64 Mr Larmor, On the Form and Position  [Jan. 31, 
only approximately by the law of Listing ; which is an additiona 
reason for the sufticiency of the result here obtained. 
Let then a,, a, be the distances of the point of vision from the 
external nodal points of the two eyes, and 2y the angle between 
the axes of vision of the two eyes. Let the radius of the second 
retina corresponding to the radius of the first which is in the 
plane of the axes of vision make an angle ¢ with that plane, owing 
to the action of the converging muscles. 
Consider two right cones of equal small angle a round the axes 
of vision of the two eyes as axes, and suppose the corresponding 
generating lines on them to be marked in such way as to identify 
them. These cones will intersect in a curve, and at two opposite 
points on this curve corresponding generators will meet one another, 
but at no other points. These two points are situated on the point 
horopter, and determine its direction in the neighbourhood of the 
point of vision. 
Taking for axis of # the bisector of the internal angle between 
the axes of vision drawn outwards, for axis of y the bisector of the 
external angle between the same lines drawn towards the first of 
them, and for axis of z the normal to the plane of the same lines, 
the co-ordinates of this point P of the horopter are easily de- 
termined. For, draw PM perpendicular to the plane of the axes 
of vision, and MN,, MN, perpendicular to the axes of the two eyes. 
If @ denote the azimuth of P round the axis of the first cone, 
measured towards z from the positive direction of the axis of y, 
then 6+ ¢ will be its azimuth round the axis of the second cone, 
We therefore have the equations 
PM=2=aa,sn0 =aa,sin(@+¢) .......... (1) 
MN, =cxsiny+ y Cosy = ad, COS O...........eceeeee (2) 
MN, =—«siny+y cosy = aa, cos (8+ @) ........(3) 
Care has been taken to introduce only distances that are mul- 
tiplied by the small quantity a, so that it is admissible to write a, 
and a, for the distances of P from the nodal points. 
Thus esiny+ycosy _ _—#siny +y cosy 22 
a, cot 0 a,(cot@cos@—sing) a, 
— a, cos 6 + a, 
a, sin 
where, by (1) cot 0 = 
Substituting this value in (4), 
asny+ycosy _—x#£siny+ycosy Zz 
—aa,cospt+a"* aa,cosp—a,’  a,a,sndg’ 
