60 Mr Larmor, On the Form and Position [Jan. 31, 
therefore 
p=f’ (a) = Ap? (1+ 2 cos*a) 
COO a as alee ZC, 
—300 yen AP hE Shee 2 "0 
3 COp cos a+ a Z 5 7) €08 a + 5" COS a. 
Eliminating © by means of (11) we obtain 
Ary? = AXy* + Ap? Zi (—- ae — Bos’ a) + = Cos al 
~ 
2 
_ 1 ale 
zp (5 2) = Sole 
ar la Rp) °84- RP 
The right-hand side is positive, hence both positions of steady 
motion given by (11) are stable. 
(2) On the Form and Position of the Horopter. By 
J. Larmor, M.A., St John’s College. 
1. When the two eyes are kept converged upon a fixed point, 
the images of another point will usually fall upon non-corre- 
sponding points of their retinas, and it will therefore be seen 
double. But there is a system of points forming a curved line 
in the field of view which are such that the images correspond, 
and they are therefore seen single. The locus of points possessing 
this property was called the horopter, first by Aquilonius. It is of 
importance in the theory of stereoscopic vision as defining the 
neighbourhood in which the images formed by the two eyes are 
perfectly fused together; and accordingly its properties have been 
investigated by Helmholtz, Hering, and other physiologists. 
The final investigation of Helmholtz was published in 1867, 
and presents the theory under an analytical form. Geometrically 
it is a case of the theory of linear congruences of the first order, 
and forms a good example of the Geometry of Rays which has 
been explicitly introduced and applied chiefly by Pliicker and his 
successors, since Helmholtz’s papers were published. 
It may be of advantage to give a brief account of the way in 
which the general results flow directly from the geometrical re- 
lations without recourse to symbolical reasoning. The direction of 
the horopter curve where it passes through the point of vision will 
then be investigated, as that would appear to be the most im- 
portant matter for practical purposes on account of the complexity 
of the complete equations of the curve in the general case. 
2. The eye being an optical instrument symmetrical round an 
axis, the aspect of external objects which is presented to its external 
