To understand this figure we must enter into the calculation of the
angles. We have an eye-distance of 60 mm., a distance of the edges from
the cornea 2000 mm., from the nodal points 2007.4 mm., the distance of
each edge from the median line 15 mm., the distance of the two edges
from each other thus 30 mm. as long as they are in the same plane. We
have to determine the angle under which each eye sees the distance of
the two edges. A simple trigonometric calculation gives the following
figures: If both eyes are in normal position, at 0°, and both edges
are in the same plane, 2000 mm. from the corneæ, the angle for each
eye is 51' 22". If the left edge is now moved to +5, the left eye sees
the distance of the edges at an angle of 51' 25", the right eye under
51' 10", the difference is thus 15"; if the left edge is at +10 mm.,
the left eye's angle is 51' 29", the right eye's angle 50' 59", the
difference 30". If the left edge is moved to -5 mm., the left eye's
angle is 51' 18", the right eye's angle 51' 33", the difference 15";
if the left edge is moved to -10 mm., the left eye's angle is 51' 14",
the right eye's angle 51' 45", the difference 31". Now we saw that with
normal eye-position when the left edge was moved the threshold was
+5.93 and -6.97; a difference of 15" to 20" between the visual angles
of the two eyes was thus amply sufficient to give a distinct experience
of different distance. When the left eye's angle was about 15" smaller
than the angle of the right eye, the difference of the retinal images
gave a sure impression of the greater nearness of the left edge.
If we now bring the eyes into the position of 30°, the angles are of
course different when both edges are in the same plane vertical to
the direction of regard. If the two edges are in the same plane, the
left eye's angle is 50' 59" and the right eye's angle 51' 45", the
difference thus 46". If we move the left edge to +5, the left angle
becomes 51' 1", the right angle 51' 34", the difference 33". If we move
the left to +10, the left angle becomes 51' 4", the right 51' 24"; the
difference is thus still 20", and we must move the left edge to +17 mm.
to get an equal angle for the left and the right eye. If we move the
left to -5, the difference becomes of course larger, the left eye sees
under 50' 56", the right eye 51' 55", the difference 59"; and at -10,
the left eye has the angle 50' 53", the right eye 52' 6", difference 1'
13". It is hardly necessary to state here the angles for the changes of
the right edge or for an eye-position of 15°, inasmuch as the maximum
differences bring out our case most clearly. With an eye-position of
15°, the edges at the same plane give angles of 51' 10" and 51'34",
that is, a difference of 24"; if the left edge is moved to -5 mm. the
difference becomes 38"; if it is moved to -10 mm. the difference is
54"; if the left edge is moved to +5 the difference decreases to 10"
and at +10 mm. to 6".
Public-domain text, read in full here on John Shaqi.
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