1887. ] of the Horopter. 61 
nodal point is projected unchanged from its internal nodal point 
upon the retina. . 
The nodal points of the eye are usually taken as coincident. 
This can always be done in an optical instrument, without sensible 
error, if their distance apart is a small fraction of the distances of 
the points in the field of vision; and in the case of the eye they 
almost coincide. But the theory which follows applies equally 
well without this simplification, as is evident from the remark at 
the beginning of this section. 
Corresponding points on the retinas are those which would 
coincide when they are superposed without perversion, 1.e. right 
corresponds to right, and left to left. 
3. In the first place, it is to be remarked that curved lines 
can be constructed to any extent which are seen by single vision 
with both eyes focussed on some given point. For draw any curve 
on one retina and the corresponding curve on the other ; join these 
to the internal nodal points by cones; transfer the vertices of these 
cones to the external nodal points without introducing any rota- 
tion; the intersection of the two cones will then be a curve 
possessing the property in question. 
For example, suppose the curves on the retinas are conics; the 
cones will be quadric cones ; their curve of intersection may include 
a conic, in which case the remaining part of it is another conic. 
If therefore a conic curve in space be such that it is seen singly 
with both eyes, there is another conic in space which is seen by 
both eyes in coincidence with it, and undistinguishable from it so 
long as no accommodation of the eyes is allowed. 
4. But the simplest group of figures of this kind is that of the 
straight lines in space which are seen singly. They are constructed 
as before: draw two corresponding lines on the retinas, and join 
them by planes to the internal nodal points; the parallel planes 
drawn through the external nodal points intersect on a line of the 
group. 
Now all lines in space may be viewed as the intersections of 
planes, one passing through each of these nodal points; but the 
intersecting planes here considered are allied to each other by two 
lineo-linear (because projective) relations derived from the cor- 
respondence of their intersections with two given planes (the 
retinas). 
Their lines of intersection therefore form a congruence of the 
first order, in the general sense that through any point in space 
one line of the congruence can be drawn. 
This property also appears more directly in the following 
manner. Consider any point in space; mark its corresponding 
points on the two retinas; these will not usually themselves 
