200

DOC.

30 FOUNDATION OF GENERAL RELATIVITY

per

revolution.

In

this formula

a

denotes the

major

semi-

axis,

c

the

velocity

of light

in

the usual

measurement,

e

the

eccentricity,

T the time

of

revolution in

seconds.*

Calculation

gives

for

the

planet

Mercury

a

rotation

of

the

orbit

of

43"

per

century, corresponding exactly

to astronomical

observation

(Leverrier);

for

the

astronomers have discovered

in

the motion

of

the

perihelion

of

this

planet,

after

allowing

for

disturbances

by

other

planets,

an inexplicable

remainder

of

this

magnitude.

* For

the calculation I refer to

the

original papers:

A.

Einstein,

Sitzungsber.

d. Preuss. Akad. d.

Wiss.,

1915, p.

831;

K. Schwarzschild,

ibid.,

1916,

p. 189.

[37]

Doc.

31

Appendix.

Formulation of

the

Theory

on

the

Basis

of

a

Variational

Principle

Not

translated for this

volume.