92 W. B. Rogers on Binocular Vision. 
Let us imagine, for example, that while the point m, fig. 66, re- 
tains its present position in @ 6 dividing that line in ‘the propor- 
tion of 1 to 4, the point », from being similarly situated in e d, 
is transferred to 0, so as to divide ed in the ratio of 1 to 3. It is 
obvious that the resultant of ¢ and o will be in some position é, 
below s, and nut in the plane of z yr, and further that all other 
pairs of points of the two figures whose relative distances from 
zy are the same as those of ¢ and o will, (by the ee dem- 
onstration) form their resultants in the plane of ryo us ap- 
pears that every change in the ratio of the breadths of ths fig- 
ures at corresponding heights is accompanied by an inflexion 
of the resultant into a new plan 
Applying this to the combination of C with A (fig. 65), we 
observe that while the breadth of C at the middle angle is nearly 
wa that of A at the same level, its breadth at the angle above 
low is about one and a fourth that of the corresponding part 
of A. The former ratio determines the direction of the plane 
containing the second and third sides of the resultant figure 
pont. from the top, and the latter that of the plane con- 
ing the first and fourth sides together with the vertical ; 
aha as the former is a ratio of greater inequality than the latter, 
it is evident that the plane of the second and third sides will 
have a steeper inclination than the other. This corresponds with 
an resultant produced by the union of D with A, but enough has 
been said to illustrate the conditions which determine the position 
generally of the resultant of right-line figures of unequal hori- 
zontal dimensions. 
27. Of the union of a straight line with a curve. 
Among the simpler cases of combination there is none which 
exemplifies more curiously the effect of binocular union than a 
coalescence of a right line with a curve. Thus when a and & 
fig. 67, are brought together by converging the 
eyes to points behind or in front of the paper, we 
are at once presented with a curve standing out 
with great clearness and in strong relief, and turn- 
ing its apex in the one case towards us and in the 
other from us, but in both positions directed a little 
to the left side. The great steepness of the flanks 
of this perspective arch is an obvious result of th 
e a ae 
considerable angle which the terminal parts of 6 make with the — 
correspondin ng parts of a. 
In this experiment the union beginning at the middle of a and 
b extends simultaneously along the wpe and lower halves includ- 
ing in this interval a total converging movement 
the distance between the middle band its chord. : 
‘ 
