174 W. B. Rogers on Binocular Vision. 
These conditions are represented in the upper part of fig. 74. 
Here the are a b and right line cd have for their binocular result- 
ant the curve rvs. Since the points m and m unite optically at 
a less distance behind the diagram than any other pair of corres- 
ponding points in ab and ed, it follows that the vertex v in 
which they combine must be the point of the resultant curve, 
nearest to the observer, and as the curve lies wholly’in the plane 
RCD it must therefore present its convexity obliquely forwards. 
According to the proportions assumed in the figure, the line 
vN is more steeply inclined than the line LA to the base of 
the cone, and in these conditions therefore the curve rvs is an 
hyperbola. But by placing ab and cd alittle nearer one another 
we may cause RN to become parallel to L’, in which arrange- 
ment the resultant will be a parabola; and if we bring a6 an 
ed still nearer together so as to make RN converge downwards 
towards Lh, we transform the curve rvs, into an arc of an 
ellipse. In the conditions included in the first case therefore the 
binocular resultant may have the form of either of the curves 
just mentioned. 
Second. When the circular are is concave towards the right 
line, and the two are united in front of the plane of the diagram. 
This case is represented in the lower part of fig. 74. Here 
the component lines are the circular are AB and the right line 
CD, which by cross-vision are made to unite in. front of the 
plane in which they are placed in the experiment. The result- 
ant curve rvs will evidently vary in form according to the dis- 
tance between ABand CD. As shown in the figure this curve 
is an hyperbola, but by increasing the interval between A B and 
CD it may be converted into a parabola or into the arc of an 
ellipse. Thus in the conditions of the second case also the bi- 
nocular resultant may have the form of either of these curves. 
 Thir en the circular arc is concave towards the right 
line and the two are binocularly combined behind the plane of 
_ the drawing. 
The combination here specified is shewn in the upper part of 
fig. 75. In this case the vertex of the resultant curve rvs being 
formed by the optical union of the two points m and n, of the 
component lines which are farthest apart, must be at a greater 
‘ 
\ 
@ 
a 
S 
, the optical conditions here su 
duced shall intersect Len produced, it follows that 
, 
t parabola but must be an elliptic arc, varying in form according 
to the interval between ab andcd. Where the visual cone 8 
