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_C_, except for F. 40, invariably puts V. nearer center than F. _O_ moves between 90 and 135, putting V. farther to F.
100, nearly symmetrical at F. 100 and 120, and after F. 120, from 100 to 135.
[Ill.u.s.tration: FIG. 12]
Exp. V. Curve II. See Fig. 12, II.
(1) Curve out.
(_a_) F. (8010), V. Curve.
In every case but one V. is nearer center than F.
(_b_) F. Curve, V. (8010).
_C_ puts V. farther from center than F. _O_ puts V. farther or symmetrical up to F. 120, then nearer than F.
(2) Curve in.
(_a_) F. 8010, V. Curve.
_C_ has V. always farther from center than F., but a second parallel set, omitting F. 40 (all second choices), of symmetrical positions. _O_ begins with V. farther from center, but from F. 120 has V. always nearer, though gradually receding from the center.
(_b_) F. Curve. V. (8010).
_C_, refusing for F. 40, continues his parallel sets, one with V. always nearer than F., another with symmetrical positions.
_O_ begins with V. nearer, changes at F. 120, and continues with V. farther.
Recapitulating these results, grouping together the outward and inward positions of the curves, and indicating the distance of the line from the center by C.-L., and of the curve from the center by C.-Cv., we have:
_Out_.
Cv. I. (_a_) Indeterminate.
(_b_) C.-Cv. < c.-l.="" (except="" where="" large="" gap="" would="" be="">
Cv. II. (_a_) C.-Cv. < c.-l.="" (all="" cases="" but="">
(_b_) C.-Cv. < c.-l.="" (except="" where="" large="" gap="" would="" be="">
_In._
Cv. I. (_a_) C.-Cv. > C.-L. (except a few cases to avoid gap).
(_b_) C.-Cv. > C.-L. (more than half of cases).
Cv. II. (_a_) C.-Cv. > C.-L. (except a few cases to avoid gap).
(_b_) C.-Cv. > C.-L. (except a few cases to avoid gap).
It is evident that in the great majority of cases when the curve turns out it is placed nearer the center, when it turns in, farther from the center, than the straight line. The numerical differences for choices of the same type for the two curves are slight, but regular, and the general tendencies are more sharply marked for the line of greater curvature. When Curve II. is 'out,' it is usually nearer the center than Curve I. for the corresponding positions of the straight line; when 'in' it is always farther from the center than Curve I. The greater curvature of II. has clearly produced this difference, and the effect of the curvature in general is evidently to make its side 'lighter' when turned toward the center, and 'heavier' when turned away. Thus, all but the exceptions already noted seem to belong to the mechanically balanced arrangement, in which the suggestion of force working in the direction of the curve has the same effect as, in Exp.
IV., the direction of the line. The exceptions noted, especially numerous choices of _O_, seem governed by some fixed law. The evidence would seem to be overwhelming that the reversals of the mechanical balance occur only where the lines would be crowded together in the center or would leave an empty gap there. The remaining exceptions--the symmetrical choices mentioned, made by _C_--are explained by him as follows. He says there are two ways of regarding the curve, (1) as a striving in the direction of the 'bulge,' and (2) as the expression of a power that presses together; and that the usual choices are the result of the first point of view, the symmetrical choices of the second. Naturally, a pressure bending down the line would be conceived as working in a vertical direction, and the line would be treated as another (8010)--giving, as is the case, symmetrical positions. Thus, we may consider the principle of the suggestion of movement by a curve, as giving the same effect as if the movement suggested had actually taken place, to have been established, the positive evidence being strong, and the exceptions accounted for.
It is worth noting that the curve-out series are always more irregular--the subject repeating that it is always harder to choose for that position. Probably the demands of s.p.a.ce-filling come into sharper conflict with the tendency to mechanical balance, which for the outward curve would always widely separate the two lines.
Exp. V. Curve III. See Fig. 12, III.
A series with the upper end turned out from the center was unanimously p.r.o.nounced as ugly. The inward position only appears in the results, which are given in full.
(_a_) F. (8010), V. CURVE.
F. V.
O. C.
40 106 126 68 73 80 106 128 109 102 120 140 88 156 110* 154 72*
160 104 66 182 80 136* 130*
200 X 52 178 220* 162
(_b_) F. CURVE, V. (8010)
F. V.
O. C.
40 126 122 73 80 80 122 128 66 112* 40 120 90 116 97 156* 55 105 160 65 43 120 182* 87 134 200 70 50 148 66
This curve exemplifies the same principles as the preceding. _O_ takes the natural mechanical choice from (_a_) F. 40 to F. 120, and from (_b_) F. 120 to F. 200. A mechanical choice, however, for (_a_) F. 120 ff., and for (_b_) F. 40 to F. 120, would have brought the lines too far apart in (_a_), and too near together in (_b_), hence the reversal. _C_ inclines always to the mechanical choice, but recognizes the other point of view in his second choices.
Exp. V. Curve IV. See Fig. 12, IV.
Curve in.
(_a_) F. (8010), V. Curve.
_C_ puts V. always further than F. and, even for F. 200, has V. 230, X. _O_ puts V. farther up to F. 120, then puts it nearer than F., and always refuses to choose for F. 200.
(_b_) F. Curve, V. (8010).
_C_ always puts V. nearer than F. _O_ puts V. farther for F.
40 and F. 80, beyond that, nearer than F.; but refuses to choose once each for F. 40, and F. 200.
The same principles of choice appear. _C_ maintains the mechanical choice, and _O_ reverses it only beyond (_a_) F.
120, and up to (_b_) F. 120, to fill s.p.a.ce well, showing his preference for the mechanical choice by changing into it at an unusually early point.
Exp. V. Curve V. See Fig. 12, V.
Curve in.
(_a_) F. (8010), V. Curve.