190 
to the light path 4B makes with the radius vector CB a largeror 
a smaller angle than the straight line AB, it does not only follow 
from this that indeed according to Einsrern’s theory out of B the 
point A will be seen in a different direction from that which was 
to be expected from the former theories, but also that the numerical 
value of this deviation may be read directly from the image. 
Notwithstanding the objection just mentioned, confusion being 
excluded, we shall not hesitate henceforth to call the curve 
p=f(e) in the Ernsrrin-plane a conic section; we only wanted to 
point out that for the final conclusion an appeal to the characteristic 
of conform representation is necessary. 
4. Let us first consider once more the paths of material points 
moving with the unit of mass according to Nrwron’s law in the 
lield of gravitation of the sun C, thought to be Euclidian, while 
for all those paths the constant A has the same value; it is already 
certain that all those paths form a system of conic sections with 
a common focus C. It is further known that the semi major axis 
of such a conic section is determined by: 
u*) 
iss 
Hence all the conic sections have equal major axes; the sign of 
the axis indicates whether we have to do with an ellipse, a hyper- 
bola or a parabola. 
Applied to the problem in question this means: 
The course of any ray of light is a hyperbola of which the sun 
is one of the foci; the length of the semi major axis is always equal 
tonale lem) 
A 
5. Now we shall determine the path of the light between 2 given 
points A and 5. 
With a view to this we describe out of Ca circle y with a 
radius 2u and out of A and B two circles touching y; the points 
of intersection of y with AC and the produced part of AC are 
called resp. A” and A’; B’ and B’ are defined in the same way. 
Each point of intersection of one of the circles with centre A and 
one of the circles with centre B forms together with C the foci of 
a hyperbola through A and B, the major axis of which is 4u. To 
begin with we find therefore 8 hyperbolas; let us now examine 
which of them gives a possible light path between A and 5. 
[f S, is a point of intersection of the circles AA" and BB’, we have 
1 Cf. e.g. P. AppELL: Traité de Mécanique rationelle, I p. 393. 
