In the final series of experiments the influence of limiting visual planes upon the determination of the subjective horizon was taken up.  It had been noticed by Dr. Muensterberg in the course of travel in hill country that a curious negative displacement of the subjective horizon took place when one looked across a downward slope to a distant cliff, the altitude (in relation to the observer’s own standpoint) of specific points on the wall of rock being largely overestimated.  Attributing the illusion to a reconstruction of the sensory data upon an erroneous interpretation of the objective relations of the temporary plane of the landscape, Dr. Muensterberg later made a series of rough experiments by stretching an inclined cord from the eye downward to a lower point on an opposite wall and estimating the height above its termination of that point which appeared to be on a level with the observing eye.  He found an illusion present similar to the case of an extended slope of country.

The first experiments of this group repeated those just described.  The previous mechanical conditions were varied only by the introduction of a slender cord which was stretched from just below the eyes to the bottom of the vertical screen.  Full results were obtained from only two observers, which are given in the following table: 

TABLE XI.

   Observer.  Const.  Err.  Av.  Dev.  Mean Var.  Exp.  Conds.

C (30) +123.92 123.92 11.94 Cord present and G (30) +66.47 66.47 15.56 consciously referred to. C (30) +126.90 126.90 6.31 Cord not present. G (30) +83.20 83.20 6.31 C (30) +126.93 126.93 6.39 Cord present but not G (30) +86.63 86.63 9.40 consciously referred to.

Averages.   I      +95.19    95.19    13.75
"      II     +105.05   105.05     6.31
"     III     +106.78   106.78     7.89

The effect of introducing such an objective plane of reference is twofold:  the mean variation is increased, and the plane of the subjective horizon is displaced downwards.  First, then, it acts as a simple factor of disturbance; it distracts from those habitual adjustments upon which the accuracy of the judgment depends.  Secondly, it enters as a source of constant error into the determination of the subjective horizon, which is attracted toward this new objective plane.  In the third section of the table are given the results of judgments made in the presence of such a plane but without conscious reference to it.[2] The figures here are of intermediate value in the case of the mean variation and of slightly greater value than the first in that of the constant error.  In other words, the introduction of such a plane cannot be wholly overlooked, though it may be greatly abstracted from.

[2] In the preceding experiments the cord was definitely to be taken into account in making the judgment.  The method of so doing was by running the eye back and forth over the cord preliminary to determining the location of the point.