1 5 0 D O C . 3 1 I D E A S A N D M E T H O D S

The field equations of gravitation we are looking for must be satisfied in a Ga-

lilean space, also for every Gaussian coordinate system to which we might refer it.

Furthermore, we know from experience that the gravitational field is determined

by its mass, i.e., according to the special theory of relativity by the energy of matter.

If one adds the condition that the desired field equations should contain—like

the Newton-Poisson equations of the classical theory—no derivatives of potentials

of higher than second order, and those should be

linear,7[53]

then the field equations

are uniquely prescribed by the theory such that their formulation becomes possible

in a mathematically deductive

manner.[54]

A. Einstein

Translator’s Notes

{1} In the second quadruple, has been corrected to .

{2} has been corrected to .

{3} The term

+

has been corrected to .

{4} Correct equation numbers have been inserted.

{5} The phrase “by 10 quantities” implies that .

7

From a mathematical point of view, this is the simplest possibility imaginable.

dt dt′

x′ 0 = t′ 0 =

1-

n2

----

1-

n2

---- –

gik gki =