On Systems of Rays. 71 
at the several near points 4, where they meet the given final plane perpendicular to 
the given element ds. In the fourth problem, we consider the initial system of right 
lines, which mark, at the luminous origin, the initial directions of the same near paths 
of homogeneous light ; and we compare these initial directions with the positions of 
the points B;. Let us now consider separately these four principal problems, respect- 
ing the geometrical relations of infinitely near rays. 
Discussion of the Four Problems. Elements of Arrangement of near Luminous 
Paths. Axis and Constant of Chromatic Dispersion. Axis of Curvature of 
Ray. Guiding Paraboloid, and Constant of Deviation. Guiding Planes, and 
Conjugate Guiding Axes. 
15. The first of these four problems, namely that in which it is required to deter- 
mine the final chromatic dispersion, by means of the two coefficients — , eB, is very 
0) / 
easily resolved: since we have the following equations for the magnitude and plane of 
this dispersion, 
Final angle of chromatic dispersion = &x ; =! + (Py 2 
ox 
: , : da op 
Final plane of dispersion..........0000. Y — =U. 
inal plane of disp Vaseig its 
(R*) 
We may geometrically construct the effect of this dispersion, by making the given 
final line of direction of the original luminous path revolve through the small angle 
&éy, in which € may be called the constant of final chromatic dispersion, round the 
following line which may be called the axis of final chromatic dispersion, 
KAN ead 6 
x Ra z=0. (S*) 
The second problem, which relates to the final curvature of the given luminous 
path, is resolved by the analogous equations, 
Final curvature of ray =f Oe); 
(T) 
Plane of curvature ......+. Y en Re? 
we have also the following equations for the axis of curvature, that is, for the axis of 
the circle of curvature, or of the final osculating circle to the given luminous path, 
ont ye il, 20s (U*) 
