of the neurotic needs through the extremely close mother-child relationship. This forms a core of the dynamic interrelation between the child and his environments which cause him anxiety.
3) In each of these cases, his family members' personalities, attitudes and feelings toward the child effect much stronger influence for his maladjustment than any technique of child care and training. From two of these cases, we can see clearly that these children's maladjustment reflects the feudalistic atmosphere in their family.
6. In conclusion, we emphasize that the typical conflict leading to anxiety in a child is that between his dependency on the mother and his hostile impulses against her. This is different from what K. Horney retrospectively revealed in the analysis of adult neurotics, namely ; the typical conflict leading to anxiety in a child is, according to Horney, that between his dependency on the parents and his hostile impulses against them.

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Psychological scales are either nominal, ordinal, interval or ratio. As no direct measurement of the psychological (intervening) variables is possible, overt behavioral variables must first be measured. The latter are based on physical scales, which may be called phenotypic or peripheral scales as contrasted with indirect, genotypic scales of psychological variables.
Thus, relationships between the two types of scales should be made clear in any psychological measurement. Many people believe that transformation of variables for homogeneity of variance, for instance, is done purely from statistical expediency. This, however, does not seem to be correct on the basis of the fact that we are always dealing with psychological or genotypic scales and not numbers per se. Transformation of scores is only legitimate if it improves the meaning of the psychological variables.
Traditional statistical tests may be used for psychological scales provided that they are additive or they have equal units. Non-parametric tests, on the other hand, are most appropriate to ordinal scales. Attention is called, however, to the fact that some nonparametric methods assume additivity of the scale and that, therefore, they should not be used for the ordinal scale.
Three uses of nonparametric statistics may be mentioned. First, the methods may be applied to ordinal and nominal scales. Second, they can be used for interval or ratio scales in place of traditional statistical methods because nonparametric tests do not have such assumptions as normal distribution, homogeneity of variance and the like. Third, nonparametric methods are superior to traditional methods in the simplicity of computation for small samples.

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