189 
B B 1+ lis 
dt = fe en (do* + 0? dy’) 
u 
A ‘A 1— — 
O 
must be equal to zero. Neglecting the same quantities as before we 
‚may therefore say that we must determine p as such a function 
of @ that 
7 2 d 
; u ‚(de ed 
SV (+ Ore (4) ]ee=o annen) 
A 
In order to solve this problem we point to another, which from 
a purely analytical point of view is equivalent to it. If in space, 
now thought to be Huclidian, a planet with the unit of mass moves 
according to Newton's law in the field of gravitation of the sun, 
according to the principle of least action its course is given by 
JV Af een 
where h is the constant of the living force. 
From this it appears that the solution of (4) 
p= f(e) 
represents at the same time the orbit of a planet round the sun, 
where A ==}, and that also the reverse is true. 
Now each of these orbits of a planet is a conic section. However 
it would not be quite exact to say that the light path in three 
dimensional space is a conic section (unless we define a conic section 
in a non-Kuclidian plane by a curve that has the same polar equation 
as a conic section; in differential geometry, however, the names 
ellipse and hyperbola are already given to different curves); by 
means of 
Greif, WOO. 20 erde Sa a en he) 
it is represented in a Euclidian plane by a conic section, where @, 
and g, are polar coordinates. 
It is of some importance to remark that the formulas (5) represent 
the plane with tbe line element 
ds* = (: SK e) (do* + 9? dep’) 
conformly on the Euclidian plane as the coefficients of the two 
fundamental forms are proportional. 
If therefore it appears that in the image plane the tangent at B 
