178 W. B. Rogers on Binocular Vision. 
to be so placed that the outer sides Lh... R& of the visual cones 
are vertical the resultant becomes a parabola, and if we imagine 
this change to be carried so far as to make these sides converge : 
downwards, = resultant takes se -form of an arc of an ellipse. 
As mand n are the points of the upper component arcs which 
are nearest spelen their resultant point v, the vertex of the re- 
sultant curve, must be nearer the observer than any other part of 
the curve; and the same conclusion follows from considering v 
as the binocular resultant of M and N, the points of the lower 
component arcs which are farthest from one another, Hence in 
“ae cases the resultant curve must be convex towards the ob- 
a ee 
ee le A ee 
plane extending upwards from zy must necessarily pass entirely j 
through both of the visual cones. Hence the resultant curve : 
rvs, which is at the same time the line of intersection of the 
two conical surfaces with one another, and that of the vertical — f 
plane with each surface, cannot be a parabola or hyperbola, but . 
must always be an arc ‘of an ellipse. From the construction it 
is evident that v, the resultant of mand n, the points of the q 
upper component arcs which are farthest apart, must be the point 
of the resultant curve rvs which is most distant from the ob- 
i and therefore that the curve will present its concavity in 
nt 
serv 
in the conditions of union represented in fig. 77, the vertical 
These several effects of the bindenler union of circular ares od 
of mote a and curvature, may be thus summed up. | 
Ww he arcs are conver to one another and they are 
ee Ee behind the plane of the components, or when they are 
concave to one another and combined in front of this plane, the 
resultant may be either an hyperbola, parabola, or éllipse, but in 
either case it will be conver towards the observer, and situated i 
a vertical plane Py 
(b.) When the ares are concave to one another and they are 
it omes ‘hae are of a circle. 
OU. her gett of the uttion of right and curve-line 
gures Rial el, if 
t rhat ha en shown of the combination of a right 
Pvith a simple and (27) and of the union of such a line 
with a figure composed of several ye lines (24), we may infer 
