Mathematics. — “On the Path of a Ray of Light in the Field 
of Gravitation of a Single Material Centre.” By Prof. W. 
VAN DER Woupe. (Communicated by Prof. J. C. Krurver). 
(Communicated at the meeting of October 29, 1921). 
1. Starting from the line element of the field of gravitation of a 
single material centre proposed at the same time by ScHwaARzscHILD *) 
and Droste’), | wish to demonstrate in this paper: 
1. the path of any ray of light is (with allowable neglect) a 
hyperbola of which the sun is one of the foci; all these light paths 
have equal major axes; 
2. by these geometrical data 8 hyperbolas are defined passing 
through 2 given points; from physical considerations however it 
appears easily that only one of the 8 hyperbolas connecting in this 
way the earth to an arbitrary star, is a path along which the light 
starting from the star, reaches the earth. 
To this l add a remark on the determination of the magnitude 
of the deviation. *) 
2. The line element of ScnwamrzscniLp—Drosrk has the following 
expression : 
u dr’ 
ds* = | 1 — — } dt? — —_—_ — r* (dO? + sin? 0 dg’), -. >. (1) 
r u 
eee 
or, after the substitution 
u 3 
r=e(1+ 5). 
40 
a lu : AOR 
B dt? — slo {do*+-07(sin?4 dy? + d6”)} (1') 
& 
1) K. SCHWARZSCHILD: Sitzungsberichte der Kon. Preuss. Akad. der Wissen- 
schaften, 1916. 
2) J. Droste: Het zwaarteveld van een of meer lichamen volgens de theorie 
van EINSTEIN. Thesis for the doctorate, Leiden, 1916. 
3) For a prior discussion of the path of light in this field cf: W. pe 
SITTER: On EINSTEIN’s Theory of Gravitation (Monthly Notices R. A. S., 
vol. LXXVI, p. 717). 
A. S. EDDINGTON: Report on the Relativity Theory of Gravitation (p. 53— 56). 
H. VAN DER LINDEN: La Trajectoire d'un rayon lumineux dans le champ 
de gravitation d'EINSTEIN-SCHWARZSCHILD (Académie royale de Belgique, Bul- 
letin, t. VI, 1920, p. 90—97). 
