~ 
90 W. B. Rogers on Binocular Vision. 
by converging the axes to a point beyond the diagram, we ob- 
tain the following results. 
The combination of B with A gives us a_ perspective figure 
having the vertical line for its near edge and having all its sides 
situated in one and the same plane, which slopes away from us 
evan the right. 
niting C with A we have aresultant consisting of parts lying 
in two differently inclined planes both of them receding towards 
the right; that formed by the sides about the middle angle slo- 
ping away from us more steeply than the part adjoining the verti- | 
cal side. | 
When we combine D with A we have a resultant figure which 
like the preceding is inflected into two planes, but in this case | 
the part next the vertical slopes towards us from that line, and 
the remaining part as before recedes towards the right. | 
It thus appears that right line figures having the same vertical | 
dimensions for all their corresponding parts, but differing in their 
horizontal breadth, afford by their binocular union two classes of 
resultant figures—those of which all the parts are situated in one 
those in-which they lie in two or more differently in- 
clined planes. | 
26. Conditions according to which the resultant will lie ¢: in one | 
or in several planes 
The geometrical conditions determining the character of the 
resultant figure in this respect are simply the following. | ee 
the figures which are to be combined are of such form that their : 
corresponding horizontal dimensions bear a constant ratio to | 
one another, for all points of the height, their Naloeselar resultant : 
will lie wholly tm one perspective plane,—when the ratio varies, 
the resultant will lie in an inflected surface composed of two or 
more mutually inclined planes, each change of ratio being . 
companied by a change of direction of the surface. me 
As this proposition | is important from its generality, and will i a 
the sequel be applied to curvilinear figures, the following short ag 
proof of it may be acceptable to the reader. 
Let a6 and ed (fig. 66) denote the horizontal breadths of the a 
larger figure at the points b and d, and m6, nd those of the nar-_ 
rower one at the same points respectively. Also let R and L be — 
the centres of the two eyes, and suppose zy to be the line in 
which, by a suitable axi convergence, the equal vertical heights 
of the figures are made to coalesce. As long as this particular de- 
pbs of convergence is maintained unaltered, it is obvious that ™ 
and x will not coincide optically with @ and c, but must continue 
to be seen at the intervals am and cn as in the diagram. By a 
farther axial movement, however, a and m are made to coincide 
at r, and again ¢ and n nats. We are now to determine the posi- 
tious of r, s and the see seenitant a ¥ — ays 
to this end we have 
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